ANALYSIS OF FLOW FEATURES IN QUEUED TRAFFIC ON A GERMAN FREEWAY ROGER VICTOR FREDRICK LINDGREN

Transcription

1 ANALYSIS OF FLOW FEATURES IN QUEUED TRAFFIC ON A GERMAN FREEWAY by ROGER VICTOR FREDRICK LINDGREN A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY in CIVIL AND ENVIRONMENTAL ENGINEERING Portland State University 25

2 ABSTRACT An abstract of the dissertation of Roger Victor Fredrick Lindgren for the Doctor of Philosophy in Civil and Environmental Engineering presented March 9, 25 Title: Analysis of Flow Features in Queued Traffic on a German Freeway Traffic was studied on a thirty kilometer section of freeway north of Frankfurt Am Main, Germany using archived loop detector data. The spatial-temporal characteristics of over eighty bottleneck activations were diagnosed with six days of data. The analysis tools used were curves of cumulative vehicle count and time mean speed versus time. These curves were constructed using data from neighboring freeway loop detectors and were transformed in order to provide the measurement resolution necessary to observe the transitions between freely-flowing and queued conditions and to identify important traffic features. The bottlenecks locations, pre-queue flows, and mean discharge flows across all lanes and on a lane by lane basis were found to be reproducible from day to day. Further, it is shown that the bottlenecks mean discharge flow was about 3-5% lower than the mean prevailing flow prior to queue formation when freely flow conditions preceded the activation.

3 Changes in key traffic parameters leading to the formation and dissolution of diverge and merge bottlenecks were investigated and were found to reproducible from day to day. The bottleneck formation triggers for diverge bottleneck activations preceded by freely flowing traffic included high flows across all lanes and high, truck dominated, flows in the right lane just upstream of the bottleneck location. For merge bottleneck activations preceded by freely flowing traffic, reproducible triggers included net lane changing to the left and increases in unmetered on-ramp flow of approximately 25%. Upon bottleneck activation, flow reductions occurring sequentially in time and space marked the passage of backward-moving shocks. Mean shock velocities were in the range of -18 km/h as they traveled upstream from the bottleneck locations. During periods of bottleneck activation, oscillations arose in the upstream congested traffic and propagated upstream at nearly constant speeds. The effects of some bottleneck activations in this study traveled upstream over 2 km, passing through several major interchanges. This research represents an important step towards a greater understanding of how and why freeways bottlenecks arise and some of their characteristics. Together with future empirical studies, this will lead to the development of improved traffic flow theories and freeway management techniques.

4 i ACKNOWLEDGEMENTS I wish to express my sincere appreciation to my advisor and friend, Professor Robert Bertini. Conducting this research and writing this dissertation would not have been possible without his guidance, his endless patience and his tireless devotion to this work. I also wish to acknowledge the support and dedication of my committee members; Professors Robert Fountain, Katharine Hunter-Zaworski, Christopher Monsere, and James Strathman. I would also like to thank Professor Roy Koch for serving on my committee at the proposal stage. I am grateful to the faculty and staff of Portland State University s Department of Civil and Environmental Engineering. The Department of Civil Engineering and Geomatics at Oregon Institute of Technology supported my efforts for several years and I am very grateful for their long term support, particularly the excellent mentorship provided to me by Dr. Joseph Sarsenski. Dr. Dirk Helbing and Martin Schönhof of the Technical University of Dresden graciously supplied the data and provided vital technical assistance during this research. Support for my earlier graduate studies was provided by the Natural Sciences and Engineering Research Council of Canada. I wish to thank Dr. Stan Teply of the

5 University of Alberta for his kind tutelage and for inspiring me to pursue a doctoral degree. ii I am grateful for the friendship and support of the all the PSU students from the ITS Laboratory. Special thanks to M. Leal, S. Tantiyanugulchai, S. Malik, E. Anderson, and A. El-Geneidy, with whom I have had the honor to study. Profound gratitude is extended to my parents, Kenneth and Violet, who have always supported my efforts with love and motivation. Finally, my graduate studies simply would not have been possible without the extraordinary patience, love and support of my wife, Cheri and my children, Nelson and Audrey. My family made this possible and it is to them that this dissertation is dedicated.

6 iii CONTENTS Acknowledgements... i List of tables... v List of figures... vi 1 Introduction Background Motivation Organization of the dissertation Data Methodology Speed contour plotting Curves of cumulative vehicle count versus time Curves of cumulative vehicle velocity versus time Analysis Day C Diagnosis of bottleneck activation C Diagnoses of early afternoon bottleneck activations Diagnoses of late afternoon bottleneck activations Diagnoses of early evening bottleneck activations Diagnosis of bottleneck activation in D26 D Diagnoses of early afternoon bottleneck activations in D6 D Diagnoses of late afternoon bottleneck activations in D6 D Bottleneck C1 discharge characteristics Summary of diverge bottleneck discharge characteristics Summary of bottleneck discharge characteristics Bottleneck C1 activation triggers Day G Diagnoses of mid afternoon bottleneck activations Diagnoses of late afternoon bottleneck activations Diagnoses of evening bottleneck activations... 66

7 iv Diagnoses of bottleneck activations in D6 D Diverge bottleneck discharge characteristics Diverge bottleneck activation triggers Day B: Isolated diverge bottleneck deactivation Bottleneck B7 diagnosis Bottleneck B7 deactivation triggers Day E: Isolated merge bottleneck activation Bottleneck E2 diagnosis Merge bottleneck E2 discharge characteristics Merge bottleneck activation triggers Traffic oscillations Reproducing the observations Reproducing diverge bottleneck activation discharge characteristics Reproducing diverge bottleneck pre-queue flows Reproducing diverge bottleneck activation triggers Reproducing diverge bottleneck deactivation triggers Reproducing merge bottleneck activation discharge characteristics Reproducing merge bottleneck activation triggers Reproducing shock speeds Reproducing oscillation wave speeds Conclusions Summary of findings Comparisons and implications Areas of further research REFERENCES Appendix A Day C speed curves Appendix B Speed contour diagrams Appendix C Weather data Appendix D Kerner literature review Appendix E Bottleneck Summary

8 v LIST OF TABLES Table 1 Autobahn A5 days analyzed Table 2 Data fidelity Table 3 Diverge bottleneck D22:D24 summary day C... 5 Table 4 Bottleneck summary day C Table 5 Diverge bottleneck D22:D24 summary all days Table 6 Possible diverge bottleneck triggers Table 7 Reproducible diverge bottleneck triggers Table 8 Merge bottleneck D7:D8 summary all days Table 9 Shock speeds A Table 1 Oscillation wave speeds A Table 11 Oscillation wave speeds comparison... 18

9 vi LIST OF FIGURES Figure 1 Active bottleneck...9 Figure 2 Site map...11 Figure 3 Speed contours day C...16 Figure 4 Constructing cumulative curves...17 Figure 5 Constructing oblique N(x,t) curves...21 Figure 6 Oblique V(x,t)...24 Figure 7 Autobahn A5 north speed diagram day C...26 Figure 8 Oblique N(x,t) for D2:D24 day C 13:4 14: Figure 9 Oblique V(x,t) for D2:D24 C1 activation...29 Figure 1 Oblique N(x,t) for D15:D24 day C 12:35 14: Figure 11 Oblique N(x,t) for D15:D24 day C 14:2 17: Figure 12 Oblique N(x,t) for D15:D24 day C 17:5 2:...39 Figure 13 Oblique N(x,t) for D26:D3 day C 14: 15: Figure 14 Oblique N(x,t) for D6:D14 day C 14: 16:...42 Figure 15 Oblique N(x,t) for D6:D14 day C 16: 19:...44 Figure 16 Oblique N(x,t) and V(x,t) for D23 day C...47 Figure 17 Oblique N(x,t) and V(x,t) for D22 day C...54 Figure 18 Oblique N(x,t) and V(x,t) trucks at D22 day C...56 Figure 19 Oblique N(x,t) for D25 off-ramp and right lane flow for D22 day C...58 Figure 2 Autobahn A5 north speed diagram day G...59 Figure 21 Oblique N(x,t) for D15:D24 day G 15:4 16:1...6 Figure 22 Oblique V(x,t) for D22:D24 day G...62 Figure 23 Oblique N(x,t) for D15:D24 day G 15:4 18: Figure 24 Oblique N(x,t) for D15:D24 day G 18: 21:...67 Figure 25 Oblique N(x,t) for D6:D14 day G 15: 18: Figure 26 Oblique N(x,t) and V(x,t) for D23 day G...71 Figure 27 Oblique N(x,t) and V(x,t) for D22 day G...74 Figure 28 Oblique N(x,t) and V(x,t) trucks at D22 day G...76 Figure 29 Oblique N(x,t) for D25 off-ramp and right lane flows for D22 day G...77

10 vii Figure 3 Autobahn A5 north speed diagram day B...79 Figure 31 Oblique N(x,t) for D25 off-ramp and trucks right lane day B...81 Figure 32 Autobahn A5 north speed diagram day E...83 Figure 33 Oblique N(x,t) and V(x,t) for D8 day E...85 Figure 34 Oblique N(x,t) for D6 on-ramp day E...86 Figure 35 N(x,t) for D7:D8 lane change day E...87 Figure 36 N-N 2 oscillation curves day A...91 Figure 37 Diverge bottleneck D22:D24 discharge flow variability...97 Figure 38 Diverge bottleneck D22:D24 pre-queue flow variability...1 Figure 39 Merge bottleneck D7:D8 discharge flow variability...15 Figure 4 Hypothetical triangular flow-density relation...123

11 1 1 INTRODUCTION This dissertation describes the spatio-temporal evolution of traffic from freely flowing to congested conditions and from congested to freely flowing conditions along a 3-km section of a German Autobahn. A large number of bottlenecks were identified at several locations by systematically examining the excess vehicle accumulation (spatial) and excess travel time (temporal) that arose between measurement locations. The analysis tools used in this study were transformed curves of cumulative vehicle count and cumulative time-mean velocity constructed from archived inductive loop detector data. These cumulative curves provided the resolution necessary to reveal the spatial and temporal aspects of dynamic freeway traffic flow phenomena. Bottlenecks became active in the vicinity of on-ramps (merges) and off-ramps (diverges) on this section of freeway. The discharge flows from each of the bottlenecks were carefully computed and were found to be reproducible from day to day across all lanes and on a lane-by-lane basis. Upon queue formation at diverge bottlenecks that were preceded by freely flowing traffic (defined here as isolated activations), the flow dropped such that the average discharge flows were approximately 4% lower than the high flows observed prior to the queue formation. At isolated merge bottlenecks, the observed flow drops were approximately 3%.

12 2 The potential triggers for several bottleneck activations were studied and several of these triggers were found to be reproducible. Reproducible diverge bottleneck activation triggers included: high pre-queue flows across all lanes with major truck count influence in the right lane upstream of the bottleneck activation station, and surges in off-ramp flows. These flows appeared to represent the maximum possible flows for this freeway location. Reproducible merge bottleneck activation triggers included: surges in on-ramp flow, and a pattern of lane changing to the left in the region where the bottlenecks formed. The potential triggers for the deactivation of diverge bottlenecks were also studied. The reproducible triggers for diverge bottleneck deactivation were: drop in off-ramp flow, and notable drop in truck flow in the right lane at the off-ramp station. 1.1 Background Freeway traffic flow data have been accumulated for over fifty years. Early work relied on manually collected data that was limited in scope both in time and in the length of freeway studied. Later, as inductive loop detectors provided automated data collection, the scope of empirical studies has expanded. Throughout these fifty years, many traffic flow models, primarily macroscopic, have been proposed. Daganzo (1999a), in a summary of the current state of knowledge in traffic flow, stated that while some of the empirical evidence supports certain theories under specific conditions, there is no single theory which describes all the observations.

13 3 To understand the details of traffic flow around locations where traffic streams merge and diverge, previous empirical studies have examined traffic conditions both upstream and downstream of freeway bottlenecks of several kinds. These include merge bottlenecks located near on-ramps (Bertini 1999; Cassidy & Bertini 1999a; Cassidy & Bertini 1999b; Bertini & Cassidy 22; Bertini & Malik 24; Cassidy & Mauch 21; Cassidy & Rudjanakanoknad 22; Bertini & Myton 24; Treiber & Helbing 1999; Treiber, Hennecke & Helbing 2), diverge bottlenecks near off-ramps (Cassidy, Anani & Haigwood 22; Muñoz & Daganzo 22b; Windover 1998; Bertini & Malik 24; Bertini, Lindgren, Helbing & Schönhof 24a; Bertini, Lindgren, Helbing & Schönhof 24b; Bertini & Myton 24) merge bottlenecks at lane drops (Leal 22; Bertini, Leal & Lindgren 23; Bertini & Leal 25) and other geometric configurations. Windover (1998) reported that bottlenecks resulted in shocks of lower speed that traveled upstream at a nearly constant rate and propagated without spreading. These studies were conducted primarily on North American highways, with one study of a British highway (Leal 22, Bertini et al. 23). None of these studies examined German freeways. A number of empirical studies of congested traffic on German Autobahns have been conducted by Kerner and his colleagues (Kerner & Rehborn 1996a; Kerner & Rehborn 1996b; Kerner 1997; Kerner & Rehborn 1997; Kerner 1998a; Kerner 1998b; Kerner 1999a; Kerner 1999b; Kerner 1999c; Kerner 2a; Kerner 2b; Kerner

14 4 2c; Kerner, Aleksic, & Rehborn 2; Kerner 21a; Kerner 21b; Kerner & Herrtwich 21; Kerner 22a; Kerner 22b; Kerner 22c; Kerner 22d; Kerner 23b; Kerner 23c; Kerner 24c; Kerner, Rehborn, Aleksic & Haug 24a; Kerner, Rehborn, Aleksic & Haug 24b). A detailed listing of Kerner s empirical studies including the highway location and study dates can be found in Appendix D. The German loop detector data used by Kerner and his colleagues was not made available to other researchers. This study is unique since it represents the first time that an independent analysis of German freeway data was possible. Furthermore, by using techniques that have been successfully applied to North American and British freeway data, this study allowed for a comparison among a number of international sites. Many of the early Kerner studies relied upon time series plots of flow, occupancy, or average speed from data measured over short time intervals (one minute). Measured traffic variables often exhibit statistical fluctuations along with time-dependent changes in the average. However, unaltered time series plots do not always reveal the distinctions between the two. Based primarily on these unaltered time series plots, Kerner and Rehborn (1996b) proposed three phases of traffic flow: 1) free flow 2) synchronized flow and 3) wide moving jam. They stated that free flow was characterized by ample vehicle passing opportunity such that average speeds in adjacent lanes were significantly different

15 5 (Kerner & Rehborn 1996b). Kerner and Rehborn (1996a, 1996b) also found that under free flow conditions truck traffic in the left lane was very low (<1%) while it was high (2 25%) in the right lane. Kerner (1999c) defined synchronized flow as occurring when vehicle density reduced passing opportunities to the extent that the average speeds in adjacent lanes were similar (±1 km/h), yet flows remained high. Finally, Kerner (1999c) defined wide jams as areas where vehicle density was very high, whereas speed and flow were very low. Expanding on earlier traffic flow phase classification work, Kerner (22b) characterized two kinds of traffic congestion occurring in traffic jams: 1) weak congestion which was observed mainly at off-ramps and 2) strong congestion which was observed mainly at on-ramps. These ramp facilities, along with other physical non-homogeneities were described by Kerner (1999c) as likely triggers of transitions among the three phases of traffic flow described above. In the transition from free flow to synchronized flow, Kerner and Rehborn (1996b) reported that the speed decreased sharply but the flow remained almost the same. They further reported that transition from free flow to traffic jam, with speed and flow decreasing sharply to zero was possible, but rare. In contrast with bottlenecks caused by physical freeway infrastructure, Kerner and Rehborn (1996a) and Kerner (22a) reported that a traffic condition called a wide moving jam spontaneously emerged in synchronized flow. The wide moving jam

16 6 was defined as a traffic disturbance causing very low flow and speed that, while short lived at any one freeway location, traveled long distances (several km) at a nearly constant speed of -15 km/h (Fig. 2 and 3 in Kerner & Rehborn 1996a). Furthermore it was reported that these disturbances showed no significant signs of spreading, that is, the disturbance lasted about the same time at each progressive upstream station. Kerner reported that traffic also broke down spontaneously from freely flowing for no obvious physical reason. Kerner (1998a) reported on an apparent breakdown in speed and flow between ramps (approximately 2.5 km downstream of the nearest ramp). In findings that have so far not been reproduced by others, Kerner (1994, 1998a, 1999b, 2c, 22d) suggested that traffic congestion can form and traffic can self-organize without a physical bottleneck. Turning to the traffic impacts of freeway bottlenecks, Kerner (1998b, 22d) stated that highway capacity in the free flow regime can be twice as high as capacity in congested traffic. This finding contrasts with all other empirical findings (Bertini 1999, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b, Bertini & Cassidy 22, Bertini & Malik 24, Cassidy & Mauch 21, Cassidy & Rudjanakanoknad 22) that show a capacity drop upon activation of a bottleneck. Cassidy and Rudjanakanoknad s (24) finding that very careful ramp metering provides a 1% capacity gain reinforces the concept that a highway s capacity drops upon the activation of a bottleneck.

17 7 Kerner (2c, 22d) further stated that the discharge flows measured at the same on-ramp bottleneck were noticeably different on different days and that this variation can be from about 1,6 veh/h to 2,7 veh/h. This finding differs from those of several other studies (Bertini 1999, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b, Bertini & Cassidy 22) which found bottleneck discharge rates to be reproducible from day to day. Variations of traffic flow within congested traffic streams have also been studied by a number of researchers. In these studies, oscillations, or changes in short term average flows, were found to propagate upstream in freeway queues at nearly constant speeds of approximately -2 km/h (Windover 1998, Cassidy & Mauch 21, Mauch 22, Mauch & Cassidy 22, Daganzo & Smilowitz 22). Mauch (22) found that these oscillations had stable amplitudes of approximately 16 vehicles per lane. These oscillations did not affect flows measured downstream of the locations where queues formed. To promote the visual identification of time-dependent features of traffic streams, many of these previous studies used curves of cumulative vehicle count and curves of cumulative occupancy constructed from data measured at neighboring freeway loop detectors. Tutorials on the use of these cumulative count curves can be found in many references (e.g., Cassidy & Windover 1995, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b, Muñoz & Daganzo 22c). The use of these curves provided the

18 8 measurement resolution necessary to observe transitions between freely flowing to queued conditions and to identify a number of notable, time-dependent traffic features of the bottlenecks. This cumulative plotting method is distinct from the time series plots used by Kerner and others since cumulative plots can actually show excess accumulation (queueing) between measurement locations resulting from bottleneck activation. In contrast, analysis of a time series plot from one point forces one to infer the presence of bottleneck activations based on changes in the measured parameter. 1.2 Motivation Understanding how a freeway system operates requires sound knowledge about the behavior of traffic on all elements of the network. These elements include long, homogeneous freeway sections as well as merge areas, diverge areas and other geometric features. Bottlenecks are undesirable, yet necessary attributes of freeway systems. A bottleneck is a restriction that separates upstream queued traffic from downstream unrestricted traffic (Daganzo 1997). Bottlenecks can be static (e.g., a tunnel entrance, lane drop, diverge area) or dynamic (e.g., an incident or a slow moving vehicle). As shown in Figure 1, a bottleneck is considered active when it meets the definition presented above and is deactivated when there is either a decrease in flow or when a queue spills back from a downstream bottleneck (Bertini et al. 23).

19 9 Queued Bottleneck Unqueued Detectors Figure 1 Active bottleneck While discussing the state of traffic flow theory, Newell (1965) stated that the main object of traffic research should be to study time-dependent flows, to determine velocities of propagations of disturbances, and to determine how traffic adjusts to some time- or space-dependent influences such as traffic lights, bottlenecks, etc. Newell expected that modern data collection and analysis techniques would soon refine the theories of the early 196 s, yet thirty years later Newell reported that little had been added to the understanding of dense traffic flow (Newell 1995). Therefore it is appropriate to study and understand freeway bottlenecks of all kinds including merges, diverges, lane drops and other configurations. This study is unique since it reports on empirical findings from a very long freeway data set that includes several interchanges, thereby allowing the study of traffic disturbances caused by a variety of highway geometric inhomogeneities. Furthermore, this study is important since it describes how traffic disturbances moved long distances upstream and influenced traffic as far as 2 km from the site of the original disturbance.

20 1 1.3 Organization of the dissertation The remainder of this dissertation is organized as follows. Section 2 describes the study site and data collection. The methodologies used for identifying key traffic features related to the formation and dissolution of freeway bottlenecks are provided in Section 3. Then, Section 4 presents the detailed analysis of the traffic features including the locations of bottlenecks, the times that they remained active, the features of queue discharge and results of analysis of the factors leading to the activation and deactivation of these bottlenecks. Finally, Section 5 summarizes the findings of this study and provides an outline of some areas of further research.

