EMPIRICAL OBSERVATIONS OF DYNAMIC TRAFFIC FLOW PHENOMENA ON A GERMAN AUTOBAHN

Transcription

1 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn 1 INSERT CHAPTER NUMBER EMPIRICAL OBSERVATIONS OF DYNAMIC TRAFFIC FLOW PHENOMENA ON A GERMAN AUTOBAHN Robert L. Bertini, Department of Civil and Environmental Engineering, Portland State University Roger V. Lindgren, Department of Civil Engineering and Geomatics, Oregon Institute of Technology Dirk Helbing, Institute for Economics and Traffic, Dresden University of Technology Martin Schönhof, Institute for Economics and Traffic, Dresden University of Technology ABSTRACT Traffic conditions were examined along a 3-km section of northbound Autobahn 5 near Frankfurt, Germany using archived inductive loop detector data recorded at one-minute intervals. By focusing on the spatio-temporal evolution of traffic between freely flowing and queued conditions, it was possible to identify a set of fifteen bottleneck activations and characterize reproducible features related to their formation, discharge and dissipation. This was accomplished by systematically probing the excess vehicle accumulation (spatial) and excess travel time (temporal) that arose between measurement locations. It is shown that bottlenecks became active in the vicinity of on-ramps and off-ramps along this Autobahn section. Further, the evolution of a steady shock of low flow and relatively short duration was traced over a 16 km distance. Its cause is not known definitively, but some indications of its formation were revealed. It is also shown that once a bottleneck became active, its queue discharge flow was reproducible across multiple activations and across multiple days. This study is distinct from some past research that has attempted to identify bottlenecks using preestablished speed thresholds. This work is also different from previous research that has reported that bottleneck discharge flow can vary widely from activation to activation. The

2 2 Insert book title here analysis tools used in this study were transformed curves of cumulative vehicle count and cumulative time-mean velocity, using loop detector in its most raw form. These cumulative curves provided the resolution necessary to reveal the spatial and temporal aspects of dynamic freeway traffic flow phenomena. With increasing availability of reliable freeway sensor data, it is important to continue the systematic empirical analysis of freeways in different countries with varying geometric configurations. The results of this kind of research program will assist with all aspects of traffic flow modeling, operations and control. INTRODUCTION The spatio-temporal evolution of traffic from freely flowing to congested conditions and from congested to freely flowing conditions was studied along a 3-km section of a German Autobahn. Several bottlenecks were identified by systematically examining the excess vehicle accumulation (spatial) and excess travel time (temporal) that arose between measurement locations. Bottlenecks became active in the vicinity of on-ramps and off-ramps on this section of freeway. For example, it is shown here that a bottleneck occurred at the crest of a vertical grade approximately 1 m upstream of a major off-ramp. Further, the evolution of a steady shock of low flow and relatively short duration was traced over a 16 km distance. Its cause is not known definitively, but some indications of its formation were revealed. It is also shown that once a bottleneck was identified, its queue discharge flow was reproducible across multiple activations on multiple days. This research project is different than some past work that has identified bottlenecks using pre-defined speed thresholds, and also distinct from past research that has reported that a particular bottleneck s discharge flows vary widely from activation to activation. 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. With widespread availability of reliable freeway sensor data, it is important to continue the systematic empirical analysis of freeways at different sites in different countries and with varying geometric configurations. The results of this kind of research program will assist with all aspects of traffic flow modeling, operations and control. BACKGROUND Among many earlier empirical studies, congested traffic conditions have been analyzed upstream and downstream of freeway bottlenecks located near busy on-ramps (Cassidy and Bertini 1999a; Cassidy and Bertini, 1999b; Treiber and Helbing, 1999; Treiber et al., 2; Treiber and Helbing, 22) and off-ramps (Munoz and Daganzo, 22; Cassidy et al., 22). Other geometric elements worth considering include long, homogeneous freeway sections, merge areas, diverge areas and segments containing other geometric features (Helbing, 23). In the study described here, a bottleneck was defined as a restriction that separates upstream

