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Paper No. 001636 $QDO\]LQJ$UWHULDO6WUHHWVLQ1HDU&DSDFLW\ RU2YHUIORZ&RQGLWLRQV Duplication for publication or sale is strictly prohibited without prior written permission of the Transportation Research Board Authors Andrzej P. Tarko, Assistant Professor Purdue University 1248, Civil Engineering Building West Lafayette, IN 47906 7UDQVSRUWDWLRQ5HVHDUFK%RDUG WK $QQXDO0HHWLQJ -DQXDU\ :DVKLQJWRQ'&

Analyzing Arterial Streets in Near-Capacity or Overflow Conditions Andrzej P. Tarko Assistant Professor of Civil Engineering Purdue University 1284 Civil Engineering Building West Lafayette, IN 47907 Phone: (765) 494-5027 Fax: (765) 496-1105 Email: tarko@ecn.purdue.edu Paper presentated at the 79th Annual Meeting of the Transportation Research Board Washington, D.C., 9-13 January 2000 1

Abstract Filtering and metering of traffic at highway bottlenecks influence delay and travel speeds along congested arterial streets. The current HCM method of analyzing urban arterial streets uses the filtering/metering adjustment factor I but do not give recommendations how to adjust traffic volumes. This paper proposes an improved method of analyzing signalized arterial streets affected by bottlenecks. A set of equations has been derived to calculate the coefficient I and to adjust the traffic volumes. The paper specifies conditions when measured or predicted volumes should be adjusted and when they do not have to. The proposed method incorporates the effect of turning volumes, a feature not present in the current HCM method. A sensitivity analysis of travel speeds along an example signalized arterial street illustrates the filtering and metering effects and compares the results produced by the existing and proposed methods. The differences in the results are considerable. In addition, the significant effect of turning volumes has been confirmed. The proposed method tends to produce travel speeds higher than the values obtained in the current method, which concurs with the comments from the users of HCM that the current method underestimates the travel speeds. The filtering equation has been derived with the assumptions of fixed capacity and no vehicles dispersion. Under the conditions violating these assumptions, the filtering equation may underestimate I. Further, the proposed method does not incorporate the effect of long queues blocking upstream lane groups. The negative effect on the travel speed estimates along the entire arterial should be limited or negligible. Key words: arterial streets, highway capacity, level of service 2

Introduction In 1997, publication of the latest edition of the Highway Capacity Manual (Transportation Research Board, 1997) introduced several new methodological elements which enhanced the then current capabilities for analyzing highway components in congested conditions. The first of these, a modified delay equation consisting three terms, was offered as an improved method for the evaluation of signalized intersections (Chapter 9) for periods following congestion conditions. In addition, a new delay formula was proposed for unsignalized intersections (Chapter 10) to deal with congestion during the period of analysis. Lastly, in an attempt to address the effect of upstream signals, particularly strong when traffic reaches capacity, the 1997 HCM incorporated a so called filtering/metering adjustment coefficient as a component in the delay function (Chapter 11). The attempt to deal with congested conditions is more obvious, however, in the new version of HCM being prepared for a 2000 edition. For example, a new chapter has been added to deal with oversaturated freeway systems. This trend in improvements of the HCM reflects the growing presence of oversaturated highway components and systems that have to be somehow analyzed and evaluated. A highway bottleneck is a spot in highway network where the arriving traffic volume exceeds the highway capacity. Such a spot influences performance of the surrounding spots in periods when the traffic volume exceeds or just reaches the bottleneck s capacity. This influence needs to be incorporated into analysis of individual highway components and of such highway systems as freeway facilities or signalized arterial streets. Arterial streets with a sequence of signalized intersections are particularly good candidates for system-wide analysis that includes the effect of internal bottlenecks. The filtering/metering adjustment factor I in the delay function introduced in the 1997 HCM was thought to address this need but, as will be shown in the remainder of this paper, this attempt was not sufficient. Let us discuss filtering and metering to point out the difference between these two phenomena and their effects on traffic. In this consideration, traffic flow is represented through a sequence of vehicle counts in consecutive signal cycles. The considered period of analysis includes a certain number of signal cycles. The traffic flow can also be represented through the variance and the mean value of such counts. The maximum number of vehicles that can pass the signal in a given cycle is called cyclic capacity. The cyclic capacities during the period of analysis together with the capacity variance and mean represent completely describe the capacity conditions. The vehicle queues (or o overflow queues) are measured at the end of cycles. The initial, final and average overflow queues are considered for a period. Metering takes place at a signalized intersection if the expected vehicle counts upstream (arrivals) and downstream (departures) of the intersection are not the same. This case occurs only if the expected queues at the beginning and the end of the period are the same. The final queue longer than the initial queue indicates the expected arrival count higher than the expected capacity. The excess of arriving flow forms overflow queue. The overflow queue decreases along the period if the initial queue is non-zero and the expected number of arrivals is less than the expected capacity. The expected number of departures is equal to the expected capacity under the permanent presence of queue and it equals the expected number of arrivals under the 3