21 11 2 DATA The study site, as shown in Figure 2, is a 3-km section of northbound Autobahn 5 (A5) near Frankfurt am Main, Germany. The freeway is equipped with thirty vehicle detector stations (labeled in this research as D1 through D3). The spacing of the stations, in meters, is shown in the figure. Each detector station consists of two closely spaced inductive loops (a speed trap ) in each travel lane. A roadside controller records counts and average vehicle speeds over one-minute periods for two vehicle types. The two vehicle types, segregated by vehicle lengths, are reported as autos and trucks. As shown in the profile portion of Figure 2, the grade is generally uphill in the northbound direction with a maximum vertical grade of 3.3% between stations D22 and D23. [m] [Sta] Elevation [m] D5 D4 D3 D2 D D7 D D11 D1 D9 D8 A66 Nordwest Kreuz A648 West Kreuz Frankfurt am Main Frankfurt am Main D16 D15 D14 D13 D D D D D2 A661 Bad HomburgerKreuz A5 Profile Figure 2 Site map D26 D25 D24 D23 D22 D21 17 D A455 Friedberg 115 D29 D28 2 D3

22 12 The data were collected for six days in 21: Friday, May 18; Friday, August 17; Friday, September 14; Wednesday, September 19; Thursday, September 2; and Tuesday, December 4. Table 1 introduces the notation (days A G) used to identify the study days and provides a brief description of the weather. The weather conditions were generally cool with light winds, partial cloudiness and small amounts of precipitation. There were no severe weather events that could have been expected to disrupt traffic flow (Weather Underground 22). Appendix C contains detailed weather data for Frankfurt am Main on the days studied. Table 1 Autobahn A5 days analyzed Day Date Weather A Friday, May 18, 21 mainly clear B Friday, August 17, 21 partly cloudy C Friday, September 14, 21 cloudy, light rain G Wednesday, September 19, 21 rain E Thursday, September 2, 21 cloudy, light rain F Tuesday, December 4, 21 cloudy, light rain The archived data were provided by Hessische Landesamt für Strassen-und Verkehrswesen (the Hessian National Office for Road and Traffic) and preliminary processing was performed by researchers at the Dresden University of Technology. This preliminary processing included the assignment of error codes during periods of detector malfunction.

23 13 The data preparation for this dissertation began with data cleaning where error codes were replaced by speed and count values interpolated linearly from adjacent time periods. The overall fidelity of the loop detector data was then assessed for each study day by cumulating the counts over the entire 24 hour data collection periods. For sections of the freeway where conservation of vehicles was possible (between interchanges), the daily totals were compared. As shown in Figure 2, there were three such sections of freeway, the first from station D6 to D14, the second from D16 to D24, and the third from D26 to D3. If each of the detector stations accurately recorded the passage of each vehicle, the totals for each section should have been very close, varying only by the difference in vehicle counts during the travel time for that section. As shown in Table 2 the station daily totals differed from the mean totals by no more than.26% for the D6 to D14 section, by no more than.52% for the D16 to D24 section, and by no more than.2% for the D26 to D3 section. There were no ramp meters on this portion of the A5 Motorway at the time the data was collected, and in general, ramp metering is extremely rare in Germany. There were no speed limits for autos on this portion of the A5. Trucks, however, were subject to an 8 km/h speed limit and were required by law to keep to the right lane (ASV 25) unless they were traveling 2 km/h faster than a slower moving truck. German drivers obey a principle of rechtsfahrgebot in which vehicles keep to the right and switch lanes only for passing others. Overtaking is only allowed by using a

24 lane to the left of the other vehicle, except in stationary traffic, and overtaking must be done as quickly as possible. 14 Table 2 Data fidelity Station Day A Diff. from Daily Mean Day B Diff. from Daily Mean Day C Diff. from Daily Mean Day E Diff. from Daily Mean Day F Diff. from Daily Mean Day G Diff. from Daily Mean D6.33%.16%.6%.26%.32%.4% D7.7%.33%.4%.7%.33%.15% D8.1%.27%.14%.17%.1%.5% D9.2%.%.3%.7%.15%.4% D1.13%.44%.9%.31%.71%.29% D11.14%.21%.1%.11%.9%.8% D12.48%.2%.18%.33%.18%.3% D13.1%.28%.9%.2%.2%.11% D14.26%.48%.17%.35%.2%.23%.16%.26%.9%.19%.18%.11% D16 n/a.22%.14%.24%.59%.67% D17.19%.18%.31%.19%.4%.3% D18.14%.36% n/a n/a.% 2.24% D19.21%.36%.24%.53%.29%.15% D2 1.41%.5%.7%.11%.3%.8% D21.31%.85%.8%.2%.18%.14% D22.45%.55%.42%.27%.44%.57% D23.28%.18%.15%.38%.27%.46% D24.61% 1.26%.25%.46%.%.38%.45%.44%.21%.27%.21%.52% D26.12%.37%.31%.13%.1%.3% D27.11%.7%.34%.2%.13%.27% D28.19%.2%.17%.11%.16%.13% D29.2%.3%.18%.13%.8%.7% D3.17%.6%.2%.5%.2%.5%.12%.15%.2%.12%.12%.11%

25 15 3 METHODOLOGY This study employed three primary plotting techniques to visually identify both the spatial and temporal limits of congested traffic: speed contour plotting, and cumulative plots of count and time mean speed. These techniques are described in the following three subsections. Cumulative plotting techniques have been used in several previous studies and are described in detail in the following references (Cassidy & Windover 1995, Muñoz & Daganzo 22c, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b, Bertini & Cassidy 22). To allow for the greatest possible precision, the data used for each of these plot types were retained in their most raw form, that is no arbitrary data aggregation was performed. 3.1 Speed contour plotting The spatial and temporal limits of congested traffic conditions were first identified by speed contour plotting as illustrated in Figure 3. The x-axis of this figure is time; the y-axis is distance with station D1 at the extreme south of the study site and station D3 in the north. The average speed of all vehicles (both autos and trucks) for each one-minute period in all travel lanes was plotted in grayscale where the lighter shades indicate high speeds with darker shades representing lower speeds. This graphing technique includes a linear interpolation from the discrete station by station speed data described in Section 2.

26 16 2 D3 D D D D26 4 D25 65 D24 65 D23 D22 11 D21 13 D2 125 D D D D16 1 D15 5 D14 7 D13 D12 12 D D1 9 D9 D D7 D D5 D4 11 D D2 D1 [m] [Sta] A455 Friedberg A661 Bad Homburger Kreuz A66 Nordwest Kreuz Frankfurt am Main A648 West Kreuz Frankfurt am Main Speed [km/h] Figure 3 Speed contours day C Elevation [m] Profile Curves of cumulative vehicle count versus time Further investigation of suspected bottleneck locations was conducted using transformed oblique cumulative plots. An unaltered cumulative plot is the graph of a function Ñ(x,t) with vehicle number (N) on the y-axis versus time, t on the x-axis at which each vehicle passes a stationary point (Daganzo 1997). As shown in Figure 4(A), a cumulative count plot of vehicles is a step-function, Ñ(x,t), in this case with equal time steps, whereas a smooth function, N(x,t) is established by interpolating a line though the near-side top of each step. All cumulative count plots in this

27 dissertation will be smooth function N(x,t). When a smooth function is used, the instantaneous flow q(t) is first derivative of N(x,t) with respect to t. 17 x 1 Travel Direction N(x,t) Slope = q(t) Ñ(x,t) 12:3 12:31 12:32 12:33 12:34 12:35 12:36 12:37 12:38 12:39 12:4 12:41 Time, x (A) N(x j,t) k Travel Direction x 1 x 2 Trip Time k N(x 1,t) N(x 2,t) Number Ref. Veh. Trip Time t 1 (B) Time, t N(x j,t) k Travel Direction x 1 x 2 Excess Trip Time N(x 1,t) Excess Accumulation N(x 2,t) (C) t 3 t 2 Time, t Figure 4 Constructing cumulative curves

28 18 Figure 4(B) presents hypothetical curves of N(x j,t), where N is the cumulative number of vehicles that pass a location x j by time t. The time, t, is measured from the passage of a hypothetical reference vehicle, k and j=1,2 (Newell 1982). The hypothetical N(x,t) in Figure 4(B) were constructed for the same collection of vehicles. Imagine an observer at the upstream station x 1 recording and cumulatively graphing the arrival times of vehicles as they pass her location, the result would be the curve N(x 1,t). If the vehicles are assumed to pass through the system in a first-in-first-out (FIFO) order (e.g., no exit or entry points and no lane changing), the times when these same vehicles pass an observer at x 2 could also be plotted cumulatively to create the curve N(x 2,t) (Bertini 1999, Windover 1998). In analyzing Figure 4(B) some important parameters are revealed. The horizontal distance between the curves at N=k for example, is the kth vehicle s trip time from x 1 to x 2. The vertical distance between the curves at t=t 1, for example, is the number of vehicles accumulated between locations x 1 and x 2. Figure 4(C) shows the upstream curve, N(x 1,t) from Figure 4(B), shifted horizontally to the right by the measured x 1 -x 2 free flow trip time. The result is a shifted N(x,t). Note that absent the queue, flow changes are passed downstream. The horizontal separation is the excess trip time, commonly called delay. The vertical distance between the curves is excess accumulation. At t=t 2, for example, the vertical distance is the number of vehicles accumulated between locations x 1 and x 2 less the

29 19 accumulated vehicles that would be expected under free-flow conditions. Very small excess accumulations can be expected even under free flow conditions since vehicles speeds will vary stochastically due to imperfect throttle control and interaction among vehicles. If the excess accumulation and delay are large enough, then a queue is present between x 1 and x 2. Furthermore, the time at which the curves diverge, for example at t=t 3 on Figure 4(C), is the time at which the tail of an upstream moving queue arrives at the upstream measurement location (assuming that the queue starts somewhere between measurement locations). Shifted N(x,t) allow delay and excess accumulations to be depicted graphically and additionally allow the time of the onset of queuing to be visually revealed. While the idealized Figure 4(C) clearly revealed a change in traffic conditions, the large scale required to display N(x,t) for freeways with high numbers of vehicles results in the loss of ability to visually locate subtle but important features such as the precise time of the onset of queuing. Figure 5 shows N(x,t) for Detector D21 on day A. Due to the y-axis scaling necessary to plot N(x,t), the two N(x,t) of Figure 5(A) appear as nearly superimposed straight lines and little can be discerned with regards to queuing. This scaling problem can be overcome by plotting N(x,t) on an oblique coordinate system, defined by two non-orthogonal families of individually labeled parallel lines as described in Muñoz and Daganzo (22c). Effectively, this involves a re-scaling of

30 2 the y-axis created by subtracting a value q o t' from each ordinate, where t' is the elapsed time from the passage of some reference vehicle and q o is the oblique scaling rate (Bertini 1999). Figure 5(B) shows the same shifted N(x,t) as those shown in Figure 5(A), added is a line with the slope q o =4, vehicles per hour (vph). The optimal q o value was chosen graphically by iteration to obtain the best visualization that magnified the traffic features of interest. The vertical difference between the line with slope q o and each N(x,t) is N(x,t)-q o t'. These vertical differences, N(x,t)-q o t', were plotted as ordinates against an x-axis scale of time. Figure 5(C) shows oblique N(x,t) for detectors D21 and D22 plotted with a relative vertical scale and with q o =4, vph. Piecewise linear average flows were also chosen graphically and are shown with dashed lines and are labeled to the nearest 1 vph. An oblique N(x,t), with a properly chosen value of q o, provides a plot with the fidelity required to identify the timedependent features of the traffic stream. Since the ordinate N(x,t)-q o t' has units of vehicles and the x-axis is time, the slopes of oblique N(x,t), like those of the N(x,t) depicted in Figure 4(A), have the dimension of vehicles per time or flow. If a plot of N(x,t) had the same slope as the q o curve, the oblique N(x,t) for the same period would have ordinates, N(x,t)-q o t' of zero and therefore plot as a horizontal line of zero slope. Positive and negative slopes of an oblique N(x,t) can be interpreted visually as flows greater than or less than, respectively, q o.

31 21 N(D21,t) N(x,t) N(D22,t) 1, 12:3 12:35 12:4 12:45 12:5 12:55 13: 13:5 13:1 Time, D21 (A) 13:15 13:2 13:25 13:3 N(D21,t) N(x,t) N(D22,t) 1, q =4, vph N(x,t)-q t 12:3 12:35 12:4 12:45 12:5 12:55 13: 13:5 13:1 Time, D21 (B) 13:15 13:2 13:25 13:3 N(x,t)-q t, q =4, vph 1 4,63 vph D21 5,25 vph 12:51 4,63 vph D22 3,96 vph 12:3 12:35 12:4 12:45 12:5 12:55 13: 13:5 13:1 13:15 13:2 13:25 13:3 Time, D21 (C) Figure 5 Constructing oblique N(x,t) curves

32 The graphical methods for choosing optimal q o values and piecewise linear flow segments can be augmented by the use of statistical curve fitting routines Curves of cumulative vehicle velocity versus time Curves of cumulative time-averaged velocity versus time were also used in these investigations to verify the features revealed by the oblique N(x,t). Oblique V(x,t) are plots of V(x,t)-v o t' versus time, t. The V(x,t) ordinate is established by plotting cumulatively the time-averaged velocity for each averaging period (i.e., 1 minute in the case of these A5 data). The V(x,t) values nominally have the dimension of velocity since they represent a cumulative total of velocity values. However, the V(x,t) values will increase at a rate that is inversely proportional to the duration of the averaging period. For example, if the averaging period were one hour, the cumulative total would simply equal the average speed over this hour; yet if the averaging period were one minute, the average hourly velocity would be obtained by multiplying the cumulative total by 1/6 hour. Thus the V(x,t) values have the dimensions of speed time, which is distance. With a construction process similar to that used for oblique N(x,t), the V(x,t) values are then plotted on an oblique axis by subtracting a value v o t' from each value, where t' is the elapsed time from the passage of a reference vehicle and v o is the oblique scaling rate. The value v o is graphically represented as the slope of an arbitrary line drawn on a cumulative velocity plot. The value v o, being the slope of a cumulative

33 time-averaged speed versus time curve, therefore has the dimensions of distance/time or velocity. 23 If a plot of V(x,t) had the same slope as v o, the oblique V(x,t) for the same period would have ordinates, V(x,t)-v o t' of zero and therefore plot as a horizontal line of zero slope. Therefore, an oblique V(x,t) exhibits a negative slope when the prevailing speed is less than v o. Positive and negative slopes of an oblique V(x,t) can be interpreted visually as speeds greater than or less than, respectively, v o. An example of this technique applied to A5 data is shown in Figure 6 which depicts oblique V(x,t) for Detector D21 on day A. This figure is plotted with a relative vertical scale and with dashed lines which represent piecewise linear average speeds (labeled to the nearest km/h). The next section of this dissertation presents the results of the application of these methodologies to several days of data from the A5 Motorway.

34 24 V(D21,t)-v t, v =4,8 km/h km/h 12:53 62 km/h 12:45 12:46 12:47 12:48 12:49 12:5 12:51 12:52 12:53 12:54 12:55 12:56 12:57 12:58 12:59 13: Time, D21 Figure 6 Oblique V(x,t)

35 25 4 ANALYSIS Data from a total of six days in 21 were analyzed. Section 4.1 describes the diagnoses of twenty bottleneck activations on September 14, 21 (hereafter called Day C). In addition to bottleneck diagnoses, Section 4.1 reports on the discharge characteristics and the apparent triggers of a Day C diverge bottleneck upstream of an off-ramp. In Section 4.2, the diagnoses of fifteen bottleneck activations on September 19, 21 (Day G) are summarized. Section 4.2 also details the discharge characteristics and the apparent triggers of two Day G diverge bottleneck activations upstream of an offramp. The diagnosis and apparent deactivation triggers of a diverge bottleneck occurring on August 17, 21 (Day B) are covered in Section 4.3. Then, Section 4.4 outlines the diagnosis and apparent activation triggers of a merge bottleneck downstream of an on-ramp on September 2, 21 (Day E). Next, Section 4.5 reports on traffic oscillations found in congested traffic conditions. And finally, traffic congestion observations that were found to be reproducible are itemized in Section Day C Using the methods illustrated in Section 3, this section summarizes the full diagnoses of twenty bottleneck activations along the A5 on Day C.

36 These bottleneck activations (labeled C1 through C2) are mapped in time and space on Figure D3 D D D D26 4 D25 65 D24 65 D23 D22 11 D21 13 D2 125 D D D D16 1 D15 5 D14 7 D13 D12 12 D D1 9 D9 D D7 D D5 D4 11 D D2 D1 [m] [Sta] A455 Friedberg A661 Bad Homburger Kreuz A66 Nordwest Kreuz Frankfurt am Main A648 West Kreuz Frankfurt am Main 12:53 13:1 Speed [km/h] C13 13:21 13:28 C14 13:22 13:33 C18 C12 13:33 14:2 14:17 14:3 C1 14:48 14:4 14:5 C2 14:5 C11 15:15 15:12 C3 15:18 15:32 15:43 15:32 C15 C4 15:51 16:1 C :8 C6 16:58 16:42 16:57 C7 17:1 C8 17:15 17:31 C9 17:5 18: 17:38 17:49 C16 18:4 C17 18:33 18:46 C19 C1 18:35 19:17 19:24 C2 19:16 Elevation [m] Profile 14 9 Figure 7 Autobahn A5 north speed diagram day C Figure 7 was constructed as described in Section 3.1 and shows speeds averaged across all lanes for each 1-minute interval and plotted using time as the x-axis, distance as the y-axis, and variation in speed in gray tones. The lighter shades indicate high speeds with darker shades representing lower speeds. It is clear from the figure that a large number of speed disturbances occurred on this day starting shortly before 13: and continuing until nearly 19:3.

37 Diagnosis of bottleneck activation C1 In order to demonstrate the diagnosis of a bottleneck activation, including its location and the time it remained active on Day C, Figure 8 shows transformed oblique curves of cumulative vehicle count, N(x,t), for detectors D2 D24 from 13:4 until 14:2. Using one-minute count data measured across all lanes, piecewise linear approximations of the cumulative counts were constructed so that the slope of the unaltered N(x,t) would be the flow past location x at any time t. The counts for each curve began (N=) such that each curve describes the same collection of vehicles. D3 2 D29 D28 21 N(x,t)-q t' q =4,3 vph 1 D27 D26 D25 D24 D23 D22 D21 D2 14:2 D C1 D22/D23 14:17 D22 13:4 13:45 13:5 13:55 14: 14:5 14:1 14:15 14:2 Time, D2 Figure 8 Oblique N(x,t) for D2:D24 day C 13:4 14:2

38 28 Note that the x-axis in Figure 8 shows the time scale for the upstream-most station (D2) and that the process of constructing such a multi-station plot results in downstream curves being shifted to the left where each curve has its own time scale. Therefore, all times shown on such plots are identified by station. All five curves in Figure 8 remained superimposed until approximately 14:, indicating that traffic flowed freely between stations D2 and D24. Shortly after 14:, Figure 8 shows that excess accumulation arose between stations D22 and D23 as indicated by the divergence of the oblique N(x,t). A subsequent divergence of curve D22 from curve D21 (and flow reduction measured at D22) marked the passage of the backward-moving queue at D22. Meanwhile curves for stations D23 and D24 remained superimposed indicating freely flowing traffic between these stations. The presence of a queue upstream of D22 and freely flowing traffic between D23 and D24 led to the diagnosis of an active bottleneck between D22 and D23 beginning at approximately 14:2, to be confirmed below. This bottleneck activation was labeled as bottleneck C1. A short time later, at 14:17, curves D22 and D23 again became superimposed followed closely by the dissolution of excess accumulations between all stations indicating freely flowing traffic throughout the section. So bottleneck C1 was activated between stations D22 and D23 for the period 14:2 14:17.