3 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn 3 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). A bottleneck is considered active when it meets the definition presented above and is deactivated when there is either an upstream decrease in flow (decrease in demand or upstream flow restriction) or when a queue spills back from a bottleneck located further downstream (Newell, 1995). In this context, other researchers (including, for example: Kerner, 22; Kerner, 1999; Kerner, 2) have reported on empirical studies of congested traffic on German Autobahns. Using other data analysis techniques, some researchers have identified variations in bottleneck discharge flow and have postulated the evolution of congested traffic seemingly without bottlenecks. The objective of this paper is to carefully diagnose the activation and deactivation of several bottlenecks using a site on a German Autobahn that has been analyzed by others in the past, and to present some of its notable features that were revealed. DATA The study site (Figure 1) is a 3 km section of northbound Autobahn 5 (A5) near Frankfurt am Main, Germany. The freeway is equipped with double inductive loop detectors (labeled here as D1 through D3) in each lane and on most ramps as shown by the black dots in the figure. The loop detector system records separate counts and average velocities for autos and trucks at one minute intervals. Archived data are available for more than 18 days in both northbound and southbound directions; the analysis described here uses data from Wednesday, September 19, 21 from the northbound direction plus data from five additional days in 21 to demonstrate reproducibility. Figure 1 also shows the spacing between detector stations (in meters) and the vertical geometry (elevations in meters) on the right hand side of the figure. As shown there is a steady uphill gradient between stations D17 and D23, with a 2.6% grade between D21 and D23. Finally, Figure 1 also shows that there are two locations (between D7 D8 and D2 D21) where local access off- and on-ramps are present, but no through traffic leaves or enters the system at these locations. A comparison of counts from upstream and downstream locations indicates that vehicle conservation is maintained. METHODOLOGY AND OBSERVATIONS Figure 1 also 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 color. The green shade indicates high speeds with the red shades representing lower speeds. It is clear from the figure that a large number of speed disturbances occurred on this day starting shortly after 14: and continuing until nearly 2:. It should be noted that September falls in Middle European Summer Time. Therefore one hour should be added to the recorded times (which are the basis for the following discussion and figures) in order to obtain the actual clock times. Using the method described below, this study adds to previous work by explicitly diagnosing the activation of fifteen bottlenecks along the A5 on September 19, 21 (referred

4 4 Insert book title here 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 14:21 14:35 14:47 G1 G2 14:35 14:51 14:58 14:47 14:58 14:55 15:3 G12 G7 G14 G3 15:3 15:34 G15 15:48 15:59 15:4 15:47 G4 15:4 15:47 15:49 16: G8 G1 G13 16:7 16:13 16:32 16:29 G9 16:46 16:42 G5 G :5 17:7 17:12 G11 19:2 Elevation [m] Figure 1: Autobahn A5 Northbound Speed Diagram. to as day G). These bottleneck activations (labeled G1 through G15) are also mapped in time and space on Figure 1. The study also examines bottleneck activations on five additional days and reports on several features that appear to be reproducible across all study days. To promote the identification of time-dependent traffic features, this study used cumulative curves of vehicle count and time-mean velocity constructed from data measured at neighboring freeway detectors (Cassidy and Windover, 1995). Transformations of these curves provided the enhanced measurement resolution necessary to observe transitions between unqueued and queued conditions and to identify notable, time-dependent features. In order to demonstrate the diagnosis of two bottleneck activations, including their locations and the times they remained active on September 19, 21, Figure 2(a) shows transformed oblique curves of cumulative vehicle count (N(x,t)) for detectors D15 D24 from 14:4 until 15:1. Using the one-minute count data measured across all lanes, piece-wise 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. As such, the curve at D15 includes the on-ramp counts so that vehicle conservation was maintained.

5 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn Figure 2: (a) Oblique N(x,t) for D15-D24 (b) Oblique V(x,t) for D22, D23, and D24. As with standard queueing analysis, the horizontal and vertical separations between unaltered N(x,t) would have been the travel times and vehicle accumulations between measurement locations, respectively (Newell, 1982; Newell, 1993). However, in Figure 2(a) the curves were altered by shifting each upstream curve to the right by the free-flow travel time from its location to detector D24. As a result, any vertical displacements between the curves would have been the excess vehicle accumulation between detector pairs, and the horizontal distance between curves would have been the excess travel time delay between the measurement locations (Newell, 1982; Newell, 1993). In order to further amplify the curves features, an oblique scaling rate, q, was applied to the N(x,t), more clearly revealing the times at which notable flow changes occurred. A suitable choice of q promotes the visual identification of changing flows directly from the oblique curve, as shown in Cassidy and Windover (1995). The same value of q was applied to all curves so that the magnitudes of the vertical separations are not affected. Note that the oblique N(x,t) are shown using an amplified vertical scale and that changes in flow can be observed clearly from the figure (note that in this and subsequent figures a relative vertical scale is shown on the left axis). This method is described in more detail in several references (Cassidy and Windover, 1995; Munoz and Daganzo, 22). It is noteworthy that this method takes advantage of the loop