permanent lack of the overflow queue. In many cases, the expected number of departures falls somewhere between the expected number of arrivals and the expected capacity. Metering decreases the average vehicle count in the periods with growing overflow queue and it makes departing counts higher than arrival counts in the periods with queue dissipation. Upstream metering has to be incorporated through the adjusted traffic volumes or the degree of saturation X. Further, the development of upstream queues has to be included in calculations too. The upstream filtering has to be incorporated into the delay calculations through the variance of counts or through the variance-to-mean coefficient I. Filtering takes place at a signalized intersection if the expected variances of vehicle counts upstream (arrivals) and downstream (departures) of the intersection are not the same. The lack of the overflow queues indicates the lack of filtering. As a matter if fact, it is sufficient to assume that the overflow queue does not change over the period to preserve the traffic variance, but the case of fixed and non-zero queue is highly unusual. In intervals with queue at the end, the number of departures equals the cyclic capacity. In other words, the variance of departures equals the variance of arrivals under the permanent lack of queues, and it equals the capacity variance under the permanent presence of queue. In most cases, the variance of departures falls somewhere between the variance of arrivals and the variance of capacity. It can be concluded, that filtering reduces the traffic variability if the variance of capacity is less than the variance of arrivals, and it increases the traffic variability otherwise. The second case is infrequent at signalized intersections. The above discussion is a summary of what is known about traffic passing a sequence of bottlenecks. It has been tailored though to the manner the HCM views highway traffic. Particularly characteristic for the HCM is the use of periods of analysis with constant traffic volumes. This representation of traffic will be discussed in one of the following sections where the effect of metering is further elaborated. One conclusion from this discussion is straightforward the effect of metering cannot be properly incorporated into calculations through the coefficient I only. This finding calls for a modified method of analyzing signalized arterial streets and individual signalized intersections affected by upstream bottlenecks. The remainder of this paper is organized as follows. First, metering and its consequences on volume data (measured and predicted) will be discussed in the following section. Input data that sufficiently defines traffic will be described. This section will present an equation, which adjusts traffic volume for the metering effect. The simplifying assumptions will be emphasized. For the completeness of presentation, the third section presents the latest advancements on filtering. The next section brings sensitivity analysis of travel speeds along an example signalized arterial street to illustrate the metering and filtering effects and to compare the results produced by the existing and the proposed methods. A discussion of the obtained results follows the sensitivity analysis. Closing remarks are presented in the last section of the paper. Metering Equation As it is explained in the introductory part of this paper, traffic volume arriving at some spot inside a signalized arterial street may be affected by the upstream bottlenecks. The traffic volumes used as an input to arterial street analysis are predicted or measured. An analysis of an 4