39 29 V(D24,t)-v t' v =5,74 km/h :4 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D24 V(D24,t)-v t' : :4 14:5 Right, v =5, km/h 2 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D Left, v =6,26 km/h 2 Mid, v =5,69 km/h 2 V(D24,t)-v t' v =5,66 km/h : :5 14:7 14:9 14:11 14:13 14:15 14:17 14:19 14:21 14:23 14:25 Time, D24 V(D23,t)-v t' v =4,79 km/h :1 7 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D23 V(D23,t)-v t' :1 Right, v =4,9 km/h 2 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D Left, v =5,19 km/h 2 Mid, v =4,78 km/h 2 V(D23,t)-v t' v =4,79 km/h : :5 14:7 14:9 14:11 14:13 14:15 14:17 14:19 14:21 14:23 14:25 Time, D23 V(D22,t)-v t' v =4,511 km/h : :5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D22 V(D22,t)-v t' :2 Left, v =4,82 km/h 2 Mid, v =4,43 km/h 2 Right, v =3,94 km/h 2 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D V(D22,t)-v t' v =4,4 km/h : :5 14:7 14:9 14:11 14:13 14:15 14:17 14:19 14:21 14:23 14:25 Time, D22 V(D21,t)-v t' v =4,74 km/h 2 V(D2,t)-v t' v =4,83 km/h :5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D : :7 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D2 V(D21,t)-v t' 1 V(D2,t)-v t' :4 Right, v =3,52 km/h 2 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D Mid, v =4,64 km/h 2 5 Right, v =4,5 km/h 2 13:5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 14:1 Time, D : Left, v =5,11 km/h 2 Mid, v =4,93 km/h 2 Left, v =5,12 km/h 2 V(D21,t)-v t' v =4,74 km/h 2 V(D2,t)-v t' v =4,12 km/h :5 14:7 14:9 14:11 14:13 14:15 14:17 14:19 14:21 14:23 14:25 Time, D :14 14: :5 14:7 14:9 14:11 14:13 14:15 14:17 14:19 14:21 14:23 14:25 Time, D2 Figure 9 Oblique V(x,t) for D2:D24 C1 activation

40 3 To confirm this bottleneck C1 diagnosis and to identify trends in mean measured velocity and to clearly identify times at which notable velocity changes occurred, oblique V(x,t) were also constructed for each detector as described in Section 3.3. V(x,t) was the cumulative time mean speed measured at detector x by time t, where the slope of the V(x,t) was a speed rate for that location. As shown in Figure 9, an oblique scaling rate of v was applied using an amplified vertical scale, and periods of nearly constant average speed (shown as trend lines and labeled in km/h) and times marking changes in average speed (marked with vertical arrows) were labeled on the figure. The left-hand column of Figure 9 shows oblique V(x,t) averaged across all lanes for stations D2, D21, D22, D23 and D24, using different values of v (labeled on the y- axes of the individual graphs). The time period of the left-hand column spans the time of activation of bottleneck C1. The middle column shows oblique V(x,t) on a lane-bylane basis for the same detector stations over the same time period. Finally, the righthand column of Figure 9 shows oblique V(x,t) for these same detector stations and spans the time of deactivation of bottleneck C1. The third row of curves in Fig 9 shows oblique V(x,t) for D22, the station immediately upstream of the bottleneck. The 14:2 activation time of bottleneck C1 was confirmed by observing that the D22 speed measured across all lanes dropped notably from 95 km/h to 45 km/h at 14:2. Figure 9 also shows that the D22 speed drop occurred at approximately the same time (14:2) in all three lanes. The speed

41 31 dropped from 12 km/h to 48 km/h in the left lane, from 91 km/h to 47 km/h in the mid lane, and from 81 km/h to 43 km/h in the right lane. Also visible in Figure 9 is that the speed variation across lanes, as expected, changed abruptly at the time of bottleneck activation. At D22, prior to the 14:2 activation of bottleneck C1, the speed difference between the right and left lanes was 21 km/h whereas the post activation speed difference was only 5 km/h. The time of deactivation of bottleneck C1 was also confirmed by observing in the right-hand column of Figure 9 that the D22 speed increased from 55 km/h to 97 km/h at 14:17. Speeds measured at D21, further upstream of the C1 bottleneck activation, are illustrated in the fourth row of curves in Figure 9. The left-hand figure shows that the speed across all lanes dropped from 89 km/h to 42 km/h at 14:4, just slightly later than the speed drop at D22 this is consistent with the passage of the queue that emanated from between D22 and D23. The middle column shows that the speed dropped in each lane at about this same time (14:4). The right-hand column indicates that an increase in speed from 59 km/h to 82 km/h occurred at approximately 14:14, some 3 minutes before the speed increased at D22 and bottleneck C1 deactivated. This finding is consistent with a wave of faster moving traffic (a recovery wave) moving downstream towards the bottleneck. Continuing upstream, the oblique V(x,t) for D2 in the left-hand column of Figure 9 shows that the speed across all lanes decreased from 8 km/h to 4 km/h at 14:7,

42 32 later than the speed decreases seen at D21 and D22. Again this is consistent with the passage of the queue that emanated from between D22 and D23. Examination of the right-hand figure for D2 reveals a speed increase from 38 km/h to 66 km/h at 14:13, earlier than the speed increase at D21, consistent with a forward moving recovery wave. Now changing the focus to the region downstream of bottleneck C1, the second row of curves in Figure 9 show V(x,t) for D23, the station immediately downstream of the bottleneck. The curve in the left-hand column shows that the speed decreased from 9 km/h to 7 km/h at 14:1, slightly earlier than the speed decrease seen at D22. This is consistent with a fast moving speed recovery wave emanating from a bottleneck located between D22 and D23. Further analysis reveals that the speed that prevailed following the C1 activation at D23, downstream of the bottleneck (7 km/h) was higher than the 45 km/h seen at D22 over the same time period. This further supports the presence of freely flowing traffic accelerating downstream of a bottleneck. Finally, the first row of curves in Figure 9 shows V(x,t) for station D24, located several hundreds of meters downstream of the bottleneck. It can be seen that the speeds remained relatively high (>9 km/h) throughout the time period and the lefthand figure shows that a slight speed drop (from 96 km/h to 92 km/h) was noted at 14:4, some two minutes after the activation of the bottleneck which is consistent with a fast moving speed recovery wave. The right-hand figure for D24 reveals that

43 the speed increased slightly from 92 km/h to 97 km/h at 14:18 following the 14:17 deactivation of bottleneck C1. 33 This section has described in detail the diagnosis of a single bottleneck (C1) between D22 and D23 for the period 14:2 14:17. First, the examination of oblique N(x,t) curves revealed that the curves for D22 and D23 separated at 14:2 while the curves for D23 and D24 remained superimposed. This clearly showed that no queue existed downstream of D23 while queueing was present upstream of D22. Next, the oblique N(x,t) curves revealed that the queue propagated upstream and that the arrival of the queue at each upstream station was accompanied by a notable reduction in flow. Then, the point at which the oblique N(x,t) for D22 and D23 became superimposed again established the timing of bottleneck deactivation (14:17). Finally, a review of oblique V(x,t) curves for several stations upstream and downstream of the bottleneck then verified the timing of key speed drops and increases which verified the activation and deactivation times. These steps, which were followed for each bottleneck activation in this study, clearly established the spatial and temporal limits of the bottleneck over which the discharge characteristics and potential activation and deactivation triggers could be later studied Diagnoses of early afternoon bottleneck activations Using the methodology described in Section 3 and detailed procedures outlined in Section 4.1.1, the first five bottleneck activations diagnosed on Day C, including bottleneck C1, are presented in Figure 1. This figure shows transformed oblique

44 34 curves of cumulative vehicle count, N(x,t), for detectors D15 D24 from 12:35 until 14:2. The curve at D15 includes the on-ramp counts so that vehicle conservation was maintained. The bottleneck names and locations are also shown on Figure 1, as are the times of activation and deactivation. N(x,t)-q t' q =5, vph 1 D26 D25 D24 D23 D22 D21 D2 D19 D18 D17 D16 D15 D14 22 D19/D2 C18 13:22 D19 13:33 D C12 D18/D19 14:3 D :53 D22 C13 13:1 D22 13:21 D22 C14 D22/D23 13:28 D22 14:2 D22 C1 D22/D23 14:17 D22 D22/D23 12:35 12:45 12:55 13:5 13:15 13:25 13:35 13:45 13:55 14:5 14:15 Time, D15 Figure 1 Oblique N(x,t) for D15:D24 day C 12:35 14:2 All ten curves in Figure 1 remained superimposed until approximately 12:53, indicating that traffic flowed freely between all stations. At about 12:53 the figure shows that excess accumulation arose between stations D22 and D23 as indicated by the divergence of the oblique N(x,t). This activation was labeled as bottleneck C13. A short time later, at 13:1, the D22 and D23 curves again became superimposed indicating freely flowing traffic. Bottleneck C13 was active between stations D22 and

45 35 D23 from 12:53 to 13:1. The activation and deactivation times for C13 (and all other diagnosed bottlenecks for Day C) were confirmed by inspection of oblique V(x,t) located in Appendix A. All oblique N(x,t) from D15 D24 in Figure 1 remained superimposed from 13:1 until approximately 13:21 when the D22 curve again diverged from the D23 curve marking the activation of bottleneck C14. The curves for D23 and D24 remained superimposed indicating freely flowing traffic downstream of D23. The D22 and D23 curves became superimposed again at 13:28 marking the deactivation of C14. Bottleneck C14 was active between stations D22 and D23 from 13:21 to 13:28. Just after the C14 activation, a separate traffic disturbance was seen upstream between D19 and D2. At approximately 13:22, as shown on Figure 1, the N(x,t) for D19 separated from D2 marking the activation of bottleneck C18. The N(x,t) for D19 and D2 became superimposed again at 13:33 indicating the deactivation of bottleneck C18. Bottleneck C18 was active between stations D19 and D2 from 13:22 to 13:33. After 13:33, the D19 and D2 curves were superimposed, while a queue persisted between D18 and D19, indicating the bottleneck had shifted upstream. The new bottleneck activation between D18 and D19 at 13:33 is labeled as bottleneck C12 and remained active until the curves for D18 and D19 became superimposed again at 14:3. At

46 about this same time, 14:2, bottleneck C1 was activated between D22 and D23 and remained active until 14:17 as described in detail in Section This section has summarized the activation and deactivation of five bottlenecks occurring in the early afternoon of Day C in the D15 D24 section of Autobahn A5 immediately upstream of the A455 interchange. These bottlenecks are also mapped in time and space on Figure Diagnoses of late afternoon bottleneck activations To examine the flow features of this stretch of freeway at a later time period on Day C and using the methodology described in Section 3 and detailed procedures outlined in Section 4.1.1, Figure 11 was constructed using the oblique N(x,t) from detectors D15 D24 from 14:2 until 17:5. The bottleneck names and locations are also shown on Figure 11, as are the times of activation and deactivation. As shown in Figure 11, for several minutes prior to 14:4, N(x,t) curves for stations D16 through D24 were essentially superimposed indicating freely flowing traffic. It should be noted that the queue between D15 and D16 at about this time was a result of the queue emanating from bottleneck C1 (see Figure 1). Bottleneck C2 was activated at 14:4 when the curves for D22 and D23 separated, while the curves for D23 and D24 remained superimposed. Examination of Figures 7 and 11 shows that bottleneck C2 was deactivated when the backward moving tail of the queue from downstream bottleneck C11 reached D24 and caused a queue to develop between

47 D23 and D24, effectively deactivating bottleneck C2 at 14:5. The features of bottleneck C11 will be discussed in a subsequent section. 37 D26 D25 D24 D23 D22 D21 15 D2 D19 N(x,t)-q t' q =4,99 vph 14:4 D22 C2 14:5 D D18 D17 D16 D15 D D22/D23 15:32 D18 15:43 D18 15:51 D19 16:1 D19 C5 C4 D19/D2 D18/D19 16:8 D17 C6 D17/D18 16:58 D23 17:1 D17 C8 D23/D24 17:5 D23 14:2 14:3 14:4 14:5 15: 15:1 15:2 15:3 15:4 15:5 16: 16:1 16:2 16:3 16:4 16:5 17: 17:1 17:2 17:3 17:4 17:5 Time, D15 Figure 11 Oblique N(x,t) for D15:D24 day C 14:2 17:5 Bottleneck C4, as shown on Figure 11, between D18 and D19 became active at 15:32 and remained active until 15:43. The C4 deactivation was followed closely by a downstream bottleneck activation, C5, which was activated between D19 and D2 at 15:51 and remained active until 16:1. As shown by the excess accumulation arising between D17 and D18 at about 16:8, a bottleneck between D17 and D18 was active as bottleneck C6 until the backward moving tail of the queue from downstream bottleneck C8 deactivated C6 at 17:1. Bottleneck C8 was activated between D23 and D24 at 16:58 and persisted until 17:5. The activation and deactivation times for

48 these late afternoon bottlenecks for Day C were confirmed by inspection of V(x,t) located in Appendix A. 38 This section has summarized, and Figure 11 has mapped, the activation and deactivation of five additional bottlenecks occurring in the late afternoon of Day C in the D15 D24 section of Autobahn A5. These bottlenecks are also mapped in time and space on Figure Diagnoses of early evening bottleneck activations Using the methodology described in Section 3 and detailed procedures outlined in Section 4.1.1, this section continues the examination of bottleneck features for the range D15 D24 through the remainder of the peak period. Figure 12 contains a set of Day C oblique N(x,t) for stations D15 D24 between 17:5 and 2:. This figure shows three more bottleneck activations including the longest lasting bottleneck activation (76 minutes) seen on this day (C1). In the period prior to 18:, the oblique N(x,t) curves for stations D2 D24 were essentially superimposed indicating freely flowing traffic between these stations. The queues that were present between stations D15 and D2 were the result of bottleneck C8 activation described in Section At 18:, the curve for D19 became superimposed with the D2 D24 curves while the curves for stations D15 D19 remained separated which indicated the activation of a new bottleneck, C1, between D18 and D19. Bottleneck C1 persisted until a forward moving wave of lower flow deactivated the bottleneck at 19:16. So bottleneck C1 was activated between D18 and D19 from 18: to 19:16. Meanwhile,

49 several kilometers downstream, bottleneck C19 was activated between D22 and D23 at 18:33 and was deactivated at 18: D26 D25 D24 D23 D22 D21 D2 D19 N(x,t)-q t' q =4,97 vph :33 D C19 18:46 D22 19:17 D2 C2 19:24 D2 D2/D21 D18 D17 D16 D15 D : D18 D22/D23 C1 D18/D19 19:16 D18 17:5 18: 18:1 18:2 18:3 18:4 18:5 19: 19:1 19:2 19:3 19:4 19:5 2: Time, D15 Figure 12 Oblique N(x,t) for D15:D24 day C 17:5 2: Finally, Figure 12 shows the latest bottleneck diagnosed on this day, C2, which was activated between D2 and D21 at 19:17 and was active until the forward moving wave of lower flow that deactivated bottleneck C1 at 19:16, finally reached D2 at 19:24. The activation and deactivation times for these 3 early evening bottlenecks for Day C were confirmed by inspection of oblique V(x,t) located in Appendix A. Figure 12 clearly shows that the oblique N(x,t) for D15 D24 are all nearly superimposed after 19:24 indicating that traffic was freely flowing throughout the

50 region until 2: and, although not shown on the figure, this continued to be the case for the rest of the evening. 4 The locations and time of activation for the last three Day C bottlenecks diagnosed in this section are summarized on Figure 12 and are also mapped in time and space on Figure 7. Figures 8 through 12 have described the activation and deactivation of thirteen bottlenecks over a 9.3 km segment of the A5 North between the interchanges with Motorways A661 and A455. Six additional bottlenecks were found to have activated in the far upstream sections of the A5 study site and one bottleneck was diagnosed in the section downstream of the A5/A455 interchange. These activations will be discussed in the following sections Diagnosis of bottleneck activation in D26 D3 Inspection of Figure 7 revealed that a single bottleneck activation (C11) occurred on Day C in the segment between D26 and D3, downstream of the interchange of Motorway A455 and A5 North. Using the methodology described in Section 3 and detailed procedures outlined in Section 4.1.1, this section presents the C11 diagnosis. Figure 13 shows this activation with oblique N(x,t) for detectors D26 D3 between 14: and 15:4. For approximately the first 45 minutes shown on Figure 13 the curves for all stations were essentially superimposed indicating freely flowing traffic. Beginning at about 14:48, excess vehicle accumulation was visible between D28 and D29 whereas the N(x,t) for D29 and D3 remained superimposed indicating freely

51 41 flowing traffic between D29 and D3. The C11 bottleneck was therefore activated at 14:48 and persisted until 15:15 when the curves for D28 and D29 became superimposed once again. These activation and deactivation times were verified with oblique V(x,t) curves shown in Appendix A and this bottleneck is also mapped in time and space on Figure 7. N(x,t)-q t' q =4,41 vph D D29 D28 D27 D26 D25 D24 14:48 D28 C11 D28/D29 15:15 D28 14: 14:1 14:2 14:3 14:4 14:5 15: 15:1 15:2 15:3 15:4 Time, D26 Figure 13 Oblique N(x,t) for D26:D3 day C 14: 15: Diagnoses of early afternoon bottleneck activations in D6 D14 Returning to Figure 7, it can be seen that six additional bottleneck activations occurred in the segment between station D6 and D14 on Day C. This section presents the first two diagnoses using the methodology described in Section 3 and detailed procedures outlined in Section

52 42 The D6 D14 section of the A5 lies between the interchanges of Motorway A66 in the south and A661 in the north. Figures 14 and 15 show the details of the six activations and include oblique N(x,t) for detectors D6 D14 between 14: and 16: (Figure 14) and between 16: and 19: (Figure 15). Counts from the D6 on-ramp are included in the D6 curve in both figures to ensure vehicle conservation. C :12 D9 D9/D1 15:32 D9 8 N(x,t)-q t' q =4,8 vph 1 D16 D15 D14 D13 D12 D11 D1 D9 D8 D7 D :5 D7 C3 D7/D8 15:18 D7 14: 14:1 14:2 14:3 14:4 14:5 15: 15:1 15:2 15:3 15:4 15:5 16: Time, D6 Figure 14 Oblique N(x,t) for D6:D14 day C 14: 16: Examination of Figure 14 revealed that traffic was freely flowing throughout the D6 D14 region from 14: until approximately 14:2, when excess vehicle accumulations were seen between D13 and D14 as a result of the backward moving queue that emanated from bottleneck C1. By approximately 14:35 the tail of this queue had propagated as far as station D6 as evidenced by the separation of N(x,t) for each station pair. Then, starting at approximately 14:4, the queue between D13 and

53 43 D14 dissipated, followed closely by the dissipation of queuing between each progressive upstream station pair. At approximately 14:5 the queue between stations D8 and D9 dissipated. Meanwhile after 14:5, the excess vehicle accumulation persisted between D6 and D8. The presence of a queue between D7 and D8 after 14:5, combined with the presence of freely flowing traffic between D8 and D9 after 14:5 resulted in the diagnosis of bottleneck C3. Bottleneck C3 was activated between D7 and D8 at 14:5 and remained active until the reduced flow governed by downstream bottleneck C15 deactivated C3 at 15:18. Shortly before the C3 deactivation and downstream, between D9 and D1, bottleneck C15 was activated at 15:12 and remained active until the backward moving tail of the queue from downstream bottleneck C2 deactivated C15 at 15:32. The activation and deactivation times for bottlenecks C3 and C15 were verified with oblique V(x,t) curves shown in Appendix A and these bottlenecks are also mapped in time and space on Figure 7. This section has diagnosed two bottleneck activations that occurred in the early afternoon of Day C in the region between D6 and D14. The next section analyzes the four additional activations that occurred later on Day C in the same region Diagnoses of late afternoon bottleneck activations in D6 D14 This section uses methodology covered in Section 3 and the procedures outlined in Section to review the last four bottleneck activations diagnosed on Day C.

54 44 N(x,t)-q t' q =4,8 vph :42 D7 C7 D7/D8 16:57 D7 17:15 D7 C9 D7/D8 17:38 D7 17:31 D7 C16 D7/D8 17:49 D7 D16 D15 D14 D13 D12 D11 D1 D9 D8 D7 D6 1 18:4 D6 C17 D6/D7 18:35 D6 16: 16:1 16:2 16:3 16:4 16:5 17: 17:1 17:2 17:3 17:4 17:5 18: 18:1 18:2 18:3 18:4 18:5 19: Time, D6 Figure 15 Oblique N(x,t) for D6:D14 day C 16: 19: As shown in Figure 15, the activation of bottleneck C7 between D7 and D8 at approximately 16:42 is indicated by the near superimposition of curves for D8 and D9 after this time (indicating freely flowing traffic) and the continued excess accumulation between D7 and D8. Bottleneck C7 persisted until the backward moving tail of the queue from downstream bottleneck C6 deactivated C7 at 16:57. Following the passage of this queue, bottleneck C9 was activated between D7 and D8 at 17:15 and persisted until the backward moving queue that emanated from a downstream bottleneck deactivated C9 at 17:31. Following the passage of this queue, a bottleneck was again activated between D7 and D8 at 17:38 and labeled as bottleneck C16. Bottleneck C16 persisted for only a short time until the backward

55 45 moving queue emanating from downstream bottleneck C8 deactivated C16 at 17:49. Following the passage of this long downstream queue, bottleneck C17 became active immediately upstream between D6 and D7 located near the interchange of the Motorway A66 on-ramp and A5 North. Bottleneck C17 became active at 18:4 and lasted until a forward moving wave of lower flow deactivated the bottleneck at 18:35. Appendix A contains oblique V(x,t) curves that verify the activation and deactivation times for the four bottlenecks described in this section and these bottlenecks are also mapped in time and space on Figure 7. The previous sections (4.1.1 through 4.1.7) have cataloged the diagnoses of twenty bottleneck activations for Day C. In each case, the bottleneck s suspected location and timing, and the sustained presence of an upstream queue was first identified by examination of oblique N(x,t) curves. Then, these spatial and temporal findings were verified by the timing of notable speed drops and increases for bottleneck activations and deactivations, respectively. Figure 7 shows all twenty activations, mapped in both time and space. With the knowledge of the location and timing of each bottleneck, now it is possible to examine the discharge characteristics of these bottlenecks.

56 Bottleneck C1 discharge characteristics Figure 7 showed the spatio-temporal changes in speed on this 3-km section of freeway and provided a map of the twenty bottleneck activations diagnosed using data from Day C. Figures 8 15 have verified the bottleneck locations, the times at which they became active, and the times that they were deactivated. Now it is possible to examine the discharge characteristics of a single bottleneck activation, C1, in detail. The discharge characteristics of bottleneck C1, which occurred between D22 and D23, and the diagnosis of which was summarized in Section 4.1.1, are illustrated in Figure 16. The upper portion of the figure contains oblique N(x,t) and V(x,t) measured across all lanes at detector D23, the first detector downstream of the bottleneck, between 13:45 and 14:3. In the figure, periods of nearly constant flow and speed were delineated using short dashed lines where the average flows are in vehicles per hour (to the nearest 1 vph) and the average speeds are in kilometers per hour (km/h). These periods of nearly constant flow and speed were determined by visual inspection of the curves and the selection of piecewise linear segments. Since the curves do not display any abrupt reductions in the oblique N(x,t) accompanied by abrupt reductions in speed during the periods when the bottleneck is active, it is apparent that there was no disruption of active bottleneck discharge caused by a queue from anywhere further downstream.