6 6 Insert book title here detector data in their most raw form (does not aggregate the data any further) and also takes into account the spatial aspects of queue formation, which is a limitation of any pure speed threshold bottleneck identification method. All ten curves in Figure 2(a) remained superimposed until approximately 14:5, indicating that traffic flowed freely between all stations. A short time before 14:5, Figure 2(a) shows that excess accumulation arose between stations D17 and D18 as indicated by the divergence of the N(x,t). A subsequent divergence of curve D17 from curve D16 (and flow reduction measured at D17) marked the passage of the backward-moving queue at D17. This activation was labeled as bottleneck G7. Note that all N(x,t) downstream of D17 remained superimposed until approximately 14:55, 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 D21 until 15:3 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 2(a). 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 14:58, upstream accumulations (and accompanying flow reductions at D22 and D21) are visible, marking the activation of bottleneck G14 between D22 D23. These activations are also labeled on Figure 1. 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. 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 2(b) for several examples, 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. Figure 2(b) 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 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 V(x,t) curves and correspond closely to the 14:58 activation time described above. Furthermore, it can be seen that the speed reduction occurred at progressively later times at D23 and D24 which is consistent with a forward-moving wave traveling downstream from the D22 23 bottleneck location. To examine the flow features of bottleneck G14 through its entire active period, Figure 3 was constructed using the N(x,t) from detectors D15 D24 from 14:4 until 17:1. Knowing that G14 was activated at 14:58, Figure 3 shows that it was deactivated at 15:3 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 2(b). A speed increase was visible at approximately 15:3 at D22, indicating the reestablishment of freely flowing

7 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn :22 D16 15:3 D2 15:34 D19 15:37 D18 15:4 D17 15:45 D15 15:42 D16 15 N(x,t) - q (t-t ), q =489 vph 14:5 D17 14:58 D22 14:58 D17 G7 G12 D2 D21 14:55 D2 15:3 D2 D17 D18 15:5 D19 15:8 D18 15:14 D17 G14 D22 D23 15:28 D21 15:3 D22 15:34 D22 G15 D22 D23 15:49 D22 15:48 D17 G8 17 D17 D18 16: D2 15:59 D17 G13 D2 D21 16:29 D17 16 G9 D17 D18 16:46 D17 16:32 D2 16:42 D15 G6 D15 D16 17:7 D15 Time, t at D15 Figure 3: Oblique N(x,t) for D15-D24. conditions between D Prior to this time, speeds were recorded between km/h, noticeably slower than the speeds measured at D23 and D24. The freely flowing traffic between D22 D23 after 15:3 was short-lived and a bottleneck was again activated between D22 D23 at 15:34 (G15). As shown in Figure 3, the N(x,t) for D23 and D24 remained superimposed indicating freely flowing traffic whereas there was notable excess accumulation between the N(x,t) at D22 and D23 beginning at about 15:34. This indicated that G15 was activated at 15:34 and remained active until 15:49 when excess upstream accumulation dissipated. The G15 activation and deactivation times can also be confirmed by examination of the second and third V(x,t) columns of Figure 2(a). The D22 V(x,t) clearly shows a speed decrease at 15:34 and a speed increase at 15:49. Figure 3 also shows that by approximately 15:, the queues that propagated upstream from bottlenecks G12 and G14 merged and propagated further upstream; the queue s progress can be mapped on Figure 3 as it passed stations D19, D18, D17 and D16 (see vertical arrows). Figure 3 also presents the diagnoses of all eight bottleneck activations during this time period. As shown by the excess accumulation arising between D17 and D18 at about 15:48, a bottleneck between D17 D18 was activated as bottleneck G8 until 15:59 (these and other activations and deactivations were verified by V(x,t) not shown here). Upon excess accumulation being visible between D2 and D21 at 16:, bottleneck G13 was activated