arterial street produces correct results if the control and traffic conditions assumed for calculations are the same as those assumed in prediction or those occurring during the measurement. The results may not be correct if the input traffic volumes are used to evaluate the arterial with redesigned or new signals and geometry. Changes of the intersections capacities may change the metering conditions along the arterial and, consequently, the actual traffic volumes may be different than used in the analysis. The preceding discussion points out that the input traffic volumes require adjustment prior to their use in calculations if the analysis evaluates an arterial with metering conditions different from those during the measurement. Since metering takes place during congested conditions, vehicle queues are long enough to affect the arterial performance even after the volumes drop below the capacities. Therefore, traffic input to the analysis must include not only traffic volumes but also initial queues present at the beginning of the period of analysis. This additional requirement is not new and has already been made in the 1997 update of HCM for signalized intersections. To have a full picture of metering conditions during which the traffic volumes were measured the capacities of bottlenecks suspected for metering traffic should be provided, too. The use of this new piece of data will be discussed later. Let us consider variables for a pair of intersections. The arriving traffic at the upstream intersection is represented through volumes v ui. The subscript u indicates the upstream intersection, the subscript i indicates the lane group. The portion of the vehicles in the upstream lane group i that intend to enter the considered segment is denoted as u i. The metering conditions in the upstream lane group i is represented by the capacity c ui, the initial queue Q ui at the beginning of period of analysis. As the effect of metering at the upstream intersection, the traffic enters the segment at the rate v ei that can be different from the rate of arrivals u i v ui. The volume entering between the intersections is denoted as v em and exiting the segment between the intersections is v xm. The volumes of movements at the downstream intersection are v dr, v dt, and v dl. Some of these variables are presented in Figure 1. The total volume of vehicles using the segment is v = v em + Σ i v ei = v xm + Σ i v di. The analysis focuses on the volume v d of some downstream lane group. The proportion p = v d /v and proportions f i = v ei, /v will be used in the further part of this presentation. Most of the variables introduced in the preceding paragraph are sensitive to the upstream traffic conditions. As explained in the introductory paragraph of this section, the control and geometry conditions for which the input data were obtained are not necessarily those for which the arterial is evaluated. The first conditions will be called input conditions and the corresponding variables will be denoted with an additional subscript 0. The later conditions will be called design conditions and the corresponding variables will be as introduced above. The proportions u i and p are rather insensitive to changes in metering conditions. These two variables will be calculated using the input volumes and used for the design conditions as well. Let us consider a pair of signalized intersections with metering of some streams at the upstream intersection. The fact that some streams are metered and some streams are not is reflected in the proposed method by breaking down the total traffic v 0 into two components: 5

(1) Total volume Σ i v ei,0 entering the segment at the upstream intersection. These volumes may be affected by changes in signals or geometry at the nearest upstream intersection and even by other intersections located further upstream. The new total volume for the design conditions is Σ i v ei. (2) Volume (v 0 - Σ i v ei,0 ) entering the arterial from the side streets and driveways between the upstream and considered intersections. This total volume is not metered and it stays the same for both the input and design conditions. The actual total volume of vehicles using the segment in the design conditions is: v = v 0 - Σ i v ei,0 + Σ i v ei (1) Since v d = p v and v d,0 = p v 0, the actual volume in the considered downstream lane group is: v d = v d0 - p (Σ i v ei,0 + Σ i v ei ) (2) The next step in deriving a practical metering equation is to propose equations for v ei,0 and v ei. Let us discuss the design conditions. The initial overflow queue Q ui in the upstream lane group i at the beginning of the period of analysis T must be given. An additional number of vehicles v ui T arrive during period T. The total number of vehicles (Q ui + v ui T) will pass the upstream intersection during time T only if this number of vehicles does not exceed the maximum number c ui T. Otherwise, the number of vehicles passing the upstream intersection equals the maximum number. This is in the case of metering. The excess of vehicles forms a residual queue that can be used as an initial queue in calculations for the next interval. The number of vehicles discharging from the upstream lane group i during the period of analysis can be expressed as min ( Qui + vui T, cui T ). The number of vehicles is then divided by T to obtain the corresponding average flow rate. The final equation for v ei is: Qui v ei = ui min + vui, cui (3) T Applying the same consideration to the input conditions yields a similar equation for v ei,0. Using Equation 3 in Equation 2 gives the following metering equation: Qui,0 Qui v d = vd 0 p ui min + vui,0, cui, 0 min + vui, cui (4) i T T Equation 4 calculates the traffic volumes at the downstream lane groups for the design conditions. It involves variables representing the design conditions at the upstream intersection. Thus, the upstream intersection has to be considered before the downstream intersection. This dependence determines the order of calculations. The first intersection on the arterial has to be considered first since no metering effect (v d = v d0 ) can be assumed for this intersection. Then, the second intersections can be treated, and so on. 6