57 47 1 N(D23,t)-q t' q =4,73 vph 519 N(D23,t) 9 1.8% : V(D23,t)-v t' v =4,8 km/h V(D23,t) D26 D25 D24 D23 D22 D21 D2 14:2 Bottleneck C1 D22/D : Left q =1,85 vph 16 2 N(D23,t)-q t' : : Mid q =1,7 vph :12 Right q =1,15 vph 13:45 13:5 13:55 14: 14:5 14:1 14:15 14:2 14:25 14:3 Time, D23 Figure 16 Oblique N(x,t) and V(x,t) for D23 day C Figure 16 shows that prior to the C1 bottleneck activation (at 14:2), a flow of 5,19 vph prevailed as measured across all three lanes. Initially upon queue discharge, a very low average discharge flow of 4,39 vph, a 15.4% drop, prevailed for 11 minutes before a flow recovery. Following this initial lower flow, the next 4 minute period was marked by a recovery flow of 5,26 vph. The intervals delineated by the

58 48 short dashed lines in Figure 16 exhibit only small deviations from piecewise linear flow. Thus, it seems reasonable to describe these flows as stable and nearly constant. Over the entire 15-minute bottleneck activation period, an average flow of 4,63 vph (shown by a long dashed line) prevailed, reflecting a 1.8% reduction in flow. By looking at the vertical scale on the left hand side of Figure 16, one can observe that while the bottleneck was active, the oblique N(x,t) curve never differed by more than 42 vehicles from the dashed line. This observation of a nearly constant discharge rate is important since it means that the bottleneck capacity does not vary with time. The lower portion of Figure 16 shows oblique N(x,t) for each lane and the lane specific q values are also shown. The figure shows that in the 2-minute period prior to activation that the flow dropped first in the right lane, followed by flow drops in the mid and left lanes. It can also be seen that the discharge flow recovery occurred first in the left lane, at 14:9, then the right lane at 14:12, and finally in the mid lane at 14:13. The average discharge flow was 1,84 vph in the left lane, 1,64 vph in the mid lane and 1,15 vph in the right lane. The flow drop upon queue discharge is consistent with some previous research (Bertini 1999, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b), as is the stability of the discharge flow itself. This section has described the discharge flow characteristics for a single bottleneck activation (C1) in detail. The next section will summarize discharge flow characteristics of several other bottlenecks that occurred in this region on Day C.

59 Summary of diverge bottleneck discharge characteristics As shown in Figure 2, the A5 interchange with motorway A455 lies immediately downstream of three relatively closely spaced detector stations; D22, D23 and D24. This D22 D24 section of freeway contains three traffic lanes and as shown on the profile portion of Figure 2, encompasses a vertical curve. The six bottlenecks that activated in this 1,3 m section on Day C appear to be closely related to the offramp at D25 and as such will be evaluated together. As described in Sections through 4.1.7, a total of six bottleneck activations were diagnosed on Day C between stations D22 and D24 including bottleneck C1, the discharge characteristics of which were examined in detail in Section As shown in Table 3, these six activations ranged from 7 minutes to 52 minutes in duration. Upon activation of the bottleneck, the discharge flow averaged 5,5 vph across all lanes with a standard deviation of 23 vph. The discharge flow in the left lane averaged 2,4 vph with a standard deviation of 11 vph, the mid lane flow averaged 1,76 vph with a standard deviation of 9 vph and the right lane flow averaged 1,25 vph with a standard deviation of 8 vph. The variance to mean ratios shown in Table 3 for the discharge flows reveal that the flow variability was approximately equal across all lanes. As shown in the table, both the pre-queue and discharge flow characteristics of the sole activation between D23 and D24 (C8) are very similar to the flow characteristics of the five activations

60 between D22 and D23. These similarities further support the decision to evaluate bottleneck activations in the region D22 D24 collectively. 5 Table 3 Diverge bottleneck D22:D24 summary day C Bottleneck No. Sta. Discharge Flow (vph) All Lanes Left Mid Rt. Time (min) Pre-queue flow (vph) All Lanes Left Mid Rt. C1 D22/D C2 D22/D C13 D22/D C14 D22/D C19 D22/D C8 D23/D Avg SD Var/Avg Four of these Day C diverge (D22 D24) bottleneck activations were preceded by freely flowing conditions that were not influenced by other traffic disturbances. These activations are referred to as isolated activations (Bertini & Cassidy 22) and the magnitude of pre-queue flows for these 4 activations are shown in Table 3 in italics. In the minutes leading up to the activation of these isolated bottlenecks, the flow averaged 5,21 vph across all lanes with a standard deviation of 12 vph. The prequeue flows in the left lane averaged 2,25 vph with a standard deviation of 15 vph, the mid lane averaged 1,84 vph with a standard deviation of 1 vph and the right lane averaged 1,11 vph with a standard deviation of 17 vph.

61 51 The variance to mean ratios for the pre-queue flows reveal that the variability of the flow in the right lane is higher than both the mid and left lanes. This increased variability may be the result of varying truck flow in the right lanes which is the subject of further investigation later in this study. The overall average flow decrease for these four isolated activations was from 5,21 vph to 5,5 vph in all lanes, or approximately 3%. The average flow decrease in the left lane was 2,25 vph to 2,4 vph or approximately 9%. The average flow decrease in the mid lane was 1,84 vph to 1,76 vph or approximately 4%. Interestingly the average flow in the right lane actually increased upon bottleneck activation, from 1,11 vph to 1,25 vph, a gain of almost 13%. This section has described the discharge characteristics of the six Day C diverge bottleneck activations in the D22 D24 region, the next section will involve an assessment of all Day C bottleneck activations Summary of bottleneck discharge characteristics Sections detailed the diagnoses of twenty bottleneck activations for Day C. Figure 7 mapped these activations in time and space. Now, Table 4 summarizes the discharge characteristics of these twenty activations. These bottlenecks occurred at a variety of freeway geometric inhomogeneities including diverge areas, merge areas and uphill vertical gradients.

62 52 Now that discharge characteristics of all twenty Day C bottleneck activations have been reviewed, attention can now be focused on the possible causes of these activations. Table 4 Bottleneck summary day C Bottleneck No. Location Condition Time start Time end Time (min) Discharge Flow (vph) All Lanes Left Mid Right C1 D22/D23 diverge 14:2 14: C2 D22/D23 diverge 14:4 14: C3 D7/D8 merge 14:5 15: C4 D18/D19 merge 15:32 15: C5 D19/D2 uphill 1.32% 15:51 16: C6 D17/D18 merge 16:8 17: C7 D7/D8 merge 16:42 16: C8 D23/D24 diverge 16:58 17: C9 D7/D8 merge 17:15 17: C1 D18/D19 merge 18: 19: C11 D28/D29 incident 14:48 15: C12 D18/D19 merge 13:33 14: C13 D22/D23 diverge 12:53 13: C14 D22/D23 diverge 13:21 13: C15 D9/D1 uphill 1.3% 15:12 15: C16 D7/D8 merge 17:38 17: C17 D6/D7 merge 18:4 18: C18 D19/D2 uphill 1.32% 13:22 13: C19 D22/D23 diverge 18:33 18: C2 D2/D21 merge 19:17 19: Bottleneck C1 activation triggers Based on this dissertation s a posteriori analysis of archived loop detector data, the causes of these bottleneck activations may not be known definitively, but a study of speed, flow, traffic composition and lane positioning has revealed possible signals of

63 53 bottleneck activation. Bottleneck C1, for example, was located between D22 and D23, approximately 1, m upstream from a major off-ramp (D25) near the crest of a vertical curve with an incoming grade of approximately 3.2%. This section discusses some of the possible triggers for the activation of bottleneck C1. Oblique lane-by-lane N(x,t) (upper) and V(x,t) (lower) were constructed for D22 for the time period surrounding the C1 activation using methods described earlier. The linear approximations of prevailing lane flows and velocities are labeled in vph and km/h respectively. These curves, presented in Figure 17, used different values of q and v noted on the figure. A lane-by-lane analysis of vehicle counts at D22, shown in the upper portion of Figure 17 revealed that flow surges in all three lanes immediately preceded the activation. During this two minute time period, the right lane flow was measured as 1,23 vph, the mid lane flow was 2,23 vph and the left lane flow was measured to be 2,43 vph. Thus the total flow for this short period was 5,89 vph. This flow does not represent the highest two minute average flow at this station, a two-minute average flow of 6,36 vph was seen later this day following the deactivation of the C2 bottleneck. However, there were very few flows of over 6, vph at D22 on this day, so the 5,89 vph seen just prior to the C1 activation is notable and when combined with other potential triggers may well have influenced its formation.

64 : Left q =1,8 vph N(D22,t)-q t' ,89 vph Mid q =1,8 vph 94 2 D26 D25 D24 D23 D22 D21 D :2 18 Bottleneck C1 D22/D23 14:17 9 Right q =1,6 vph V(D22,t)-v t' Left v =5,7 km/h 2 Mid v =5,19 km/h 2 Right v =4,46 km/h 2 13:15 13:3 13:45 14: 14:15 14:3 Time, D22 Figure 17 Oblique N(x,t) and V(x,t) for D22 day C Inspection of the lower portion of Figure 17 shows that in the period before the 14:2 C1 activation, the average lane speeds were 81 km/h, 94 km/h, and 12 km/h in the right, mid, and left lanes respectively. That the speeds begin to decrease in all lanes just as this local maximum two-minute average flow (5,89 vph) occurs is further indication that the high flows were associated with the collapse of flow.

65 55 The data set used in this study, as described in Section 2, is unique in the fact that it provided speed and flow data for each lane according to two vehicle types, autos and trucks. Up to this point, all oblique V(x,t) evaluations (such as those in the lower portion of Figure 17) have included both vehicle types. However, the ability to track flow and velocity changes discretely by vehicle type would undoubtedly aid in the evaluation of potential bottleneck activation. Capitalizing on the data set s vehicle-specific data, and because trucks have vastly different performance characteristics than cars, a detailed analysis of truck flow and velocity patterns was conducted just upstream of the C1 bottleneck activation. Also noteworthy is the fact that German traffic laws require trucks to remain in the right lane except for passing. Figure 18 shows oblique Truck N(x,t) (upper) and Truck V(x,t) (lower) for each lane at station D22. The oblique Truck N(x,t) are annotated with linear approximations, which are labeled to the nearest 1 trucks/h. The upper curves of Figure 18 revealed that trucks indeed remained in the right lane during periods of uncongested flow. Notice that in surges lasting a few minutes and prior to C1 activation, a 144% truck flow increase was observed in the right lane while increases of 35% and 15% were seen in the mid and left lanes respectively. During these two-minute surges in truck flow, there were 3 trucks counted in the right lane, 6 trucks in the mid lane and 5 trucks in the left lane.

66 Left q =45 trucks/h Truck N(D22,t)-q t' % (5 trucks in 2 min.) % 18 (6 trucks in 2 min.) % 88 (3 trucks in 2 min.) 14:2 9 14:9 14:8 Bottleneck C1 D22/D23 14: D26 D25 D24 D23 D22 D21 D2 Mid q =8 trucks/h Right q =48 trucks/h Truck V(D22,t)-v t' Left v =5,37 km/h 2 Mid v =5,2 km/h 2 Right v =4,2 km/h 2 13:15 13:3 13:45 14: 14:15 14:3 Time, D22 Figure 18 Oblique N(x,t) and V(x,t) trucks at D22 day C The lower portion of Figure 18 contains oblique Truck V(x,t) for each lane at D22. Notable drops in truck velocity were seen in all three lanes around the time of activation of bottleneck C1 at 14:2. At C1 activation, the right lane truck speeds dropped from 78 to 7 then to 46 km/h, the mid lane from 96 to 75 then to 54 km/h, and the left lane from 15 to 9 then to 52 km/h. This may indicate that the C1

67 57 bottleneck and associated long shock were triggered in part by a surge in truck flows in the mid and left lanes creating a blockage for car drivers who would have preferred to travel at higher speeds in these lanes. Owing to the presence of a major interchange approximately 1, m downstream of the location of the C1 bottleneck, the search for possible activation triggers must include evaluation of traffic characteristics at the D25 off-ramp. The upper portion of Figure 19 contains oblique N(x,t) for the off-ramp near D25, where linear approximations to the N(x,t) are labeled to the nearest 1 vph. The C1 bottleneck activation at 14:2 was preceded by a 76% surge in off-ramp flow, which was measured as 9 vph for 6 minutes before activation, after a lower flow of 51 vph was measured over the previous 4 minutes. As illustrated in Figure 17 the C1 activation also coincided with a period of high flow in the right lane at D22 (the upstream station of the bottleneck). Because of the German trucks to the right law, a proper accounting for trucks in the right lane must be accomplished in order to understand the right lane flows. As shown in the lower portion of Figure 19, the C1 activation was preceded by a D22 right lane flow of over 1,2 vph, 9 of which are trucks. This 9 trucks/hr flow represents a tripling of the truck flow measured in the previous 1 minute increment.

68 58 2 D22 Right Lane Flow (vph) Cars Trucks D26 D25 D24 D23 D22 D21 D % 9 (9 veh in 6 min.) C1 Activation 46 1 N(D25 off,t)-q t' q =7 vph :5 13:52 13:54 13:56 13:58 14: 14:2 14:4 14:6 14:8 Figure 19 Oblique N(x,t) for D25 off-ramp and right lane flow for D22 day C Section 4.1 has provided exhaustive diagnoses of all twenty bottleneck activations on Day C. The discharge characteristics of each bottleneck were examined and the potential triggers of a diverge bottleneck were explored. The next section reports on the results of similar analyses conducted on a different day for the same 3-km section of the A Day G Using the methods described in Section 3, and following the same investigative pattern as Section 4.1, this section reviews the diagnoses of the activation of fifteen bottlenecks along the A5 on September 19, 21 (referred to as Day G). These

69 bottleneck activations (labeled G1 through G15) are mapped in time and space on Figure D3 D D D D26 4 D25 65 D24 65 D23 D22 11 D21 13 D2 125 D D D D16 1 D15 5 D14 7 D13 D12 12 D D1 9 D9 D D7 D D5 D4 11 D D2 D1 [m] [Sta] A455 Friedberg A661 Bad Homburger Kreuz A66 Nordwest Kreuz Frankfurt am Main A648 West Kreuz Frankfurt am Main 15:21 15:35 15:47 G1 G2 15:35 15:51 15:58 15:47 15:58 15:55 16:3 G12 G7 G14 G3 16:3 16:34 G15 16:48 16:59 16:4 16:47 G4 16:4 16:47 16:49 17: G8 G1 G13 17:7 17:13 17:32 17:29 G9 17:46 17:42 G5 G :5 18:7 18:12 G11 2:2 Speed [km/h] Elevation [m] Profile 14 9 Figure 2 Autobahn A5 north speed diagram day G This speed contour map, Figure 2, was constructed using the same procedure as that discussed for Figure 7 in Section 4.1. In examining Figure 2, it is clear that a large number of speed disturbances occurred on this day starting shortly after 15: and continuing until nearly 21: Diagnoses of mid afternoon bottleneck activations To demonstrate the diagnoses of two bottleneck activations, including their locations and the times they remained active on Day G, analyses similar to those described in

70 Section were conducted. Figure 21 shows oblique N(x,t) for detectors D15 D24 from 15:4 until 16: D26 D25 D24 D23 D22 D21 D2 D19 D18 D17 D16 D15 Figure 21 Oblique N(x,t) for D15:D24 day G 15:4 16:1 All ten curves in Figure 21 remained superimposed until approximately 15:5, indicating that traffic flowed freely between all stations. At approximately 15:51, Figure 21 shows that excess accumulation arose between stations D17 and D18 as indicated by the divergence of the oblique N(x,t). A subsequent divergence of curve D17 from curve D16 (and flow reduction measured at D17) marked the passage of the

71 backward-moving queue at D17. This activation was labeled as bottleneck G7 and was active until 15: Note that all oblique N(x,t) downstream of D17 remained superimposed until approximately 15:55, when excess accumulation arose between D2 and D21. A short time later, there was a deviation of curve D2 from curve D19 (and a visible flow reduction measured at D2), mapping the queue passage time at D2. Thus, bottleneck G12 was briefly activated between D2 and D21 until 16:3 at which time bottleneck G12 was deactivated. Shortly after the G12 activation, excess vehicle accumulation was visible between D22 and D23 as shown in Figure 21. For the remainder of the period shown in the figure, curves for D23 and D24 remained superimposed, indicating that freely-flowing traffic prevailed in this section. Shortly after 15:58, upstream accumulations (and accompanying flow reductions at D22 and D21) were visible, marking the activation of bottleneck G14 between D22 and D23. These activations are also labeled on Figure 21. Figure 21 has shown that bottleneck G7 was activated between D17 and D18 from 15:51 15:58 and that bottleneck G12 was activated between D2 and D21 from 15:55 16:3. The activation of bottleneck G14, located between D22 and D23, occurred at 15:58 and continued to be active for the time period shown on Figure 21. A subsequent figure (Figure 23) will cover this section of freeway over a longer time period and will show the deactivation of bottleneck G14. Now that the activation

72 times have been established using oblique N(x,t), attention can be turned to key changes in speed that coincided with these activations. 62 V(D24,t)-v t' v =5,978 km/h :57 92 V(D24,t)-v t' v =5, 4 km/h :34 16:36 86 V(D24,t)-v t' v =5,8 km/h : : :33 15:38 15:43 15:48 15:53 15:58 16:3 Time, D24 16:15 16:2 16:25 16:3 16:35 16:4 16:45 Time, D24 16:45 16:5 16:55 17: 17:5 17:1 17:15 Time, D24 V(D23,t)-v t' v =5,15 km/h : :51 15:54 15:57 16: 16:3 Time, D23 V(D23,t)-v t' v =4,533 km/h :31 16:35 16:15 16:2 16:25 16:3 16:35 16:4 16:45 Time, D23 V(D23,t)-v t' v =5,144 km/h : :8 16:45 16:5 16:55 17: 17:5 17:1 17:15 Time, D23 V(D22,t)-v t' v =5,79 km/h :56 87 V(D22,t)-v t' v =4,115 km/h : : V(D22,t)-v t' v =5,417 km/h :49 17: :41 15:44 15:47 15:5 15:53 15:56 15:59 16:2 Time, D22 16:1 16:15 16:2 16:25 16:3 16:35 16:4 Time, D22 16:45 16:5 16:55 17: 17:5 17:1 17:15 Time, D22 Figure 22 Oblique V(x,t) for D22:D24 day G Figure 22 shows a set of three oblique V(x,t) for D22, D23 and D24, using different values of v (labeled on the y-axes of the individual graphs). The oblique V(x,t) in the first column correspond to the time that bottleneck G14 became active. While speeds at D23 and D24 remained relatively high, minor speed reductions associated with the activation of bottleneck G14 are shown in the first column of curves and correspond closely to the 15:58 activation time described earlier in this section. The speeds at D22, the station immediately upstream of the bottleneck, decreased from 1 km/h to

73 63 87 km/h at 15:56, which is very near the 15:58 activation time determined from oblique N(x,t) analyses. Furthermore, it can be seen that the speed reduction occurred at progressively later times at D23 and D24 which is consistent with a forwardmoving wave that traveled downstream from the D22 D23 bottleneck location. This section has described the locations as well as activation times for three bottlenecks seen on the afternoon of Day G and ensured the presence of upstream queues. The diagnostic tools used were oblique N(x,t) curves for initial determination of bottleneck position and timing, then oblique V(x,t) curves were used to verify these spatio-temporal characteristics. The following sections will summarize the diagnoses of additional bottlenecks for this day Diagnoses of late afternoon bottleneck activations To examine the flow features of bottleneck G14 through its entire active period employing the methodology described in Section 3 and detailed procedures outlined in Section 4.1.1, Figure 23 was constructed using the oblique N(x,t) from detectors D15 D24 from 15:4 until 18:1. Knowing that G14 was activated at 15:58, Figure 23 shows that it was deactivated at 16:3 when excess accumulation between D22 and D23 was no longer present. This deactivation time can be verified by the oblique V(x,t) shown in the second column of Figure 22. A speed increase visible (from 77 km/h to 95 km/h) at approximately 16:3 at D22, indicated the reestablishment of freely flowing conditions between D22 and D23. Prior to this time, the recorded

74 speeds were km/h, noticeably slower than the speeds measured at D23 and D The freely flowing traffic between D22 and D23 after 16:3 was short-lived and a bottleneck was again activated between D22 and D23 at 16:34 (G15). As shown in Figure 23, the oblique N(x,t) for D23 and D24 remained superimposed indicating freely flowing traffic whereas there was notable excess accumulation between the curves at D22 and D23 beginning at about 16:34. This indicated that G15 was activated at 16:34 and remained active until 16:49 when excess upstream accumulation dissipated. The G15 activation and deactivation times can also be 1 N(x,t) - q t ' q = 4,89 vph 15:51D17 15:58 D22 15:58 D17 G7 G12 D2 D21 15:55 D2 16:3 D2 D17 D18 16:5 D19 16:8 D18 16:14 D17 G14 D22 D23 16:22 D16 16:3 D2 16:28 D21 16:3 D22 16:34 D19 16:37 D18 16:4 D17 16:34 D22 16:45 D15 16:42 D16 G15 D22 D23 16:49 D22 16:48 D17 G8 17 D17 D18 17: D2 16:59 D17 G13 D2 D21 17:32 D2 17:29 D G9 D17 D18 17:46 D17 17:42 D15 D26 D25 D24 D23 D22 D21 D2 D19 D18 D17 D16 D15 D14 G6 D15 D16 18:7 D15 Time, D15 Figure 23 Oblique N(x,t) for D15:D24 day G 15:4 18:1

75 65 confirmed by examination of the second and third columns of Figure 22. The D22 curves clearly show that the speed decreased at 16:34 (95 km/h to 7 km/h) and that the speed increased at 16:49 (72 km/h to 96 km/h). Figure 23 also shows that by approximately 16:, the queues that propagated upstream from bottlenecks G12 and G14 merged and propagated further upstream. The upstream progress of this queue can be mapped on Figure 23 as it passed stations D19, D18, D17 and D16 (see vertical arrows). In addition, Figure 23 summarizes the diagnoses of all eight bottleneck activations during this time period. As shown by the excess accumulation arising between D17 and D18 at about 16:48, a bottleneck between D17 and D18 was activated as bottleneck G8 until 16:59. These and other activations and deactivations were verified by oblique V(x,t) (not shown). Since excess accumulation was visible between D2 and D21 at 17:, bottleneck G13 was activated between D2 and D21 and remained active until the reduced flow governed by an upstream bottleneck (G9) deactivated G13 at 17:32. Bottleneck G9 became active between D17 and D18 at 17:29, marking the third activation at this location on this day. G9 remained active until the reduced flow from an upstream bottleneck (G6) deactivated G9 at 17:46. Bottleneck G6 was activated at 17:42 between D15 and D16 near where merging traffic from Motorway A661 entered the A5 at an on-ramp downstream of D15. Bottleneck G6 remained active between 17:42 and 18:7.