8 8 Insert book title here N(x,t) - q (t-t ), q =425 vph 1 d24 d23 d22 d21 d2 d19 d18 d17 d16 d15 17:12 D19 17:17 D17 17:14 D G11 D19 D :2 D15 19:5 D16 19:8 D17 19:17 D18 19:2 D19 Time, t at D15 Figure 4: Oblique N(x,t) for D15-D24. between D2 D21 and remained active until the reduced flow from an upstream bottleneck (G9) deactivated G13 at 16:32. Bottleneck G9 became active between D17 D18 at 16:29, 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 16:46. Bottleneck G6 was activated at 16:42 between D15 D16 near where merging traffic from Motorway A661 entered the A5 at an on-ramp downstream of D15. Bottleneck G6 remained active between 16:42 and 17:7. To continue the examination of bottleneck features through the remainder of the afternoon peak period, Figure 4 contains a set of N(x,t) for stations D15 D24 between 17: and 2: for September 19, 21. Figure 4 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 17:12, 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 17:17. G11 persisted until a forward moving wave of lower flow deactivated the bottleneck at 19:2. Figure 4 clearly shows that N(x,t) for D15 D24 are all nearly superimposed after 19:2 indicating that traffic was freely flowing throughout the region until 2: and, although not shown on the figure, this continued to be the case for the rest of the evening. Figures 2 4 have described the activation and deactivation of nine bottlenecks over a 9.3 km segment of the A5. Figure 1 showed that six additional bottleneck activations occurred in the segment between station D6 and D14 on September 19, 21. Figure 5 shows the details of these six activations and includes N(x,t) for detectors D6 D14 between 14: and 17:1 (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 14:21, indicating that G1 was activated between D7 D8 at 14:21. G1 remained active until the reduced flow from upstream bottleneck G2 deactivated G1 at 14:35. Shortly before and just upstream, between D6 D7, bottleneck G2 was activated at 14:35 and remained active until the backward moving tail of the queue from downstream bottleneck G3 deactivated G2 at

9 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn 9 N(x,t) - q (t-t ), q =489 vph 15:46 D14 15:49 D13 15:51 D12 15:55 D11 16:1 D1 16:5 D9 16:8 D8 16:12 D7 16:15 D6 1 14:21 D7 G1 14:35 D6 14:47 D7 G2 G3 15:4 D7 15:47 D G4 G1 16:7 D7 16:13 D8 D7 D8 D6 D7 D7 D8 D5 D6 D7 D8 D8 D G5 17:5 D9 Time, t at D6 Figure 5: Oblique N(x,t) for D6-D14. 14:47. The activation of bottleneck G3 is indicated by the excess accumulation between D7 and D8 beginning just before 14:47; G3 persisted until the reduced flow from upstream bottleneck G) deactivated G3 at about 15:4. Bottleneck G4, located near the off-ramp between D5 D6 was activated briefly from 15:4 15:47. Bottleneck G1, activated between D7 D8, represents the third activation in this location on the study day. G1 became active at 15:47 and persisted until the tail of the long downstream queue deactivated G1 at 16:7. Following the dissipation of this long downstream queue, bottleneck G5 became activate immediately downstream between D8 D9. G5 became active at 16:13 and persisted until the backward moving tail of the queue from downstream bottleneck G6 deactivated G5 at 17:5. Consistent with what was described above, Figures 3 and 5 show the propagation of a shock of lower flow that emanated from between D21 and D22 at approximately 15:28. The shock s passage can be traced upstream (see circular markers on Figures 3 and 5) as far as D6 more than 45 minutes later. The backward recovery wave was also traced in Figures 3 and 5 (square markers), which reached D6 by approximately 16:21. The velocities of the shock and recovery wave appeared to be stable and were also reproducible from day to day. Possible origins of this phenomenon will be discussed below. Figure 1 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 September 19, 21. Figures 2 5 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 several bottleneck activations (G14 and G15) in detail.

10 1 Insert book title here 525 N(d23,t) N(d23,t) - q (t-t ), q =49 vph 1 14:49 D :58 D G14 D22 D23 15:3 D :34 D23 74 G15 D22 D23 15:49 D23 91 V(D23,t) 1 V(D23,t) -v (t-t ), v =46 km/h per hour Time, t at D23 Figure 6: Oblique N(x,t) and V(x,t) for D23. The discharge characteristics of bottlenecks G14 and G15, both of which occurred between D22 D23 are illustrated in Figure 6. 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 14:3 and 16:. In the figure, 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). Since the curves do not display any abrupt reductions in the 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. It is shown that prior to the G14 bottleneck activation (at 14:58), a flow of 567 vph prevailed as measured across all three lanes. Upon initial queue discharge, an average discharge flow of 532 vph prevailed, reflecting a 6% reduction in flow. It is further shown that upon queue discharge of the G15 bottleneck activation, a flow of 525 vph prevailed. The flow drop upon queue discharge is consistent with some previous research, as is the stability of the discharge flow itself. OBSERVATION OF BOTTLENECK TRIGGERS Based on this 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 have revealed possible signals of bottleneck activation. Bottleneck G14, for example, was located between D22 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 7 contains oblique N(x,t) for the off-ramp near D25, where linear approximations to the N(x,t) are labeled in vph. The G14 activation at 14:58 was accompanied by a 66% surge in off-ramp flow, which was measured as 136 vph for the 3 minutes