The analysis should start with the first interval T affected by changes in metering. Typically, the first interval is the one during which no metering takes place along the arterial during the measurement and for the assumed design conditions (all volumes are below corresponding capacities). It is obvious that if the arterial is analyzed for the existing conditions (no change in capacities and in metering conditions), then v d = v d0 for all intersections. Another case occurs when the input volumes v d0 are predicted with the assumption of no capacity constraints. Such an assumption entails volumes below capacities (v ui,0 < c ui,0 ) and lack of overflow queues (Q ui,0 = 0). Equation 4 simplifies to the following: Qui v d = vd 0 p ui vui,0 min + vui, cui (5) i T Of course, no volume adjustments are needed (all v d = v d0 ) if no overflow takes place in both the input and design conditions (all v ui,0 < c ui,0 and v ui,0 < c ui ). Notice that in this case, all v ui,0 = v ui. Example Calculations An example pair of intersections is shown in Figure 1. The data describe current conditions. The volumes shown were measured in the field. Traffic conditions are poor in the upstream lane group no. 2 due to the lack of capacity. The conditions will be improved by increasing this capacity from the original 1760 veh/h to 2200 veh/h. The task is to estimate delays at the both intersections for both the present and design conditions. Evaluating the current conditions does not require adjusting traffic volumes, since the measured values already reflect the effect of the upstream metering. The traffic volumes coming from the side streets are not metered in the input conditions, as indicated by the capacities and the zero average overflow queues. Further, the design capacities are the same as the input values, thus the entering volumes v e1 and v e3 are equal to u 1 v u1 = 100 veh/h and u 2 v u2 = 150 veh/h, respectively. All the capacities, queues, and volumes describing these two streams are the same in both the input and design conditions. An increase of the capacity from 1760 veh/h to 2200 veh/h is expected for the second upstream lane group. Since the traffic in this lane is metered in the input conditions, this change will affect the downstream volume. The following calculations estimate this effect on the traffic arriving in the downstream lane group carrying right-turn and through movements. Splitting proportions u i and p u 2 = v ut2 /v u2 = 1800/2000 = 0.900 v 0 = v xm + v dr0 + v dt0 + v dl0 = 45 + 184 + 1471 + 184 = 1884 veh/h v d0 = v dr0 + v dt0 = 184 + 1471 = 1655 veh/h p = v d0 /v 0 = 1655/1884 = 0.879 7

Downstream volume in design conditions v d Since the side street volumes are the same in the input and design conditions, they are not included in Equation 4. EQu 2,0 E 2 0 2 min 2,0, 2,0 Qu vd = vd p u + vu cu min + vu2, cu2 T T vd = 1655 0.879 0.9 [ min( 0 / 0.25 + 2000, 1760) min( 0 / 0.25 + 2000, 2200) ] vd = 1655 0.879 0.9 ( 240) = 1845 veh/h Filtering will be estimated for the input and design conditions after the method is introduced in the following section. Filtering Equation Let us consider a lane group at a signalized intersection influenced by another signalized intersection located upstream of the considered one. Typically, three lane groups at the upstream intersection (one on the arterial street and two on the side streets) are used by vehicles that eventually arrive in the considered downstream lane group. In addition, some vehicles enter the arterial street between the two intersections. The vehicle streams crossing the upstream stop-lines are subject to filtering, thus their initial variations can be altered at the upstream intersection. This effect can be described with a filtering equation applied to each filtered stream: 0.627 Qu I e = I u exp 1.3 (6) I uc vu / 3600 where: I e = variance-to-mean coefficient for the stream entering the street at the upstream intersection after being filtered, I u = variance-to-mean coefficient of the stream arriving in the upstream lane group, EQ u = average overflow queue in the upstream lane group during the analyzed period, v u = volume using the upstream lane group during the analyzed period. Equation 1 was developed by Van As (1991). An alternative equation that does not include the overflow queue can be found in Tarko and Rajaraman (1998). The alternative equation is applicable only to steady state traffic. Both the equations were compared for the steady state conditions and were found to produce very similar results. The stream passing the upstream stop-line splits at the upstream intersection and only some vehicles proceed towards the downstream lane group. This splitting -- equivalent to random selection of vehicles -- increases the variations of vehicle streams heading towards the downstream lane group. This effect is described with the following equation (Tarko and Rajaraman, 1998): I = u (1 I ) (7) 1 e 8