76 66 This section has presented the diagnoses of eight bottlenecks from the afternoon hours of Day G. The next section continues this evaluation for the remainder of Day G for the D15 D24 section of the A Diagnoses of evening bottleneck activations Using the methodology described in Section 3 and detailed procedures outlined in Section this section continues the examination of Day G bottleneck features through the remainder of the evening peak period. Figure 24 contains a set of N(x,t) for stations D15 D24 between 18: and 21: for Day G. The figure shows the final and longest lasting bottleneck activation (128 minutes) seen on this day (G11). Excess accumulation between stations D17 and D18 was visible beginning at 18:12, and the queue s propagation past D18 is indicated by the excess accumulation between stations D16 and D17 and the flow reduction measured at D17 at 18:17. G11 persisted until a forward moving wave of lower flow deactivated the bottleneck at 2:2. Figure 24 shows that oblique N(x,t) for D15 D24 are all nearly superimposed after 2:2 indicating that traffic was freely flowing throughout the region until 21: and, although not shown on the figure, this continued to be the case for the rest of the evening.

77 67 Figures 21 through 24 have described the activation and deactivation of nine Day G bottlenecks over a 9.3 km segment of the A5 North between the interchanges with Motorways A661 and A N(x,t) - q t ' q =4,25 vph D26 D25 D24 D23 D22 D21 D2 D19 D18 D17 D16 D15 D14 18:12 D19 18:17 D17 18:14 D G11 D19 D :2 D15 2:5 D16 2:17 D18 2:8 D17 2:2 D19 Time, D15 Figure 24 Oblique N(x,t) for D15:D24 day G 18: 21: Six additional bottleneck activations were diagnosed in the far upstream sections of the A5 study site. These activations will be discussed in the following sections Diagnoses of bottleneck activations in D6 D14 Figure 2 showed that six additional bottleneck activations occurred in the segment between station D6 and D14 on Day G. This section of the dissertation executes the

78 methodology described in Section 3 and detailed procedures outlined in Section to characterize these six activations. 68 Figure 25 shows the details of these six activations and includes oblique N(x,t) for detectors D6 D14 between 15: and 18:1 (counts from the D6 on-ramp are included in the D6 curve to ensure vehicle conservation). Excess vehicle accumulation was visible between D7 and D8 beginning just before 15:21, indicating that G1 was activated between D7 and D8 at 15:21. G1 remained active until the reduced flow from upstream bottleneck G2 deactivated G1 at 15:35. Shortly before and just upstream, between D6 and D7, bottleneck G2 was activated at 15:35 and remained active until the backward moving queue that emanated from the downstream bottleneck G3 deactivated G2 at 15:47. The activation of bottleneck G3 was indicated by the excess accumulation between D7 and D8 that began just before 15:47. Bottleneck G3 persisted until the reduced flow from an upstream bottleneck deactivated G3 at about 16:4. Bottleneck G4, located near the off-ramp between D5 and D6 was activated briefly from 16:4 16:47. Bottleneck G1, activated between D7 and D8, represents the third activation in this location on this day. G1 became active at 16:47 and persisted until the tail of a long downstream queue deactivated G1 at 17:7.

79 69 q =4,89 vph ' N(x,t) - q t D16 D15 D14 D13 D12 D11 D1 D9 D8 D7 D6 16:46 D14 16:49 D13 16:51 D12 16:55 D11 17:1 D1 17:5 D9 17:8 D8 17:12 D7 17:15 D :5 D8 1 15:21 D7 G1 15:35 D6 15:47 D7 G2 G3 16:4 D7 16:47 D6 G4 G1 17:7 D7 17:13 D8 D7 D8 D6 D7 D7 D8 D5 D6 D7 D8 D8 D9 G5 Time, D6 Figure 25 Oblique N(x,t) for D6:D14 day G 15: 18:1 Following the dissipation of this long downstream queue, bottleneck G5 became active immediately downstream between D8 and D9. Bottleneck G5 became active at 17:13 and persisted until the backward moving queue that emanated from the downstream bottleneck G6 deactivated G5 at 18:5. Consistent with what was described above, Figures 23 and 25 show the propagation of a shock of lower flow that emanated from between D21 and D22 at approximately 16:28. The shock s passage can be traced upstream (see circular markers on Figures 23 and 25) as far as D6 more than 45 minutes later. This shock traveled approximately 16 kilometers in just under 47 minutes for an average shock speed equal to -2.6 km/h. The slope of the dashed lines connecting the circular markers on

80 7 Figures 23 and 25 represent the shock s velocity and it can be seen that slope varies only slightly between each station pair. It therefore seems reasonable to describe the shock s speed as stable. The backward recovery wave, which was also traced in Figures 23 and 25 (square markers), reached D6 by approximately 17:21. Figure 2 showed the spatio-temporal changes in speed on this 3-km section of freeway and provided a map of the fifteen bottleneck activations diagnosed using data from Day G. Figures have verified the bottleneck locations, the times at which they became active, and the times that they were deactivated. Now it is possible to examine the discharge characteristics of two bottleneck activations (G14 and G15) in detail Diverge bottleneck discharge characteristics The discharge characteristics of bottlenecks G14 and G15, both of which occurred between D22 and D23 are illustrated in Figure 26. The figure, which was constructed using the techniques introduced in Section 4.1.8, contains oblique N(x,t) and V(x,t) measured across all lanes at detector D23, the first detector downstream of the bottleneck, between 15:3 and 17:. Since the curves do not display any abrupt reductions in the oblique N(x,t) accompanied by abrupt reductions in speed during the periods when the bottleneck was active, it is apparent that there was no disruption of active bottleneck discharge caused by a queue from anywhere further downstream.

81 71 1 N(D23,t)-q t' N(D23,t)-q t' q =4,9 vph 5 N(D23,t) 93 D26 D25 D24 D23 D22 D21 D2 V(D23,t) % 15: : Bottleneck G14 D22/D23 16:7 16:13 16:16 16: :26 16:34 16:3 Bottleneck G15 D22/D : V(D23,t)-v t' v =4,6 km/h 2 1 Left q =2,1 vph Mid q =1,835 vph Right q =1,29 vph 15:3 15:4 15:5 16: 16:1 16:2 16:3 16:4 16:5 17: Time, D23 Figure 26 Oblique N(x,t) and V(x,t) for D23 day G Examination of the upper portion of Figure 26 shows that prior to the 15:58 activation of bottleneck G14, a flow of 5,76 vph prevailed as measured across all three lanes. Initially upon queue discharge, a somewhat lower average discharge flow of 5,6 vph, a 12.1% drop, prevailed for several minutes before a flow recovery. The intervals delineated by the short dashed lines in Figure 26 exhibit only small

82 72 deviations from piecewise linear flow. Over the entire 32-minute bottleneck activation period, an average flow of 5,32 vph prevailed, which represents a 7.6% reduction in flow. By looking at the vertical scale on the left hand side of Figure 26, one can observe that while the bottleneck was active, the oblique N(x,t) curve never differed by more than 4 vehicles from the dashed line. Thus, it seems reasonable to describe these flows as stable and nearly constant. The lower portion of Figure 26 shows oblique N(x,t) for each lane and reveals the average discharge flow was 2,12 vph in the left lane, 1,93 vph in the mid lane and 1,27 vph in the right lane. The flow drop upon queue discharge is consistent with some previous research (Bertini 1999, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b), as is the stability of the discharge flow itself. Figure 26 further shows that upon queue discharge of the G15 bottleneck activation, a flow of 5,26 vph prevailed, comprised of 2,7 vph in the left lane, 1,83 vph in the mid lane, and 1,36 vph in the right lane. A summary of the discharge characteristics of all Day G activations (and all other study days) can be found in Appendix E. Sections through have defined the spatio-temporal boundaries of the fifteen Day G bottleneck activations and the discharge characteristics of the G15 activation. Attention may now be focused on the possible causes of these activations.

83 Diverge bottleneck activation triggers Applying the procedures detailed in Section , a study of speed, flow, traffic composition and lane positioning have revealed possible signals of bottleneck activations on Day G. Bottleneck G14, for example, was located between D22 and D23, approximately 1, m upstream from a major off-ramp near the crest of a vertical curve with an incoming grade of approximately 3.2%. Figure 27 contains oblique lane-by-lane N(x,t) (upper) and V(x,t) (lower) for D22 for the time period surrounding the G14 activation using methodologies described earlier. A lane-by-lane analyses of vehicle counts at D22, shown in the upper portion of Figure 27 reveals that in the two-minute period before G14 activation, the right lane flow was 1,18 vph, the mid lane flow was 2,4 vph and the left lane flow was measured to be 2,76 vph. Thus the total flow for this short period was 6,34 vph. This flow represents the highest two minute average flow measured at this station on Day G, and one of only four daily values to exceed 6, vph. Thus, the daily maximum two-minute average flow of 6,34 vph is notable and when combined with other potential triggers may have influenced the activation of bottleneck G14. The lower portion of Figure 27 shows that during this brief period of high flow preceding the G14 activation, the average lane speeds dropped from 18 km/h to 86

84 km/h in the left lane, from 98 km/h to 82 km/h in the mid lane, and from 83 km/h to 74 km/h in the right lane Left q =1,8 vph N(D22,t)-q t' V(D22,t)-v t' ,34 vph : :4 16:4 16: Bottleneck G14 D22/D : D26 D25 D24 D23 D22 D21 D : Mid q =1,8 vph Right q =1,6 vph Left v =4,81 km/h 2 Mid v =4,48 km/h 2 Right v =4, km/h 2 16:27 15:45 15:5 15:55 16: 16:5 16:1 16:15 16:2 16:25 16:3 16:35 16:4 16:45 Time, D22 Figure 27 Oblique N(x,t) and V(x,t) for D22 day G That the speeds began to decrease in the mid and left lanes just as this daily maximum two-minute average flow (6,34 vph) occurred is further indication that the high flow

85 was associated with the collapse of flow, that is, that it was a trigger for bottleneck activation. 75 Using separate truck count and speed data, Figure 28 shows oblique Truck N(x,t) (upper) and Truck V(x,t) (lower) for each lane at station D22. Notice that several minutes prior to the 15:58 activation G14, the truck flow in the left lane surged to 15 trucks per hour. Then, coinciding with activation, a 52% truck flow increase was observed in the right lane, followed closely by movement of trucks to the middle lane where a 17% increase in truck flow was observed. The lower portion of Figure 28 contains Truck V(x,t) for each lane at D22. Notable drops in truck velocity were seen in all three lanes around the time of activation of bottleneck G14 at 15:58. The right lane truck speeds dropped from 79 to 68 km/h, the mid lane from 93 to 82 km/h, and the left lane from 18 to 9 km/h. This may indicate that the bottleneck and associated very long shock were triggered by a surge in truck flows in the middle and left lanes creating a blockage for car drivers who would have preferred to travel at higher speeds in these lanes. To further understand how flows at D22, upstream of the bottleneck activation and also at the D25 off-ramp, downstream of the activation, influenced the formation of the bottleneck, detailed analyses of these flows were conducted.

86 Left q =3 trucks/h Trucks N(D22,t)-q t Trucks V(D22,t)-v t (5 trucks in 2 min.) % (2 trucks in 6 min.) 52% 93 (3 trucks in 2 min.) 15:58 Bottleneck G14 D22/D :4 16:4 16:3 16:6 16:1 16: :24 16: :3 D26 D25 D24 D23 D22 D21 D Mid q =8 trucks/h Right q =4 trucks/h Left v =5,61 km/h 2 Mid v =5,8 km/h 2 Right v =4,36 km/h 2 15: 15:1 15:2 15:3 15:4 15:5 16: 16:1 16:2 16:3 16:4 16:5 17: Time, D22 Figure 28 Oblique N(x,t) and V(x,t) trucks at D22 day G Figure 29 contains oblique N(x,t) for the off-ramp near D25, where linear approximations to the N(x,t) are labeled to the nearest 1 vph. The G14 activation at 15:58 was accompanied by a 66% surge in off-ramp flow, which was measured as

87 1,36 vph for the 2 minutes following activation, after a lower flow of 82 vph was measured during the previous 5 minutes. 77 The G14 activation also coincided with a period of high flow at D22 that was marked by substantial truck flows. As shown in the lower portion of Figure 29, the G14 activation was preceded by a notable increase in truck flow in the right lane at D22. Furthermore the truck flow measured at 15:57 was one of the highest truck flow values recorded at any time on the study day. 28 D22 Right Lane Flow (vph) D26 D25 D24 D23 D22 D21 D G14 Activation 66% 136 (45 veh in 2 min.) 72 2 N(D25 off,t)-q t', q =87 vph Cars Trucks :3 15:35 15:4 15:45 15:5 15:55 16: 16:5 16:1 16:15 16:2 16:25 16:3 Time, Figure 29 Oblique N(x,t) for D25 off-ramp and right lane flows for D22 day G

88 78 Section 4.2 has provided complete diagnoses of all fifteen bottleneck activations on Day G. The discharge characteristics and the potential activation triggers of diverge bottleneck G14 were examined. Along with Section 4.1, these two sections have explored many bottlenecks associated with a variety of freeway physical inhomogeneities such as off-ramps and on-ramps. Of note is that several Day C and Day G diverge bottlenecks were found to have been isolated, that is, preceded by freely flowing traffic as described in However, none of the diverge bottleneck deactivations on Days C and G were isolated deactivations, that is, deactivations that originated at or near the activation location. Similarly, all the merge bottleneck deactivations on Days C and G were non-isolated, the result of either reduced flow from upstream or the result of a backward moving queue that emanated from a downstream bottleneck. Therefore, the next section explores the traffic characteristics associated with an isolated diverge bottleneck deactivation found on a different day. 4.3 Day B: Isolated diverge bottleneck deactivation This section describes the diagnosis of an isolated diverge bottleneck (bottleneck B7) that occurred along the A5 on Day B. This bottleneck, as well as the seven other bottleneck activations diagnosed on this day (labeled B1 through B8) are mapped in time and space on Figure 3.

89 79 Figure 3, a speed contour map for Day B, was constructed using the same procedure presented in Section 4.1 for Figure 7. In examining Figure 3, it is clear that a number of speed disturbances occurred on this day starting shortly after 12: and they continued until nearly 21:. Bottleneck B7, located between D23 and D24 is of particular interest since its deactivation appears to originate near the location of the bottleneck. 2 D3 D D D D26 4 D25 65 D24 65 D23 D22 11 D21 13 D2 125 D D D D16 1 D15 5 D14 7 D13 D12 12 D D1 9 D9 D D7 D D5 D4 11 D D2 D1 [m] [Sta] A455 Friedberg A661 Bad Homburger Kreuz A66 Nordwest Kreuz Frankfurt am Main A648 West Kreuz Frankfurt am Main 12:36 13:4 B1 B2 13:32 13:49 14: B3 14:49 15: B4 15:42 16:16 16: B6 B5 17: 16:48 16:53 B7 17:36 18:15 B8 2:14 Speed [km/h] Elevation [m] Profile 14 9 Figure 3 Autobahn A5 north speed diagram day B

90 Bottleneck B7 diagnosis Using the diagnostic techniques described in Section 3 and the detailed procedures followed in Section 4.1.1, it was determined that bottleneck B7 was activated between stations D23 and D24 at 17: and remained active until 17:36. This location was less than 1, m upstream of the detector D25 (Motorway A455) off-ramp. Employing the procedures used in Section 4.1.8, the detailed discharge characteristics of bottleneck B7 were determined. Upon the activation of bottleneck B7, the average discharge flow was 4,63 vph measured across all lanes, with 1,97 vph in the left lane, 1,65 vph in the mid lane, and 1,1 vph in the right lane. Bottleneck B7 was preceded by freely flowing traffic, making it an isolated activation, with 13 minutes of pre-queue flows measured at 2,23 vph in the left lane, 1,7 vph in the mid lane, and 1,31 vph in the right lane for a total of 5,24 vph across all lanes. This represented a flow drop of 11.6% across all lanes. The deactivation of bottleneck B7 differs from the diverge bottleneck deactivations seen on Days C and G (as described in Sections 4.1 and 4.2) in that the deactivation does not appear to have been caused by spillback of a queue from a downstream bottleneck nor by a reduction in flow caused by an upstream disturbance. The deactivation appears to have been triggered by changes in traffic characteristics in the immediate vicinity of the off-ramp, thereby making its deactivation isolated. The next section will explore possible triggers to this diverge bottleneck deactivation.

91 Bottleneck B7 deactivation triggers Figure 31 contains oblique N(x,t), constructed as described in previous sections, for traffic flows at D25, the station containing an off-ramp for Motorway A455. The figure contains oblique N(x,t) for the off-ramp (upper) and oblique Truck N(x,t) for the right lane (lower) at D25, where linear approximations to the N(x,t) are labeled in vph and trucks/h respectively. 31% 2 52 vph 75 vph 52 vph Off-Ramp q =59 vph N(D25,t)-q t' 44 trucks/h 3% B7 Deactivation D26 D25 D24 D23 D22 D21 D2 31 trucks/h Right q =35 trucks/h 2 17: 17:1 17:2 17:3 17:4 17:5 18: Time, D25 Figure 31 Oblique N(x,t) for D25 off-ramp and trucks right lane day B The lower portion of Figure 31 shows that the bottleneck B7 deactivation at 17:36 was preceded immediately by a 3% drop in truck flow in the right lane at D25, which was measured at 44 trucks/h for 18 minutes prior to deactivation, followed by a 16 minute average flow of 31 trucks/h. The upper portion of Figure 31 shows that

92 82 the bottleneck deactivation also coincided with a 31% drop in flow at the D25 offramp where the flow dropped from 75 vph to 52 vph. This may indicate that the deactivation of the B7 bottleneck was triggered by a drop in off-ramp flow and a drop in the truck flow in the right lane immediately upstream of the diverge area. This section has provided the diagnosis of a diverge bottleneck (B7) that possessed both an isolated activation and an isolated deactivation. The discharge characteristics and the potential deactivations triggers of diverge bottleneck B7 were examined. Sections have explored many bottleneck activations associated with diverges near off-ramps and merges near on-ramps. Of note is that none of the merge bottleneck activations diagnosed on Days B, C or G were found to have been isolated, that is, preceded by freely flowing traffic. Further investigation was conducted and the next section explores the traffic characteristics associated with an isolated merge bottleneck activation.

93 Day E: Isolated merge bottleneck activation This section describes the diagnosis of an isolated merge bottleneck activation (bottleneck E2) that occurred along the A5 on Day E. This bottleneck, as well as the nine other bottleneck activations diagnosed on this day (labeled E1 through E1) are mapped in time and space on Figure D3 D D D D26 4 D25 65 D24 65 D23 D22 11 D21 13 D2 125 D D D D16 1 D15 5 D14 7 D13 D12 12 D D1 9 D9 D D7 D D5 D4 11 D D2 D1 [m] [Sta] A455 Friedberg A661 Bad Homburger Kreuz A66 Nordwest Kreuz Frankfurt am Main A648 West Kreuz Frankfurt am Main Speed [km/h] 14:55 15:8 E1 E2 15:57 16:3 16:4 E3 16:34 16:34 E4 17:15 17:47 17:4 E :9 E6 18:58 19:2 E7 2:5 2:11 2:7 2:32 E8 E9 E1 21: 21:16 21:13 Elevation [m] Profile 14 9 Figure 32 Autobahn A5 north speed diagram day E The speed contour map for Day E, Figure 32, was constructed using the same procedure presented in Section 4.1 for Figure 7. Figure 32 shows speeds for Day E averaged across all lanes for each 1-minute interval.

94 Bottleneck E2 diagnosis Looking at Figure 32, it is apparent that a traffic disturbance occurred downstream of the interchange of Motorway A66 and the A5 North just after 15:. Following the methods described in Section 3 and analyses of oblique N(x,t) and V(x,t) like those described in detail in Section 4.1.1, bottleneck E2 was diagnosed between D7 and D8. E2 activated at 15:8 and deactivated at 16:4 when the tail of a long queue emanating from a downstream bottleneck passed this location. This bottleneck is of particular interest since it is one of only two bottlenecks diagnosed at this merge location on the study days that was preceded by freely flowing traffic. This type of activation will be called an isolated merge bottleneck activation. The next section will examine the discharge characteristics of this bottleneck Merge bottleneck E2 discharge characteristics The discharge characteristics of bottleneck E2, which occurred between D7 and D8 is illustrated in Figure 33. The figure contains oblique N(x,t) and V(x,t), constructed as before, with flow and speed measured across all lanes at detector D8, the first detector downstream of the bottleneck, between 14:5 and 16:1. In Figure 33, periods of nearly constant flow and speed were delineated using dashed lines where the average flows are in vehicles per hour (vph) and the average speeds are in kilometers per hour (km/h).