11 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn 11 following activation, after a lower flow of 82 vph was measured during the previous 5 minutes. The activation also coincided with a period of high flow at D22 that was marked by substantial truck flows. To account for the impact of trucks on the traffic flow, an D25 Off Ramp Oblique N(x,t) : Time, t 14:3 14:4 14:5 15: 15:1 15:2 15: % 348 pc/hr [58 pc/min] , 6, 5, 4, 3, 2, 1, D22 Right Lane Equivalent Count Figure 7: Oblique N(x,t) for Off Ramp for D25 and Right Lane Equivalent Count for D22. approximate relation of one truck being equivalent to three passenger cars was adopted and the flows computed in passenger car units per hour (pc/hr). As shown in the lower portion of Figure 7, the G14 activation was preceded by a flow of 348 pc/hr in the right lane at D22 at 14:56, the highest value recorded at any time on the study day. Further lane-by-lane analyses of vehicle speeds and counts at D22 revealed that the surge noted above in the right lane corresponded with high flows also measured in the middle and left lanes. The oblique lane-by-lane N(x,t) (upper) and V(x,t) (lower) of Figure 8 were constructed as before, with different values of q and v noted on the figure. Linear approximations of prevailing lane flows and velocities are labeled in vph and km/h respectively. Figure 8 reveals that in the two-minute period surrounding the 14:58 G14 activation, the right lane flow was measured as 1,18 vph, the left 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. During this time, the average lane speeds were 74 km/h, 82 km/h, and 86 km/h in the right, middle, and left lanes respectively. In general, the rules of the road in Germany require trucks to remain in the right lane except for passing. Because trucks have vastly different performance characteristics than cars, a detailed analysis of truck flow and velocity patterns was conducted just upstream of the G14 bottleneck activation. Using separate truck count and speed data, Figure 9 shows oblique N(x,t) (upper) and V(x,t) (lower) for each lane at station D22. The N(x,t) are annotated with linear approximations, which are labeled to the nearest 1 veh/hr. These curves reveal that trucks indeed remained in the right lane during periods of uncongested flow prior to 14:58. Notice that several minutes prior to activation G14, the truck flow in the left lane surged to

12 12 Insert book title here Oblique N(22,t) : Time, t 27 veh/hr Left Lane q =18 vph Middle Lane q =18 vph Right Lane q =16 vph Oblique V(22,t) 1 18 km/hr Left Lane v =485 km/h 2 Middle Lane v =4483 km/h 2 Time, t Right Lane v =3988 km/h 2 14:45 14:5 14:55 15: 15:5 15:1 15:15 15:2 15:25 15:3 Figure 8: Oblique N(x,t) and V(x,t) for D trucks per hour. Then, coinciding with activation, a 94% truck flow increase was observed in the right lane, followed closely by movement of trucks to the middle lane where an increase to 19 trucks per hours was observed. Oblique N(22,t) Left/Middle Trucks Only trucks/hour 9 15 (5 trucks/2 min) (+94%) Time, t Right Lane q =4 vph 1 Middle Lane q =8 vph Left Lane q =3 vph Oblique N(22,t) Right Lane Oblique V(22,t) Left/Middle 1 Trucks Only 114 km/hour Time, t Left Lane v =561 km/h 2 65 Middle Lane v =58 km/h 71 2 Right Lane v =436 km/h 2 Oblique V(22,t) Right Lane 14: 14:1 14:2 14:3 14:4 14:5 15: 15:1 15:2 15:3 15:4 15:5 16: Figure 9: Oblique N(x,t) and V(x,t) for Trucks at D22.