where: I = variance-to-mean coefficient of the stream resulted from the splitting, u = sub-stream volume divided by the original stream volume, I e = the variance-to-mean coefficient of the original stream. The streams flowing from the upstream intersection legs merge into one stream and then merge again with vehicles entering the arterial street between the two signals. The combined new stream the total stream approaching the downstream intersection has the variance-to-mean coefficient I: I c where: I c = variance-to-mean coefficient of the combined (merged) stream, f i = volume of original stream i divided by the volume of the combined stream, I i = variance-to-mean coefficient of original stream i. = n i= 0 f The total stream approaching the downstream intersection undergoes one more transformation when it splits between the considered and other lane groups on the downstream approach. The combined effect of filtering, splitting, and merging taking place between the two intersections can be described with the following equation: i I i (8) I = 1 p f u (1 I ) (9) d i i i where p = v d /v, f i = v ei /v, and u i = v uki /v ui, and v d = volume in the downstream lane group, v = total volume of vehicles using the segment, v uki = volume of vehicles arriving in the upstream lane i and intending to enter the segment (movement k), v ui = arriving volume in the upstream lane group i, I ei = variance-to-mean coefficient of the stream entering the segment from the upstream lane group i (calculated using Equation 6). Equations 6 and 9 suffice to estimate the downstream coefficient I d. It should be mentioned here that Equation 6 was derived assuming fixed capacity of the upstream bottleneck (zero variance of capacity). The proposed method does not include the effect of dispersion too. The estimate is close to the true value for closely spaced signals, but it may be an underestimation in cases of a considerable dispersion of vehicle platoons between signals. This weakness can be mitigated by adding a function of the distance between the signals as an adjustment to the equation. ei This section has presented only the primary points of the method of estimating the coefficient I d for lane groups affected by upstream traffic signals. The reader is asked to refer to Tarko and Rajaraman (1998) for the details of derivation and discussion. 9

Example Calculations Figure 1 provides an example pair of intersections and data needed to calculate the variance-tomean coefficient for a selected lane group at the downstream intersection. Two cases are considered: input (existing) and design conditions. Existing conditions The streams entering the segment between the signalized intersections are assumed Poisson streams. Since I e = 1 for such streams, terms representing them in Equation 9 are equal zero and are not included. Total volume on the segment v 0 = 1884 veh/h v d0 = 184 + 1471 = 1655 veh/h Splitting proportions u i and p and merging proportions f i u 1 = 100/300 = 0.333 u 2 = 1800/2000 = 0.900 u 3 = 150/150 = 1.0 p = v d0 /v 0 = 1655/1884 = 0.879 v e1,0 = u 1 v u1,0 = 0.333 300 = 100 veh/h v e2,0 = u 2 min[q u2,0 /T + v u2,0, c u2,0 ] = 0.9 min[0/0.25 + 2000, 1760] = 1584 veh/h v e3,0 = u 3 v u3,0 = 1.0 150 = 150 veh/h f 1,0 = v e1,0 /v 0 = 100/1884 = 0.053 f 2,0 = v e2,0 /v 0 = 1584/1884 = 0.841 f 3,0 = v e3,0 /v 0 = 150/1884 = 0.080 Coefficients I e for the entering upstream streams I ei,0 = Iui,0 exp 1.3 I e,0 = 1.0 exp 1.3 I e,0 = 1.0 exp 1.3 I e3,0 = 0.566 I ui,0 EQ Cv ui,0 ui,0 / 3600 0.627 0.627 1 = 33.7 1.0 120 2000 / 3600 0.5 1.0 120 300 / 3600 0.627 2 = 0.042 0.664 10

I d for the downstream left-turn and through lane group I = p f u (1 I ) d,0 1 i,0 i ei, 0 i I d,0 = 1-0.879 [0.053 0.300 (1-0.664) + 0.841 0.900 (1-0.042) + 0.080 1.0 (1-0.566)] I d,0 = 1-0.879 0.765 = 0.328 Design conditions Total volume on the segment v e2 = u 2 min[q u2 /T + v u2, c u2 ] = 0.9 min[0/0.25 + 2000, 2200] = 1800 veh/h v = v em + v e1 + v e2 + v e3 = 50 + 100 + 1800 +150 = 2100 veh/h Splitting proportions u i and p and merging proportions f i Splitting proportions are the same as for the input conditions. f 1 = v e1 /v = 100/2100 = 0.048 f 2 = v e2 /v = 1800/2100 = 0.857 f 3 = v e3 /v = 150/2100 = 0.071 Coefficients I e for the entering streams Only the upstream through stream has to be reconsidered. The vales of Ie for other stream do not change compared to the input conditions. I I e2 e2 = I u2 exp 1.3 = 1.0 exp 1.3 I u 2 EQ Cv u2 u2 / 3600 0.627 = 4.3 1.0 120 2,000 / 3600 0.627 = 0.419 I d for the downstream left-turn and through lane group I = 1 p f u (1 I ) d i i i ei I d = 1-0.879 [0.048 0.300 (1-0.664) + 0.857 0.900 (1-0.419) + 0.071 1.0 (1-0.566)] I d = 1-0.879 0.484 = 0.574 11