95 85 N(D8,t)-q t' q =4,9 vph 2 D11 D1 D9 D8 D7 D6 5 N(D8,t) % : : : : : :53 16: V(D8,t)-v t' v =4,425 km/h 2 V(D8,t) 15:8 Bottleneck E2 D7/D8 16:4 14:5 15: 15:1 15:2 15:3 15:4 15:5 16: 16:1 Time, D8 Figure 33 Oblique N(x,t) and V(x,t) for D8 day E Since the curves in Figure 33 do not display any abrupt reductions in the oblique N(x,t) accompanied by abrupt reductions in speed during the periods when the bottleneck was active, it is apparent that there was no disruption of active bottleneck discharge caused by a queue from anywhere further downstream. It is shown that prior to the E2 bottleneck activation (at 15:8), a flow of 5,22 vph prevailed as measured across all three lanes. Immediately following the activation, a flow of 4,79 vph, a 8.2% drop, prevailed, followed by a series of flow recoveries before bottleneck deactivation. The average discharge flow across all lanes over the activation period was 5,15 vph. This discharge flow was comprised of 2,24 vph in the left lane, 1,83 vph in the mid lane and 1,8 vph in the right lane. The flow drop

96 86 upon activation was therefore from 5,22 vph to 5,15 vph, a drop of approximately 1.3%. Now that the location, timing and discharge characteristics of this bottleneck are known, the next section will explore possible triggers to this merge bottleneck activation Merge bottleneck activation triggers The causes of bottleneck activation E2 and others at similar merge locations may be associated with the Motorway A66 interchange with the A5 that occurs immediately upstream of the D7 D8 location. This section summarizes the analyses of on-ramp flows and also the merge activity that occurred directly downstream of the on-ramp. Figure 34 contains oblique N(x,t) for the on-ramp near D6 for the period 14:3 to 15:3, where linear approximations to the N(x,t) are labeled in to the nearest 1 vph. N(D6on,t)-q t' q =1,57 vph 2 D11 D1 D9 D8 D7 D % E2 Activation 18 14:3 14:4 14:5 15: 15:1 15:2 15:3 Time, D6 Figure 34 Oblique N(x,t) for D6 on-ramp day E

97 87 The bottleneck E2 activation at 15:8 was preceded by a 26% surge in on-ramp flow, which was measured as 1,43 vph for nearly 3 minutes prior to activation, followed by a 2 minute average flow of 1,8 vph. This notable increase in on-ramp flow may have had the potential to impact the traffic on the A5. The next section will examine the impact that this merging traffic may have had on the lane changing of traffic in this region. To illustrate net lane change behavior, Figure 35 was constructed from unaltered N(D7,t)-N(D8,t) for each of the three lanes. 1 veh/min Left Lane -2 veh/min N(D7-D8 lane change, t) 2 1 veh/min -6 veh/min -1 veh/min -1 veh/min 6 veh/min 5 veh/min D11 D1 D9 veh/min D8 E2 Activation D7-3 veh/min D6 Mid Lane Right Lane 15: 15:5 15:1 15:15 15:2 Time, D7 Figure 35 N(x,t) for D7:D8 lane change day E

98 88 While the data do not allow for the tracing of individual vehicles, by subtracting the cumulative totals at D8 from the cumulative totals at D7 for each one-minute period, the net effect of lane changing can be observed. In other words, if more vehicles are counted at D8 than at D7 for a particular lane, then N(D7,t)-N(D8,t) would be negative and this would indicate that more vehicles moved out than moved in to this lane. As shown in Figure 35, the activation of bottleneck E2 coincided with an abrupt change in the net lane changing in the D7 to D8 region. The figure shows that in the period preceding the activation there were only small random net lane changes in the right lane between stations D7 and D8, with no average net change over the period. Then, coinciding with activation, there was an abrupt change in lane changing behavior that lasted approximately twelve minutes during which the right lane experienced a net loss of 36 vehicles while the left lane experienced a net gain of 35 vehicles. This type of lane changing behavior was also analyzed for diverge bottleneck activations and deactivations in the course of this study, however the results of these analyses indicated no strong relationship between net lane changing and start and end of bottleneck activations. This may indicate that the E2 bottleneck was triggered by a surge in on-ramp flow followed by movement out of the right lane and into the mid and left lanes creating a

99 blockage for drivers who would have preferred to travel at higher speeds in these lanes. 89 It should be noted that there were no merge bottlenecks that possessed isolated deactivations diagnosed on this 3-km section of the A5 on the days studied. These types of deactivations and their potential triggers should be the subject of future research on this and other freeway sites. Sections have discussed the diagnoses of a large number of bottleneck activations on six days in 21. Additionally, these sections have analyzed in detail the discharge characteristics and potential triggers of a number of merge and diverge bottleneck activations. A complete listing of all activations diagnosed over these six days, along with relevant pre-queue flow and queue discharge characteristics, is located in Appendix E. The next section describes the presence of oscillations or start-stop waves, a traffic flow feature that appeared in congested traffic on the A Traffic oscillations The phenomena of traffic oscillations have been observed in queued conditions in a variety of empirical freeway traffic studies (Bertini & Leal 25, Kerner & Rehborn 1996a, Mauch 21, Mauch & Cassidy 22). Mauch and Cassidy (22) characterized traffic oscillations in queued traffic as sharp increases in flow followed by sharp reductions in flow. To a motorist in a queue, oscillations appear as stop-

100 9 and-go or slow-and-go driving conditions. Mauch (22) has reported that oscillations on a Canadian freeway arose only in queues, that they were stable, and that they propagated at a nearly constant speed of km/h. Kerner and Rehborn (1996a) investigated oscillations on the same German Autobahn, A5, as the current study. They found that these waves propagated with stable velocities (15 km/h) and that they traveled through multiple interchanges without substantial change in structure. To investigate traffic oscillations on the A5 for this study, a procedure was adapted from Mauch and Cassidy (22). The procedure involved transforming flow data such that the slopes of the transformed curve were deviations from 2-minute moving average flows. Each N(x,t) was reduced by [N(t+1 minutes) + N(t-1 minutes)]/2 which results in a value N-N 2. These curves are analogous to residual plots, where the residuals are the difference between an observed variable and some model predicting this variable. In this case, the variable of interest is N, and the predicting model is the 2-minute moving average of N. Figure 36 was constructed from Day A data from the A5 and shows N-N 2 curves for detectors D1 D24, a distance of approximately 22 km. Bottleneck activations were diagnosed between D23 and D24 from 11:59 12:31 (A1) and again from 12:48 16:41 (A2) and also between D7 and D8 from 13:1 13:45 (A3). These and all other activations for Day A are mapped in time and space on a speed contour map found in

101 91 Appendix B. The vertical distance between each curve on Figure 36 is proportional to the distances between the detectors along the freeway. As shown, the oscillations only occurred upstream of the bottleneck (D1 D23). D26 95 D25 4 D24 65 D23 65 D22 11 D21 A1 active A2 active 13 D2 125 D D D D D15 1 A661 Bad Hom-burger Kreuz 2 D14 5 D13 7 D12 12 D11 9 D1 1 D9 9 D8 11 D7 8 D D5 D4 A66 Nordwest Kreuz Frankfurt am Main N-N 2 A648 West Kreuz Frankfurt am Main A3 active D D2 D1 [m][sta] 12: 12:1 12:2 12:3 12:4 12:5 13: 13:1 13:2 13:3 13:4 13:5 14: 14:1 14:2 14:3 Time Figure 36 N-N 2 oscillation curves day A The N-N 2 remained essentially smooth for the detector downstream of the bottleneck (D24). The flow deviations made prominent on the upstream curves after bottleneck

102 92 activation are the oscillations. Included in the figure are dashed trace lines that connect the peaks of several oscillations. The lines show that the oscillations propagated upstream, against the flow of traffic. The near-parallel nature of the statistically determined trace lines indicates that the wave speeds were nearly constant, despite the presence of 3 major interchanges. This finding is similar to that reported by Kerner and Rehborn (1996a). The trace lines have a nearly constant speed of -17 km/h. The amplitude of each oscillation on Figure 36 became rather uniform and is in the order of 2 vehicles (or about 7 vehicles per lane). This oscillation amplitude is notably higher than the findings reported by Mauch (22) who found amplitudes of approximately 16 vehicles per lane on a Canadian freeway and Bertini and Leal (25) who reported amplitudes of approximately 22 vehicles per lane on a British freeway. Sections have discussed the diagnoses of a large number of bottleneck activations on six days in 21. Additionally, these sections have analyzed in detail the discharge characteristics and potential triggers of a number of merge and diverge bottleneck activations. A complete listing of all 81 activations diagnosed over these six days, along with relevant pre-queue flow and queue discharge characteristics, is located in Appendix E. This last section, Section 4.5, has explored traffic behavior

103 and the start-stop waves seen within congested traffic. The next section will explore the reproducibility of the key findings of this study Reproducing the observations The relatively large number of bottleneck activations diagnosed and cataloged in this freeway study provides an opportunity to determine if some of the notable findings such as the magnitudes of discharge flows, the triggers for bottleneck activations and deactivations, and the propagation speed of traffic oscillations within congested traffic are reproducible when compared to the results of similar activations. For example, if found to be reproducible, the average discharge flows for bottleneck activations at a particular location, could then be considered to be the bottleneck s capacity. In an effort to determine if the findings contained thus far in this dissertation are reproducible, the analyses described in Sections were repeated using data from all six study days on this same section of the A5. The reproducibility of diverge bottleneck activation discharge characteristics is assessed in Section The reproducibility of pre-queue flows for several isolated diverge activations is considered in Section Then, Sections and detail the reproducibility of diverge bottleneck activation and deactivation triggers, respectively. Section describes the reproducibility of merge bottleneck activation discharge characteristics. Then, Section covers the reproducibility of the activation triggers of this type of

104 bottleneck. Next, Section illustrates the reproducibility of shock speeds and finally, Section discusses the reproducibility of oscillation wave speeds Reproducing diverge bottleneck activation discharge characteristics A bottleneck arose between stations D22 and D24, immediately upstream of an offramp diverge, a total of 22 times over the six days. Table 5 shows key characteristics of the 22 activations. The discharge flows across all lanes and in each lane were carefully measured for each activation. As first discussed in Section 4.1.9, bottleneck activations in the region D22 D24 were evaluated collectively. As shown in Table 5, the average discharge flows, on both a lane by lane and total basis, of the D22 D23 activations are similar in magnitude to the discharge flows of the D23 D24 activations. The pre-queue flows for activations in the D22 D23 region were notably higher in the left and mid lanes when compared to the D23 D24 activations, yet the right lane pre-queue average flow was lower. However, the variance to mean ratios shown on Table 5 reveal that both the pre-queue and discharge flows in the D22 D23 region showed greater variability than those in the D23 D24 region.

105 95 Table 5 Diverge bottleneck D22:D24 summary all days Bottleneck No. Location Discharge Flow (vph) All Lanes Left Mid Rt. Time (min) Pre-queue flow (vph) All Lanes Left Mid Rt. A6 D22/D B6 D22/D C1 D22/D C13 D22/D C14 D22/D C19 D22/D C2 D22/D E1 D22/D E3 D22/D F12 D22/D F2 D22/D F9 D22/D G14 D22/D G15 D22/D D22/D23 avg D22/D23 SD Var/Avg A1 D23/D A2 D23/D B2 D23/D B3 D23/D B7 D23/D B8 D23/D C8 D23/D F5 D23/D D23/D24 avg D23/D24 SD Var/Avg ALL avg ALL SD isolated avg isolated SD non isolated avg non isolated SD

106 96 For all diverge bottleneck activations in the D22 D24 region, the mean discharge flow measured across all lanes was 4,89 vph with a standard deviation of 31 vph. This discharge flow was comprised of 1,97 vph in the left lane with a standard deviation of 12 vph, 1,7 vph in the mid lane with a standard deviation of 13 vph, and 1,22 vph in the right lane with a standard deviation of 1 vph. The discharge duration ranged between 7 and 223 minutes. This confirms some past research (Bertini 1999, Cassidy & Bertini 1999a) that suggested that queue discharge flows are reproducible from day to day across all lanes and in the individual lanes. A visual representation of the variability of the discharge flows from this diverge bottleneck is provided in Figure 37. This figure displays points which represent the average discharge rates measured across all lanes and in individual lanes. The magnitude of the flows (in vph) is shown on the vertical axis and each of the six observation days are shown on the horizontal axis. In the four quadrants of the figure, each mean discharge flow is shown as a solid horizontal line. In order to show where each observation falls with respect to the standard deviation of each day s flows, a dashed horizontal line is shown at plus and minus one standard deviation. One can see from the figure that the flow in the mid lane shows the highest variability.

107 All Lanes: Mean 489 vph, SD 31 vph SD Mean SD A B C E F G 17 2 Mid Lane: Mean 17 vph, SD 13 vph SD Mean SD A B C E F G Left Lane: Mean 197 vph, SD 12 vph + 1 SD 21 Mean SD A B C E F G Right Lane: Mean 122 vph, SD 1 vph SD Mean SD A B C E F G Figure 37 Diverge bottleneck D22:D24 discharge flow variability

108 98 Also evident from inspection of Figure 37 is that Day G discharge flows were notably higher than the other observation days in each lane. The next section will examine the flows that occurred just prior to bottleneck activation for those activations that were preceded by freely flowing traffic (so-called isolated activations) Reproducing diverge bottleneck pre-queue flows Twelve of the 22 diverge bottleneck activations described in were preceded by freely flowing conditions that were not influenced by other traffic disturbances. These activations are referred to as isolated activations and the values for the durations and magnitudes of pre-queue flows for these 12 activations are shown in Table 5 in italics. These pre-queue periods ranged between 3 and 14 minutes and the pre-queue flows averaged 5,11 vph with a standard deviation of 29 vph. The mean pre-queue flow measured in the left lane was 2,16 vph with a standard deviation of 19 vph, while the mid lane average pre-queue flow was 1,74 vph with a standard deviation of 16 vph, and the right lane average pre-queue flow was 1,21 vph with a standard deviation of 13 vph. As shown in Table 5, mean discharge flows for these 12 isolated activations averaged 4,89 vph. The mean discharge flow measured in the left lane was 1,98 vph with a standard deviation of 14 vph, while the mid lane average discharge flow was 1,7 vph with a standard deviation of 14 vph, and the right lane average discharge flow was 1,21 vph with a standard deviation of 1 vph.

109 99 A visual representation of the variability of the pre-queue flows for the isolated activations of these diverge bottlenecks was created using the methods described in section and is provided in Figure 38. One can see from the figure that the discharge flow in the right lane shows the least variability. Similar to the results of discharge flow variability shown in Figure 37, Figure 38 shows that Day G pre-queue flows were notably higher than the other observation days, particularly in the left and mid lanes. Returning to the examination of Table 5, there was a reduction of average flow from 5,11 vph to 4,89 vph (or 4.3%) that accompanied the twelve isolated bottleneck activations. The left lane average flow reduction was 2,16 vph to 1,97 vph (8.8%), while the mid lane average flow went from 1,74 vph to 1,7 (2.2%), and the right lane average flow remained nearly steady (1,21 vph compared to 1,22 vph). This is consistent with past research (Bertini 1999, Cassidy & Bertini, 1999a) that have documented flow reductions accompanying queue formation on North American freeway sections Reproducing diverge bottleneck activation triggers In analyzing the potential triggers for the C1 and G14 isolated diverge activations described in Sections and 4.2.6, a series of flow and speed features were examined as potential triggers for activation. Table 6 contains a comprehensive list of possible triggers, including several that were not found to be reproducible.

110 All Lanes: Mean 511 vph, SD 3 vph SD 522 Mean SD A B C E F G Mid Lane: Mean 174 vph, SD 16 vph + 1 SD Mean SD A B C E F G Left Lane: Mean 216 vph, SD 19 vph SD 226 Mean SD A B C E F G Right Lane: Mean 121 vph, SD 13 vph + 1 SD Mean SD A B C E F G Figure 38 Diverge bottleneck D22:D24 pre-queue flow variability

111 11 Table 6 Possible diverge bottleneck triggers Bottleneck C1 (D22/D23 14:2-14:17, Sep. 14) D21 right lane truck counts surge (5-13) at 13:59, then D22 (5-15) at 14:, then D23 (5-9 at 14:, 9-12 at 14:1) D23 also shows truck surge in mid lane (2-5 at 14:, then to 4 at 14:1) this surge was not seen at D22, so between D22 and D23 there is movement of trucks from right to mid lane left lane counts steady at about 2 per minute D21-D23 D23, total flows in mid lane peak first (14:), then left (13:1), then right (13:2) The extra trucks at D23 mid lane are accompanied by speed drop (76-61) D25 off-ramp demand grows from 51 vph to 9 vph at 13:55 (sustained until 14:1), this surge is preceded by surges in right lane flow in D23 (starts 13:53) then at D24 (starts 13:54) Net truck lane change into mid lane D22-D23 (13:59-14:2), these trucks are coming from right lane Net truck lane change out of mid lane D24-D25 (14:-14:2) Net truck lane change out of mid lane D23-D24 (14:-14:2) Very high pc flow, 816 pc/h across all lanes at D22, at D22 14:1, 36 pc /h in right lane Bottleneck G14 (D22/D23 15:58-16:3, Sep.19) Similar trigger noted. D21 right lane truck counts surge (4-12) at 15:54, then D22 (6-13) at 15:55, then D23 (9-16) at 15:56 Similar trigger noted. D22 mid lane truck counts surge (- 2) at 15:57, then D23 (-3) at 15:57, Trucks also move to left lane at D23 (1-4) at 16: n/a peaking occurs at the same time n/a no speed drop seen Similar trigger noted. D25 off-ramp flow surges from 82 vph to 136 just prior to activation Similar trigger noted-weak. Slight net truck lane change into mid lane D22-D23 and D23-D24 (15:57-16:2), these trucks are coming from right lane n/a n/a Similar trigger noted-strong. very high pc flow value, 852 pc/h, at D22 (15:56), D22 right lane high pc flow (36 pc/h) accompanied by speed drop (7-59) at 14:2 D25 ramp 14:1-14:5 truck portion (31%) is higher than any other surge in near period Similar trigger noted-strong D22 right lane high pcu flow (348 pc/h) at 15:58 (daily max) n/a D23 truck % increases at 14: % right n/a lane, 3-23% mid lane (the mid lane 23% is an hourly maximum) D25 mid lane truck % increases (-25%) at 14:1 Similar trigger noted. D25 mid lane truck % increases (- 11) at 15:58 while right lane surges for 7 minute average of 8% D24 right lane truck % increases (35-58%) at 14:1 n/a

112 12 The strongest potential triggers for the C1 and G14 isolated diverge activations can be summarized by a) surge in off-ramp flow b) high pre-queue flow in all lanes, and c) high, truck dominated flow in the right lane. Analyses of all 12 isolated bottleneck activations found these three triggers to be highly reproducible. As shown in Table 7, there was a surge in off-ramp flow observed prior to 7 of the 12 activations. In all 12 activations, high flows in all lanes with particularly high truck flows in the right lanes were observed at the station immediately upstream of the bottleneck. Date Bottleneck No. Table 7 Reproducible diverge bottleneck triggers Off-ramp Flow Surge High Pre-Queue Flow All Lanes (vph) High Pre-Queue Flow Right Lane (pc/hr) Sep. 19 G14 Sep. 14 C1 Sep. 14 C2 Sep. 14 C8 Dec. 4 F2 Dec. 4 F9 Sep. 2 E3 Aug. 17 B2 Aug. 17 B7 Aug 17 B8 May 18 A Reproducing diverge bottleneck deactivation triggers There were just two isolated diverge bottleneck deactivations diagnosed on the six study days, bottlenecks B7 and A1. The triggers shown in Figure 31 describing bottleneck B7 showed a drop in D25 off-ramp flow and a drop in truck flow in the

113 13 D25 right lane. These same two triggers were also found to be present in the deactivation of bottleneck A Reproducing merge bottleneck activation discharge characteristics The merge bottleneck activation analysis described in Section was repeated using data from all six days. A bottleneck arose between stations D7 and D8 a total of twelve times over the six days. Table 8 shows key characteristics of the twelve activations. The discharge flows across all lanes and in each lane were carefully measured for each activation. The mean discharge flow measured across all lanes was 5,4 vph with a standard deviation of 42 vph. The mean discharge flow measured in the left lane was 2,9 vph with a standard deviation of 2 vph, while the mid lane average discharge flow was 1,84 vph with a standard deviation of 17 vph, and the right lane average discharge flow was 1,11 vph with a standard deviation of 9 vph. The discharge duration ranged between 11 and 73 minutes. This confirms some past research (Bertini 1999, Cassidy & Bertini 1999a) that suggested that queue discharge flows are reproducible from day to day across all lanes and in the individual lanes. The variability of the discharge flows for these isolated merge bottleneck activations is shown in Figure 39. This figure was created using the methods described in section One can see from the figure that, as was the case for diverge activations, the discharge flow in the right lane shows the least variability. The Day A discharge flows are notably low across all lanes. Further investigation revealed that there were

114 14 only two isolated merge activations on this day and one of these activations had very low discharge flows which impacted the daily means. Table 8 Merge bottleneck D7:D8 summary all days Bottleneck No. Discharge Flow (vph) All Lanes Left Mid Rt. Time (min) Pre-queue flow (vph) All Lanes Left Mid Rt. A A B C C C C E E G G G ALL avg ALL SD Var/Avg isolated avg isolated SD Reproducing merge bottleneck activation triggers Two of the merge bottleneck activations described in Section were preceded by freely flowing conditions that were not influenced by other traffic disturbances. These activations are referred to as isolated activations and the values for the durations and magnitudes of pre-queue flows for these activations are shown in Table 8 in italics. These 2 isolated diverge bottleneck activations were B1 and E2.