13 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn 13 The lower portion of Figure 9 contains 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 14:58. The right lane trucks speeds dropped from 79 to 68 km/h, the middle 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. REPRODUCING THE OBSERVATIONS The analyses described above were repeated using data from five additional days on this same section of this Autobahn. A bottleneck arose between stations D22 and D24 a total of 19 times over the six days. Table 1 shows key characteristics of the 19 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 483 vph with a standard deviation of 297 vph. The mean discharge flow measured in the left lane was 195 veh/hr with a standard deviation of 13 veh/hr, while the middle lane average flow was 167 veh/hr with a standard deviation of 14 veh/hr, and the left lane average flow was 121 veh/hr with a standard deviation of 11 veh/hr. The discharge duration ranged between 13 and 223 minutes. This confirms some past research (e.g., Cassidy and Bertini 1999a) that suggested that queue discharge flows are reproducible from day to day across all lanes and in the individual lanes. Eleven of these activations (including bottleneck G14 which was described in detail above) 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 11 activations are shown in Table 1 in italics. These pre-queue periods ranged between 2 and 14 minutes and the pre-queue flows averaged 516 vph with a standard deviation of 266 vph. Since the mean discharge flows for these 11 isolated activations averaged 482 vph, there was, on average, a 6.2% flow reduction that accompanied these 11 bottleneck activations. This is consistent with past research (e.g., Cassidy and Bertini, 1999a) that have documented flow reductions accompanying queue formation on North American freeway sections. Research is ongoing to investigate the reproducibility of bottleneck activation at other locations on the A5 on other days. The potential triggers for the G14 activation shown in Figures 7 9 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 11 isolated bottleneck activations found these three triggers to be highly reproducible. As shown in Table 2, there was a surge in off-ramp flow observed prior to 7 of the 11 activations. In all 11 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. Research is continuing to examine other potential bottleneck activation triggers at additional locations on the A5, as well as on additional days.

14 14 Insert book title here Table 1 Reproducibility of Discharge and Pre-Queue Flow in D22 D24 Region Pre- Pre- Queue Queue Flow Dur. (vph) (min) Discharge Flow (vph) Isolated Discharge Flow (vph) Dur. Left Mid Right Date BN Location (min) (vph) (vph) (vph) Sep. 2 E1 D22/D Sep. 2 E3 D22/D Sep. 14 C2 D22/D Sept. 19 G14 D22/D Aug. 17 B6 D22/D Dec. 4 F12 D22/D May. 18 A6 D22/D Dec. 4 F9 D22/D Dec. 4 F2 D22/D Sept. 19 G15 D22/D May. 18 A2 D23/D Aug. 17 B8 D23/D Aug. 17 B3 D23/D Sep. 14 C8 D23/D Aug. 17 B7 D23/D May. 18 A1 D23/D Aug. 17 B2 D23/D Sep. 14 C1 D22/D Dec. 4 F5 D23/D Mean SD FINAL COMMENTS This study has analyzed traffic conditions along a 3-km freeway segment over a six-hour period on one day. Oblique curves of cumulative vehicle count and time mean speed versus time provided the measurement resolution necessary to diagnose fifteen distinct bottleneck activations and deactivations, where queued traffic prevailed upstream of each bottleneck and unqueued traffic was present downstream. After diagnosing each bottleneck s location and the times it remained active, this study examined discharge flow characteristics and found that discharge flows appeared to be approximately reproducible from day to day, on the six days examined. Further, this study identified a set of bottleneck activations that were considered to be isolated, and documented measurable flow reductions upon queue formation. This work has verified similar findings from past studies using data from North American freeways.

15 Empirical Observations of Dynamic Traffic Flow Phenomena on a German Autobahn 15 Table 2 Reproducibility of Isolated Bottleneck Activation Triggers in D22 D24 Region Trigger Date BN 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 A1 Toward identifying the potential causes of bottleneck activation near an off-ramp, the study focused on the traffic patterns that preceded and followed bottleneck activation by vehicle type and in each travel lane. It is shown that surges in off-ramp flow, high pre-queue flow in all lanes, and high, truck dominated flow in the right lane preceded 11 activations on this freeway near the off-ramp. Research is continuing at this site on other days and in other locations (e.g., near the on-ramp near station D8) to identify additional potential bottleneck activation triggers and explore their reproducibility. This freeway site provides 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. Therefore, further analyses are being conducted at this site and other sites in Europe and the United States. ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of the Hessische Landesamt für Strassen-und Verkehrswesen for generously providing the archived data used in this study. In addition, a portion of this work was funded by the Department of Civil and Environmental Engineering at Portland State University, and support was provided by the Department of Civil Engineering and Geomatics at the Oregon Institute of Technology.

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