115 All Lanes: Mean 54 vph, SD 42 vph Left Lane: Mean 29 vph, SD 2 vph SD SD Mean Mean SD 459 A B C E G SD 187 A B C E G Mid Lane: Mean 184 vph, SD 17 vph 14 Right Lane: Mean 111 vph, SD 9 vph + 1 SD 13 Mean SD SD Mean SD A B C E G A B C E G Figure 39 Merge bottleneck D7:D8 discharge flow variability.

116 16 The bottleneck activation triggers shown in Figures 34 and 35 describing bottleneck E2 showed a surge in D6 on-ramp flow and net lane changing from the right lane into the left lane between D7 and D8. These same two flow triggers were also present in the activation of bottleneck B1The pre-queue periods for these two isolated merge bottleneck activations were both 3 minutes in duration and the pre-queue flows averaged 5,26 vph with a standard deviation of 6 vph. The mean pre-queue flow measured in the left lane was 2,25 vph with a standard deviation of 7 vph, while the mid lane average pre-queue flow was 1,92 vph with a standard deviation of 4 vph, and the right lane average pre-queue flow was 1,1 vph with a standard deviation of 5 vph. Since the mean discharge flows for these two isolated merge activations averaged 5,13 vph, there was, on average, a 2.5% flow reduction Reproducing shock speeds Shocks of lower speed and flow were found to emanate from bottleneck activation locations and travel upstream. Using the procedures described in Section 4.2.4, average shock speeds were computed for all six study days. As shown in Table 9, the shock speeds were found to be approximately reproducible from day to day. A total of 14 shocks were examined, the average shock speed across all days was km/h with a standard deviation of 2.2 km/h.

117 17 Day Table 9 Shock speeds A5 Average shock speed (km/h) Number of shocks (n) A B C E F G Average SD Reproducing oscillation wave speeds The backward moving oscillation waves described in Section 4.5 were examined for all six days in the study. As shown in Table 1, the speeds of these waves were approximately reproducible from day to day. The average speed of the 16 waves seen on these six days was km/h with a standard deviation of.9 km/h. These results are consistent with the findings of several recent empirical studies (Kerner & Rehborn 1996a, Windover 1998, Mauch 22, Bertini & Leal 25). As shown in Table 11, the average oscillation wave speed found in this study (-17.7 km/h) is somewhat higher than the -15 km/h reported by Kerner & Rehborn (1996a) on this same German freeway (A5) and is somewhat lower than the oscillation wave speeds found on other freeways in the UK and North America.

118 18 Table 1 Oscillation wave speeds A5 Day Average wave speed (km/h) Number of measurements (n) A B C E F G Average SD Table 11 Oscillation wave speeds comparison Study Location Average wave speed (km/h) Kerner and Rehborn (1996a) A5 Hessen, Germany -15 Windover (1998) I-88 California USA Mauch (22) Bertini and Leal (25) Lindgren 25 QEW Ontario, Canada M5 London, UK A5 Hessen, Germany -17.7

119 19 5 CONCLUSIONS This final section contains a summary of the study, comments on the implications of this research, and provides an outline of some areas for further research. 5.1 Summary of findings This study has analyzed traffic conditions along a 3-km German freeway over six separate days. The data consisted of speed and count for both autos and trucks for one minute periods. This study represents the first time that data from this German freeway were analyzed using cumulative oblique curves. These suitably transformed oblique curves of cumulative vehicle count and time mean speed versus time provided the measurement resolution necessary to diagnose more than eighty bottleneck activations and deactivations, where queued traffic prevailed upstream of each bottleneck and unqueued traffic was present downstream. This is particularly important since several studies (i.e., Kerner & Rehborn 1996, Kerner 1998a, Kerner 1999b) that had controversial findings failed to consistently determine the spatiotemporal limits of bottleneck activations before computing characteristics such as discharge flow. After diagnosing each bottleneck s location and the times it remained active, the presence of an upstream queue was verified as was the absence of downstream queueing. This study then examined discharge flow characteristics and found that total discharge flows and lane by lane discharge flows appeared to be approximately

120 11 reproducible from day to day, on the six days examined. This finding was consistent with past empirical freeway studies in North America (e.g., Bertini 1999, Cassidy & Bertini 1999a), but the first such finding for a German site. Further, this study identified a set of bottleneck activations at both diverge and merge locations that were considered to be isolated, such that unqueued conditions were present prior to bottleneck activation. The study then documented flow reductions that were measured upon queue formation at both. The discharge flows in the active bottleneck periods fluctuated about a nearly constant mean flow. This observation of a nearly constant discharge rate is important since it means that the bottleneck capacity does not vary with time. These important findings confirmed that the long run discharge flows were the bottlenecks capacities given that the rates were sustained over long periods and were approximately replicated each day. There has been a debate about the definition and techniques for measuring capacity for many years. This concept of empirically measuring the capacity of a particular bottleneck provides freeway managers an alternative to using non-site-specific capacity values prescribed by handbooks such as the Highway Capacity Manual (Transportation Research Board 2) or to the use of empirical flows erroneously measured while the bottleneck was not active. This type of empirical capacity measurement allows freeways to be managed much more effectively. This research is important since it has shown that each bottleneck location has a unique capacity.

121 111 Questions have been raised by researchers in the past about whether there is a propensity for dense traffic to break down without the presence of a bottleneck or some exogenous contributing factor. However, it is shown that all 81 bottlenecks diagnosed in this study activated at predictable locations (e.g., merge, diverge, vertical curves) and appeared to be linked to particular triggers rather than occurring spontaneously as suggested by some researchers (Kerner & Konhäuser 1994, Kerner 1998a, 1999b). There has been another longstanding debate about whether the two-capacity theory (Banks 1991) is valid or not. In this study, bottleneck discharge flows were somewhat lower (3 5%) than the immediate pre-activation flow when unobstructed downstream. This finding therefore supports the two-capacity theory. This is consistent with the findings of Bertini and Cassidy (22) that found empirical evidence of a drop in flow and with the Cassidy and Rudjanakanoknad (24) findings that have shown that flows can be increased with careful ramp metering. The presence of very high flows, particularly in the mid and left lanes, for several minutes prior to bottleneck activation validates empirical evidence summarized by Daganzo (see finding E1 in Daganzo 1999a). The finding that high flows exist prior to activation and that flow reductions occur at both diverge and merge locations is a significant contribution since there have been very few empirical evaluations of traffic at diverge locations (Daganzo 1999a). However, these findings are inconsistent

122 112 with the findings of some other studies (Kerner 1998b, Kerner 22a) that suggest there is up to a 5% capacity difference between free flow and congested traffic. This is attributed to that fact that these previous studies did not definitively establish the spatio-temporal limits of the bottleneck activations and verify activation criteria. The inability of some of these previous studies (e.g. Kerner 1998b, Kerner 2c, Kerner 22a) to pinpoint activation and deactivation times may have influenced their findings that discharge flows varied widely from day to day. In contrast, the bottleneck discharge flows in this study were found to be essentially reproducible over several days, across all lanes and in the individual lanes. An important aspect to this study was the categorization of activations as isolated or non-isolated. In isolated bottleneck activations, that is, activations that were preceded by freely flowing traffic, the pre-queue flows in both the diverge and merge bottleneck activations studied were found to be approximately reproducible from day to day and across lanes and were higher than the discharge flows. This confirms the two-capacity phenomenon suggested by Banks (1991) and is in keeping with results of several other North American empirical studies (Bertini 1999, Cassidy & Bertini 1999a, Cassidy & Bertini 1999b, Cassidy & Rudjanakanoknad 24). Similarly, in bottleneck activations that were not preceded by freely flowing traffic (non-isolated), the discharge flows were measured immediately upon bottleneck

123 113 activation and were also found to be approximately reproducible from day to day and across lanes. This finding is consistent with the findings of Bertini (1999) and Bertini and Cassidy (22). A number of descriptive terms for traffic flow have gained considerable attention recently, principally as a result of the efforts of Kerner and his colleagues to better understand empirical data from traffic flow on German freeways, especially under congested conditions. Kerner s three phases of traffic are: free-flow, synchronized flow, and traffic jam (Kerner & Rehborn 1996b, Kerner 2b, Kerner 22a). The lane by lane speed analyses conducted in this study revealed that aspects of Kerner s three phases of traffic flow were valid on the A5. Freely flowing traffic, where speeds in adjacent lanes were notably different was seen often in non-peak hours in this study. The other two traffic phases in Kerner's lexicon, synchronized flow and wide moving jams (Kerner & Rehborn 1996b, Kerner 22b, Kerner & Klenov 23) are both said to occur in congested traffic. In the current A5 study, traffic flows were observed in which speeds across all lanes were notably lower than in freely flowing conditions and more consistent (within 1 km/h) across all lanes. This phenomenon was observed in congested flows upstream of the bottleneck following activation. This tends to match Kerner s synchronized flow definition. Banks (1999) also reported on instances of synchronized and jam flows on a California freeway, but cautioned that they did not necessarily represent different types of traffic flow but rather were the result of random variations. Finally, this study revealed several

124 114 occurrences of congested patterns in which a relatively short duration traffic disturbance traveled several kilometers upstream. This would appear to match Kerner s definition of a wide moving jam. These findings are important because they represent some of the first apparent independent validations of Kerner s traffic phase findings using different analysis techniques. Past research has examined bottlenecks located in the vicinity of metered and unmetered ramps (Bertini 1999, Bertini & Cassidy 22, Cassidy & Rudjanakanoknad 22). Recent research (Cassidy & Rudjanakanoknad 24) has shown that careful ramp metering can restore high pre-queue flows. Despite the widespread interest in merge behavior, this study revealed only two instances of onramp merge bottleneck activations that were preceded by freely flowing traffic conditions. Both of these isolated activations appear to have been triggered by net lane changing to the left through the section immediately downstream of the on-ramp and both activations were preceded by increases in unmetered on-ramp flow of approximately 25%. This finding is important since Germany is proposing to introduce ramp metering to its freeways and it implies that a careful ramp metering scheme may inhibit the formation of these merge bottlenecks. This type of empirical finding also contributes to the body of knowledge required to allow freeway managers to develop improved ramp metering algorithms.

125 115 The fact that so few merge bottlenecks arose from previously freely flowing traffic on this section of freeway is, in part, due to the very long queues that emanated from bottleneck activations located far downstream. In fact, the effects of some bottleneck activations in this study traveled upstream over 2 km and passed through major interchanges. This finding is consistent with the findings of Kerner & Rehborn (1996a) and is further validation of findings summarized by Daganzo (see C8 in Daganzo 1999). These far-reaching queues were the result of backward moving shocks of lower speed and flow which emanated from bottlenecks on the study freeway. Several shocks over the six days were examined and they traveled at speeds in the range of km/h. This finding is consistent with studies by Kerner and Rehborn (1996a) which found shocks speeds on the order -15 km/h on this same freeway. Some other empirical studies found shock speeds of km/h on a California freeway (Windover 1998), km/h on a British highway (Bertini & Leal 25) and an average of -23 km/h on a Canadian freeway (Mauch 22). This study also sought to determine whether disturbances arose within the queued traffic stream. Several recent studies (e.g., Mauch 22, Bertini & Leal 25) have shown that oscillations, or changes in short term average flows, were found to propagate upstream in queued traffic. In this study on the A5, oscillations were found to travel at nearly constant speeds of approximately -18 km/h. This finding is similar to those reported by a number of recent studies (Windover 1998, Cassidy & Mauch 21, Mauch & Cassidy 22, Daganzo & Smilowitz 22). The A5 oscillations

126 116 were found to have stable amplitudes of not more than 7 vehicles per lane. This amplitude is notably higher than Mauch (22) who reported amplitudes of approximately 16 vehicles per lane on a Canadian freeway and Bertini and Leal (25) who reported amplitudes of approximately 22 vehicles per lane on a British freeway. Whether the German speed laws and the relatively fast speeds seen in mid and left lanes influenced these large slow-and-go wave amplitudes should be the topic of future research. Some past research has also examined bottlenecks at diverge locations (Windover & Cassidy 21, Cassidy et al. 22, Muñoz & Daganzo 22b). In this study, diverge bottleneck activations were often accompanied by flows of approximately 1,2 vph in the right lane at the station immediately upstream of the bottleneck. These flows were dominated by high truck flow (65-75% of the total flow) in the time periods immediately preceding the bottleneck activation. This finding is important since it shows that sudden surges in truck traffic may have been triggering bottleneck activations. This uniqueness of studying both auto and truck flows allowed this potential trigger to be discovered. Furthermore, this finding of apparent prepositioning in anticipation of the off-ramp is similar to results presented by Muñoz and Daganzo (22b) where they noted that between the bottleneck and the off-ramp drivers may segregate themselves by destination.

127 117 This tendency towards pre-positioning in anticipation of an off-ramp is also important in determining the physical inhomogeneity that led to a bottleneck s formation. Freeway diverge bottlenecks associated with freeway off-ramps in this study were located some distance (1.5 2 km) upstream of the actual off-ramp, seemingly as a result of drivers segregating themselves by destination. This finding is consistent with a study of a California freeway (Muñoz & Daganzo 22b) which found a bottleneck approximately 2 km upstream of the off-ramp. In examining the potential triggers of the diverge bottleneck activations in this study, it was found, as expected, that activations were accompanied by surges in off-ramp flows. This finding is consistent with Muñoz and Daganzo (22b) who found that relatively small changes in off-ramp flows can have notable effect on the mainline traffic flow. In addition, diverge bottleneck deactivations were accompanied by drops in off-ramp flow and lower truck flow in the right lane at the off-ramp station. These findings are important for two reasons. Firstly it demonstrates the utility of having speed and flow data for autos and trucks separately. Muñoz and Daganzo (22b), for example, had only combined vehicle speeds and flows and could not investigate the impact that trucks had on the right lane near the off-ramp. Secondly, these findings allow freeway managers to focus on off-freeway improvements such as improved offramp geometry, improved traffic signal control that would incorporate freeway speed and flow measurements, and increased capacity of roads leading away from the freeway.

128 118 In queued conditions upstream of the bottleneck during periods where the bottleneck was active, traffic speeds were found to be nearly equal (e.g., ±1 km/h) in all lanes. This is in sharp contrast to the wide difference in speeds seen across lanes under heavy but unqueued conditions prior to bottleneck activation, particularly on German freeways where left lane auto speeds can be very high and drivers tend to adhere rigorously to the keep to the right law. This finding is consistent with the summary of freeway traffic findings summarized by Daganzo (see B2 in Daganzo 1999a) and is likely associated with difficulty of lane changes in queued conditions. In sum, this freeway site provided a valuable opportunity to document the systematic empirical observation of traffic flow phenomena in a way that can be replicated by other researchers in the future. This research is only an initial step toward understanding bottleneck behavior in relation to geometric features of the roadway. The next section will focus on the implications of some of the findings of this study. 5.2 Comparisons and implications The analysis of this rich data set of freeway speeds and flows for both autos and trucks from a German Autobahn has revealed numerous findings as discussed in Section 5.1. In this section of the dissertation, the implications of some of these findings will be explored.

129 119 This study represents the first comprehensive analysis of the characteristics of bottleneck activations on a German freeway. Along with recent studies of the German A9 freeway (Bertini, Hansen & Bogenberger 24), this study sought to definitively locate the physical position of the bottlenecks and establish precise times for their activations and deactivations while guaranteeing upstream queue and no downstream effects. This is a critical point since other work, most notably the series of empirical studies by Kerner and his colleagues (see Appendix D), for example, made claims about the variability of discharge flows without clearly defining the spatio-temporal limits of the bottleneck or making data available to others. Without careful and methodical diagnosis, the limits of bottleneck activation cannot be definitively established and therefore characteristics such as pre-queue flows and bottleneck discharge flows cannot be measured properly. In this study, eighty one bottleneck activations were carefully diagnosed before their characteristics were studied. It is hoped that this study will spur further research on German freeways that employ these precise diagnostic techniques such that key bottleneck characteristics from a variety of freeways can be further compared. This study demonstrated that it was important to analyze data in their most raw form, which was 1 minute aggregation. Thirty six of the eighty one bottlenecks diagnosed in the course of this work were found to have relatively short durations, less than 2 minutes. Had the data been further aggregated, the details of these bottleneck activations could not have been discernable.

130 12 Another important feature of the data used in this study was the sorting that was done at the collection site, based on vehicle lengths, that provided speed and flow data for autos and trucks separately. Having separate truck data allowed for analysis of the influence that truck flows and speeds had upon bottleneck formation. A prime finding of this study was the frequent activation of a diverge bottleneck upstream of the A5/A455 interchange (see, for example Figure 7). The location of this D22 D24 bottleneck 1 2 km upstream of the actual freeway off-ramp implies that German drivers are willing to segregate themselves according to their destinations for relatively long distances. This information could be used by freeway traffic managers to use intelligent transportation systems (ITS) methodologies such as changeable message signs to promote segregation in a gradual and controlled manner to minimize the potential for bottleneck formation. This finding, however, is not necessarily transferable to other sites. German traffic laws concerning travel in the right lane and passing may influence driver behavior and studies of diverge behavior. The use of video for evaluation of discrete vehicle movements by extracting individual vehicle trajectories could reveal important destination based vehicle prepositioning. As noted in Section 2, this freeway did not contain ramp metering. Germany has been slower than the United States to adopt this technology, but this appears to be changing (Weiss 25). The results of this and other empirical studies will be

131 121 valuable to freeway managers when designing ramp metering strategies to reduce the probability of bottleneck activation in on-ramp merge locations. Furthermore, the finding in this study that changes in off-ramp flows trigger diverge bottleneck activations and deactivations could be valuable to freeway designers in improving off-ramp geometry and downstream control as well as ensuring adequate capacity on roads exiting from the freeway. To adequately study the true demand for off-ramp movements, an origin-destination study would need to be performed. Another implication of this work is the observation that traffic disturbances on this freeway sometimes traveled very long distances (greater than 2 km). This is important since it means that the evaluation of an interchange or a homogeneous freeway segment should not be conducted in an isolated fashion. These long traffic disturbances reinforce the concept that freeways must be considered as a system. One method of achieving a system-wide analysis is the use of more empirical observations that would improve computerized microscopic traffic simulation efforts. Microscopic simulation tools are used to model the behavior of individual vehicles and the interaction of those vehicles with other vehicles as well as the freeway infrastructure (e.g., vertical and horizontal alignment, etc.). The results presented in this dissertation and other similar empirical studies can be used to calibrate and validate such a model. A simulation should evaluate long stretches of the freeway and be tailored to include all the physical constraints such as horizontal and vertical

132 122 curvature, shoulders, merge and diverge lengths, lane widths, etc. A properly calibrated and validated model would need to rely upon the empirically established capacities of the different bottlenecks that comprise the freeway system as well as the measured wave velocities. The results of this study also provide valuable information for the validation of existing macroscopic traffic models. Macroscopic models work at a higher level and do not consider individual vehicles but instead look at macroscopic highway features such as number of lanes and flows to predict traffic characteristics such as capacity and shock speed. The observed traffic features described in Section 4 are consistent with Newell s (1993) Simplified Theory of Kinematic Waves in Highway Traffic and a triangular flow-density relation as shown in Figure 4. In the hypothetical function of Figure 4, all flow-density (q-k) states are presumed to lie on the triangular function. As described in Windover (1998), the velocity of vehicles in a given state is the slope of a line from the origin to the q-k position. Traffic states in the left side of the function are uncongested and those on the right side are congested. When there is a change in traffic states, the discontinuity between these states will propagate in the traffic stream (Windover 1998). Thus, the discontinuity between any two uncongested traffic states, such as the forward moving recovery wave described in Section 4.1.1, move along the left side branch of the figure at free-flow speed. Disturbances in congested

133 123 traffic, such as the backward moving shock described in Section 4.2.4, move along the right side branch with a nearly constant negative speed. Flow, q q max Free-flow speed Disturbance speed Density, k k j Figure 4 Hypothetical triangular flow-density relation This discussion of implications of this research has uncovered some areas where further research is required. The next section summarizes more areas that are worthy of investigation. 5.3 Areas of further research The loop detector data used in this study, with 1 minute aggregation of data for autos and trucks separately, may have masked some important traffic dynamics. For

134 124 example, forward moving recovery waves traveled at free-flow speeds downstream of the bottleneck activations. With 1 minute data aggregation and relatively close detector spacing, this meant that the determination of the time of arrival of these waves was imprecise. Thus, cumulative curves like those constructed in this study could be supplemented with video of the freeway sections being studied from which individual vehicle trajectories could be extracted to reveal more detailed mechanisms involved with bottleneck activations and deactivations. This study sought to identify reproducible triggers for bottleneck formation. Future studies should be conducted to determine if these triggers are reproducible at other freeway locations, both in Germany as well as other countries. This study revealed the importance of evaluating auto and truck flow and speed data discretely. This type of vehicle-specific analysis is particularly important given the large increase in truck freight tonnage expected over the next 15 years in the United States. According to a recent report (FHWA 22) the nationwide growth in truck freight tonnage was predicted to increase 82% over the period The graphical analyses conducted in the course of this research relied on visual evaluation of speed and flow trends such as when they were divided into piecewise linear segments. Future research in this area should include the use of mathematical signal processing techniques such as peak-finding algorithms that would automate

135 125 these tasks. This type of automation may lead to the ability for freeway managers and researchers to employ these types of analyses in an on-line mode instead of the post processing required in this study. This study of a freeway segment nearly 3 km in length allowed for traffic disturbances to be traced over long distances and has revealed the presence of very long traffic disturbances, some stretching over 2 km. The extent to which long distance queue propagation at other German autobahn sites and freeways in other countries reveal similar patterns should be studied. These types of disturbances are rarely seen on North American freeways. Therefore research should be conducted on how factors such as speed limits, traffic laws, driver behavior, auto/truck differences, and vehicle dynamics related to lane positioning may influence these disturbances. Germany, along with several other countries, use variable speed limits and lane changing restrictions on some sections of their freeways, although not on the study section of the A5. The impact of these variable speed limits on bottleneck formation should be studied, by analyzing the same freeway segment in a before and after study. Certain German highways have fixed speed limits, while others, such as the A5 in this study do not. The degree to which the presence of speed limits influences both bottleneck formation and queue propagation should be investigated. Research that

136 126 compares the impact of speed limits on North American freeway congestion versus European freeway congestion is also required. In addition to variable speed limits, there is growing use of variable message signs (VMS) on German freeways as well as other countries. These signs can, for example, warn drivers of downstream incidents, report on queue locations due to recurrent congestion and suggest detours around congestion and accidents. Research on how this type of advanced warning influences driving behavior and the formation of bottlenecks is needed. This study has found that drivers appear to pre-position themselves several kilometers in advance of off-ramps. Further study is required on the tendency of certain drivers and certain vehicle types to favor certain lanes in the region upstream of off-ramp bottleneck areas and the impact that this pre-positioning has on the location and function of the bottleneck. This study showed that bottlenecks activate regularly in areas where macroscopic changes in roadway geometry occurred such as the merge areas following on-ramps and in the diverge areas preceding off-ramps. Since the causes of freeway bottlenecks are numerous and potentially contributory, more detailed studies of how smaller scale changes in such things as longitudinal grade, lane width, shoulder width combine with these macroscopic geometric features to influence bottleneck formation. This

137 127 work could be complemented by computerized microscopic simulation as discussed in Section 5.2. There are currently many handbooks used for the determination of a roadway s capacity. National manuals are in use in the U.S. (Transportation Research Board 2), Germany (FGSV 21), and Japan (Japan Road Association 1984) for example. Further research which compares the capacity determination methods found in these manuals should be conducted. Furthermore, the manner in which various manuals account for the impact of trucks on the traffic stream, generally by means of some type of passenger car equivalent value should also be studied. The empirical study reported in this dissertation is an important contribution to the understanding of congested traffic conditions and some of their causes. However, as this final section has described, there are a large number of areas ripe for further work. This research, therefore, represents just one step towards a greater understanding of how and why freeways bottlenecks arise and some of their key characteristics. Together with future empirical studies, this body of knowledge may lead to the development of improved traffic flow theories and freeway management and information systems.

138 128 REFERENCES ASV 25, Hessian National Road Office, viewed 9 April, 25, < Banks, JH 1991, Two-capacity phenomenon at freeway bottlenecks: a basis for ramp metering?, Transportation Research Record, 132, pp Bertini, RL 1999, Time-dependant traffic flow features at a freeway bottleneck downstream of a merge, Doctoral dissertation, University of California, Berkeley. Bertini, RL & Cassidy, MJ 22, Some observed queue discharge features at a freeway bottleneck downstream of a merge, Transportation Research, Part A, vol. 36, no. 8, pp Bertini, RL 23a, Detecting signals of bottleneck activation for freeway operations and control, Intelligent Transportation Systems Journal, vol. 9, no. 1, pp (In Press) Bertini, RL 23b, Toward the systematic diagnosis of freeway bottleneck activation, Proceedings of the 6th IEEE Annual Conference on Intelligent Transportation Systems, Shanghai. Bertini, RL, Leal, MT & Lindgren, RV 23, Examination of features of a freeway bottleneck surrounding a lane drop, in Proceedings of the 82nd Annual Meeting of the Transportation Research Board, Washington. D.C. Bertini, RL, Lindgren, R, Helbing, D & Schönhof, M 24a, Empirical analysis of flow features on a German autobahn, Proceedings of 83rd Annual Meeting of the Transportation Research Board, Washington. D.C. Bertini, RL, Lindgren, R, Helbing, D & Schönhof, M 24b, Empirical observations of dynamic traffic flow phenomena on a German autobahn, Proceedings of the 16th International Symposium on Transportation and Traffic Theory (Submitted). Bertini, RL & Malik, S 24, Observed dynamic traffic features on a freeway section with merges and diverges, Transportation Research Record, 1867, pp Bertini, RL, Hansen, S & Bogenberger, K 24, Empirical analysis of traffic sensor data surrounding a bottleneck on a German autobahn, Transportation Research Record, (accepted).

139 129 Bertini, RL & Myton, A 24, Using PeMS data to empirically diagnose freeway bottleneck locations in Orange County, California, Transportation Research Record, (accepted). Bertini, RL, & Leal, M 25, Empirical study of traffic features at a freeway lane drop, ASCE Journal of Transportation Engineering, vol. 131, no. 6 (In Press). Cassidy, MJ & Windover, JR 1995, Methodology for assessing dynamics of freeway traffic flow, Transportation Research Record, 1484, pp Cassidy, MJ & Bertini, RL 1999a, Observations at a freeway bottleneck in Transportation and Traffic Theory, 14th International Symposium on Transportation and Traffic Theory, Jerusalem, pp Cassidy, MJ & Bertini, RL 1999b, Some traffic features at freeway bottlenecks, Transportation Research, Part B, vol. 33, no. 1, pp Cassidy. MJ & Mauch, M 21, An observed traffic pattern in long freeway queues, Transportation Research, Part A, vol. 35, no. 2, pp Cassidy, MJ, Anani, SB & Haigwood, JM 22, Study of freeway traffic near an offramp, Transportation Research, Part A, vol. 36, no. 6, pp Cassidy, MJ & Rudjanakanoknad, J 22, Empirical study of ramp metering and capacity, Institute of Transportation Studies UCB-ITS-RR-22-5, Berkeley. Cassidy, M J & Rudjanakanoknad, J 24, Increasing freeway merge capacity by metering its on-ramp, Transportation Research Record, (accepted). Daganzo, CF 1997, Fundamentals of Transportation Engineering and Traffic Operations, Elsevier Science, Oxford. Daganzo, CF 1999a, A behavioral theory of multi-lane traffic flow part I: long homogeneous freeway sections, Institute of Transportation Studies UCB-ITS-RR-99-5, Berkeley. Daganzo, CF 1999b, A behavioral theory of multi-lane traffic flow part II: merges and the onset of congestion, Institute of Transportation Studies UCB-ITS-RR-99-6, Berkeley. Daganzo, CF, Cassidy, MJ & Bertini, RL 1999, Possible explanations of phase transitions in highway traffic, Transportation Research, Part A, vol. 33, no. 5, pp

140 Daganzo, CF & Smilowitz, KR 22, Reproducible features of congested highway traffic, Mathematical and Computer Modeling, vol. 35, no. 5-6, pp Daganzo, CF & Laval, JA 23a, Moving bottlenecks: A numerical method that converges in flows, Institute of Transportation Studies UCB-ITS-RR Daganzo, CF & Laval, JA 23a, On the numerical treatment of moving bottlenecks, Institute of Transportation Studies UCB-ITS-PWP FHWA 22, Freight Analysis Framework, viewed 13 April, 25, < FGSV 21, Handbook for the Measurement of Street Sites (in German), Köln. Japan Road Association 1984, Traffic Capacity of Roads (in Japanese), Tokyo. Kerner, BS & Konhäuser, P 1994, Structure and parameters of clusters in traffic flow, Physical Review E, vol. 5, no. 1, pp Kerner, BS, Konhäuser, P & Rodiger 1995, Appearance of moving local clusters of vehicles on highway with bottlenecks, in Proceedings of 2nd World Congress on ITS, Yokohama. Kerner, BS, Konhäuser, P & Schilke, M 1995, Deterministic spontaneous appearance of traffic jams in slightly inhomogeneous traffic flow, Physical Review E, vol. 51, no. 6, pp Kerner, BS, Konhäuser, P & Schilke, M 1996, Formation of traffic jams caused by fluctuations and random processes in traffic flow, in Proceedings of 7th World Conference on Transport Research, Sydney, pp Kerner, BS, & Rehborn, H 1996a, Experimental features and characteristics of traffic jams, Physical Review E, vol. 53, no. 2, pp. R1297-R13. Kerner, BS, & Rehborn, H 1996b, Experimental properties of complexity in traffic flow, Physical Review E, vol. 53, no. 5, pp. R4275-R4278. Kerner, BS 1997, Experimental characteristics of traffic flow for evaluation of traffic modeling, in Transportation Systems 1997, 8th IFAC/IFIP/IFORS Symposium, Chania, Greece. Kerner, BS, Klenov, SL, & Konhäuser, P 1997, Asymptotic theory of traffic jams, Physical Review E, vol. 56, no. 4, pp

141 Kerner, BS & Rehborn, H 1997, Experimental properties of phase transitions in traffic flow, Physical Review Letters, vol. 79, no. 2, pp Kerner, BS 1998a, Experimental features of self-organization in traffic flow, Physical Review Letters, vol. 81, no. 17, pp Kerner, BS 1998b, A theory of congested traffic flow, 3rd International Symposium on Highway Capacity, Copenhagen, pp Kerner, BS 1999a, Congested traffic flow: observations and theory, Transportation Research Record, 1678, pp Kerner, BS 1999b, Theory of congested traffic flow: self-organization without bottlenecks, in Transportation and Traffic Theory, 14th International Symposium on Transportation and Traffic Theory, Jerusalem, pp Kerner, BS 1999c, The physics of traffic, in Physics World, August, pp Kerner, BS 2a, Experimental features of the emergence of moving jams in free traffic flow, Journal of Physics A, vol. 33, no. 26, pp. L221-L228. Kerner, BS 2b, Phase transitions in traffic flow, in Traffic and Granular Flow 99, September 1999, International Workshop, Stuttgart, pp Kerner, BS 2c, Theory of breakdown phenomenon at highway bottlenecks, Transportation Research Record, 171, pp Kerner, BS, Aleksic, M & Rehborn, H 2, Automatic tracing and forecasting of moving traffic jams using predictable features of congested traffic flow in Control in Transportation Systems 2, 9th IFAC Symposium on Control in Transportation Systems, Braunschweig, Germany, pp Kerner, BS, H, Aleksic, Rehborn, M & Haug, A 2, A method for tracing and prediction of traffic flow patterns in the congested regime, in Proceedings of 7th World Congress on ITS, Torino. Kerner, BS 21a, Complexity of synchronized flow and related problems for basic assumptions of traffic flow theories, Networks and Spatial Economics, vol. 1, no. 1-2, pp Kerner, BS 21b, Tracing and forecasting of congested patterns for highway and traffic management, in Proceedings of 4th Annual IEEE Conference on Intelligent Transportation Systems, Oakland, pp

142 132 Kerner, BS & Herrtwich, RG 21, Traffic flow forecasting, at- Automatisierungstechnik, vol. 49, no. 11, pp Kerner, BS, Rehborn, H, Aleksic, M & Haug, A 21, Methods for tracing and forecasting of congested traffic patterns on freeways, Traffic Engineering and Control, vol. 42, no. 8, pp Kerner, BS, Rehborn, H, Aleksic, M, Haug, A & Lange, R 21, Online automatic tracing and forecasting of traffic patterns, Traffic Engineering and Control, vol. 42, no. 1, pp Kerner, BS 22a, Empirical features of congested patterns at highway bottlenecks, Transportation Research Record, 182, pp Kerner, BS 22b, Empirical macroscopic features of spatial-temporal patterns at highway bottlenecks, Physical Review E, vol. 65, no. 4. Kerner, BS 22c, Synchronized flow as a new traffic phase and related problems for traffic flow modeling, Mathematical and Computer Modeling, vol. 35, no. 5-6, pp Kerner, BS 22d, Theory of congested highway traffic: empirical features and methods of tracing and prediction, in Transportation and Traffic Theory in the 21st Century, 15th International Symposium on Transportation and Traffic Theory, Adelaide, pp Kerner, BS & Klenov, SL 22, A microscopic model for phase transitions in traffic flow, Journal of Physics A, vol. 35, no. 3, pp. L31-L45. Kerner, BS, Klenov, SL & Wolf, DE 22, Cellular automata approach to threephase traffic theory, Journal of Physics A, vol. 35, no. 37, pp Kerner, BS, 23a, Automatic cruise control influence on spatial temporal congested traffic patterns at highway bottlenecks, in Proceedings of 1 th World Congress on ITS, Madrid. Kerner, BS, 23b, Comparison of ASDA/FOTO application for tracing of spatialtemporal congested patterns on freeways, in Proceedings of 1 th World Congress on ITS, Madrid. Kerner, BS 23c, Dependence of empirical fundamental diagram on spatialtemporal traffic patterns features, viewed 2 January, 25, <

143 Kerner, BS & Klenov, SL 23, Microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks, Physical Review E, vol. 68, no Kerner, BS, 24a, Control of spatial temporal congested traffic patterns at highway bottlenecks in Proceedings of the 83rd Annual Meeting of the Transportation Research Board, Washington. Kerner, BS 24b, The physics of traffic, Springer, Berlin. Kerner, BS 24c, Three phase traffic theory and highway capacity, Physica A, vol. 333, February, pp Kerner, BS, Rehborn, H, Aleksic, M & Haug, A 24a, Methods for automatic tracing and forecasting of spatial-temporal congested patterns: a review, in Human Behavior and Traffic Networks, eds M Schreckenberg & R Selten, Springer, Berlin, pp Kerner, BS, Rehborn, H, Aleksic, M & Haug, A 24b, Recognition and tracking of spatial-temporal congested traffic patterns on freeways, Transportation Research, Part C, vol. 12, no. 5, pp Leal, MT 22, Empirical analysis of traffic flow features of a freeway bottleneck surrounding a lane drop, M.S. project, Portland State University. Mauch, M 22, Analyses of start-stop waves in congested freeway traffic, Doctoral Dissertation, University of California, Berkeley. Mauch, M & Cassidy, MJ 22, Freeway traffic oscillations: observations and predictions, in Transportation and Traffic Theory in the 21st Century, 15th International Symposium on Transportation and Traffic Theory, Adelaide, pp Muñoz, JC & Daganzo, CF 22a, Moving bottlenecks: a theory grounded on experimental observation, in Transportation and Traffic Theory in the 21st Century, 15th International Symposium on Transportation and Traffic Theory, Adelaide, pp Muñoz, JC & Daganzo, CF 22b, The bottleneck mechanism of a freeway diverge, Transportation Research, Part A, vol. 36, no. 6, pp Muñoz, JC & Daganzo, CF 22c, Fingerprinting traffic from static freeway sensors, Cooperative Transportation Dynamics, vol. 1, pp , viewed 3 December 22 <

144 134 Newell, GF 1965, A review of traffic flow theory, Lecture at University of California, Berkeley, 25 February Newell, GF 1982, Applications of queuing theory, Chapman and Hall, Cambridge. Newell, GF 1995, Theory of highway traffic flow , Institute of Transportation Studies, Berkeley. Newell, GF 1993, A simplified theory of kinematic waves in highway traffic, I: general theory, II: queueing at freeway bottlenecks, III: multi-destination flows, Transportation Research, Part B, vol. 27, no. 4, pp Smilowitz, KR, Daganzo, CF, Cassidy, MJ & Bertini, RL 1999, Some observations of highway traffic in long queues, Transportation Research Record, 1678, pp Transportation Research Board 2, Highway Capacity Manual 2, National Academy of Sciences, Washington, D.C. Treiber, M & Helbing D 1999, Macroscopic simulation of widely scattered synchronized traffic states, Journal of Physics A,. vol. 32, no. 1, pp. L17-L23. Treiber, M, Hennecke, A & Helbing D 2, Congested traffic states in empirical observations and microscopic simulations, Physical Review E, vol. 62, no. 2, pp Weather Underground 22, viewed 7 August 22 < ml> Weiss 25, viewed 1 February 25 < Windover, JR 1998, Empirical studies of the dynamic features of freeway traffic, Doctoral dissertation, University of California, Berkeley. Windover, JR & Cassidy, MJ 21, Some observed details of freeway traffic evolution, Transportation Research, Part A, vol. 35, no.1, pp

145 135 APPENDIX A DAY C SPEED CURVES Figures show oblique V(x,t) for Day C. These figures were constructed using concepts described in Section 3.1. V(D23,t)-v t' v =4,99 km/h : : :8 65 V(D23,t)-v t' v =4, 86 km/h : : V(D23,t)-v t' v =4,65 km/h : : :5 12:52 12:54 12:56 12:58 13: 13:2 13:4 13:6 13:8 13:1 Time, D23 13:15 13:17 13:19 13:21 13:23 13:25 13:27 13:29 13:31 13:33 13:35 Time, D23 14:3 14:35 14:4 14:45 14:5 14:55 15: Time, D23 V(D23,t)-v t' v =5,1 km/h : :1 1 V(D23,t)-v t' v =5,415 km/h : :28 95 V(D22,t)-v t' v =4,23 km/h : :5 12:52 12:54 12:56 12:58 13: 13:2 13:4 13:6 13:8 13:1 Time, D22 13:15 13:17 13:19 13:21 13:23 13:25 13:27 13:29 13:31 13:33 13:35 Time, D22 14:3 14:35 14:4 14:45 14:5 14:55 15: Time, D22 Figure 41 Oblique V(x,t) day C

146 136 V(D24,t)-v t' v =5,64 km/h :58 91 V(D24,t)-v t' v =5, 61 km/h :5 96 V(D23,t)-v t' v =5,2 km/h : : :5 16:52 16:54 16:56 16:58 17: 17:2 17:4 17:6 17:8 17:1 Time, D24 17:4 17:42 17:44 17:46 17:48 17:5 17:52 17:54 17:56 17:58 18: Time, D24 18:25 18:3 18:35 18:4 18:45 18:5 18:55 Time, D23 V(D23,t)-v t' v =4,49 km/h :58 7 V(D23,t)-v t' v =4,84 km/h :5 88 V(D22,t)-v t' v =5,23 km/h : : :5 16:52 16:54 16:56 16:58 17: 17:2 17:4 17:6 17:8 17:1 Time, D23 17:4 17:42 17:44 17:46 17:48 17:5 17:52 17:54 17:56 17:58 18: Time, D23 18:25 18:3 18:35 18:4 18:45 18:5 18:55 Time, D22 Figure 42 Oblique V(x,t) day C V(D2,t)-v t' v =5,6 km/h :24 13: :1 13:15 13:2 13:25 13:3 13:35 13:4 V(D18,t)-v t' v =5, 22 km/h :3 13:3 13:35 13:4 13:45 13:5 13:55 14: 14:5 14:1 V(D2,t)-v t' v =5,77 km/h : : :1 19:15 19:2 19:25 19:3 19:35 19:4 Time, D2 Time, D18 Time, D2 V(D19,t)-v t' v =5,445 km/h : :33 7 V(D18,t)-v t' v =4,15 km/h : :43 72 V(D19,t)-v t' v =4,62 km/h : :1 9 13:1 13:15 13:2 13:25 13:3 13:35 13:4 Time, D19 15:25 15:3 15:35 15:4 15:45 15:5 Time, D18 15:45 15:5 15:55 16: 16:5 Time, D19 Figure 43 Oblique V(x,t) day C

147 137 V(D29,t)-v t' v =6,25 km/h : :16 11 V(D9,t)-v t' v =5,455 km/h : V(D9,t)-v t' v =4,42 km/h : :4 14:45 14:5 14:55 15: 15:5 15:1 15:15 15:2 15:25 15:3 Time, D29 15: 15:5 15:1 15:15 15:2 Time, D9 15:2 15:25 15:3 15:35 15:4 Time, D9 V(D28,t)-v t' v =5,72 km/h : :15 V(D7,t)-v t' v =2,99 km/h : :18 45 V(D18,t)-v t' v =4,72 km/h : :4 14:45 14:5 14:55 15: 15:5 15:1 15:15 15:2 15:25 15:3 Time, D28 14:45 14:5 14:55 15: 15:5 15:1 15:15 15:2 Time, D7 19: 19:5 19:1 19:15 19:2 19:25 19:3 Time, D18 V(D17,t)-v t' v =3,75 km/h : V(D17,t)-v t' v =2,83 km/h :1 55 V(D7,t)-v t' v =5,88 km/h : : 16:5 16:1 16:15 Time, D17 16:55 17: 17:5 17:1 17:15 Time, D17 18:25 18:3 18:35 18:4 18:45 18:5 Time, D7 Figure 44 Oblique V(x,t) day

148 138 APPENDIX B SPEED CONTOUR DIAGRAMS Figures 45 and 46 show speed contour plots for days A and F respectively. These figures were constructed using concepts described in Section D3 D D D D26 4 D25 65 D24 65 D23 D22 11 D21 13 D2 125 D D D D16 1 D15 5 D14 7 D13 D12 12 D D1 9 D9 D D7 D D5 D4 11 D D2 D1 [m] [Sta] A455 Friedberg A661 Bad Homburger Kreuz A66 Nordwest Kreuz Frankfurt am Main A648 West Kreuz Frankfurt am Main 11:59 Speed [km/h] A1 12:31 12:48 13:1 A3 13:45 A2 A4 15: 15: :31 16:23 16:4 A5 A6 16:41 17:2 17: 17:7 A7 A8 17:39 18:1 17:38 17:37 18:6 18:13 A9 A1 A14 A11 A12 A13 A16 18:13 18:26 18:33 18:41 18:41 18:52 18:55 19:14 19:2 19:14 19:3 A15 19:3 Elevation [m] Profile 14 9 Figure 45 Autobahn A5 north speed diagram day A