Sensitivity Analysis The 1997 update of Highway Capacity Manual does not clearly instruct how to deal with the metering effect of upstream signals on signalized arterial streets. The term filtering/metering adjustment factor used for the variance-to-mean coefficient I may incorrectly prompt that the metering is incorporated. No recommendations are made as to how to adjust the volumes along the arterial street under the presence of upstream congestion. Consequently, the user of HCM can limit the consideration of filtering and metering to the application of the adjustment factor I. The volumes, whether measured in the field or predicted, are very likely to be used directly to calculate delay at intersections and to estimate the travel speed along arterial streets. Let us compare the results obtained using this approach with the approach proposed in this paper to show and discuss the differences. An arterial street to be considered has eight signalized intersections. The straight-ahead movements along the arterial street use exclusive two lanes at each intersection. Capacities of the straight-ahead lane groups listed in the order of intersections are 1600, 1500, 1400, 1300, 1300, 1400, 1500, and 1600. It is assumed that the turning volumes experience neither metering nor filtering. In this setup, and with strong straight-ahead movement, metering can occur at some intersections along the first half of the street section. No metering or weak metering is expected along the second half of the section. The filtering effect is growing along the arterial and it reaches its maximum strength at the fifth and following signals. On the considered arterial, volume of traffic entering and exiting the arterial street through the side streets is the same at each intersection. This means that if, for example, 10% of the traffic observed beyond the first intersection has entered the arterial street from the side street at the first intersection, then 10% of the traffic exits the arterial at the second intersection. The proportion of turning volume is the same at the first and at all the remaining intersections. Thus, if there is no metering, all the straight-ahead lane groups should carry the same traffic volume (but not necessarily the same vehicles). The traffic on this arterial can be represented with one straight-ahead volume on the entrance to the arterial and through one proportion of turning volumes. Please notice that since the arterial lane group carries exclusively the straight-ahead movement, the proportion u equals 1. The proportions p and f are equal one to another. For the example using 10% turning volumes, the proportions p and f take the value of 0.9. The example with balanced turning volumes has been chosen for the convenient representation of traffic pattern along the entire arterial. Any general conclusions should not be affected by this simplification, though. A set of volumes ranging from 800 through 1800 veh/h has been considered for three turning patterns: virtually no turning volumes (p=f=1), moderate turning volumes (p=f=0.8), and strong turning volumes (p=f=0.5). Other arterial characteristics are shown in Table 1. The following algorithm was used in the calculations: 1. Assume no filtering (I u = 1) and no changes in metering upstream of the first signal (v d = v d0 ). Calculate delays and other performance measures for the first signal. 12

2. For the next signal: Calculate v d for all lane groups using Equation 11 or 12. Qui0 If vd 0 < p ui min + vui0, cui0 (negative none-metered volumes) i T Qui then assume v d = p ui min + vui, cui. i T Calculate I d for all lane groups using Equations 1 and 5. Calculate delays and other performance measures for this signal. 3. If there are more signals then repeat step 2, otherwise move to step 4. 4. Calculate the aggregated performance measures for the entire arterial (travel speed). The travel speeds of through vehicles along the arterial street are compared in Figure 2. In the proposed method, arterial performance is sensitive to the level of turning volumes. This is as expected. Strong turning volumes (50% of total traffic in this case) convert the arterial system into a collection of nearly isolated intersections. By the way, this fact should also be reflected in the type of arrivals that should be assumed as for isolated intersections. We did not do this to expose the differences produced by filtering and metering. The present method generates one line since it does not distinguish between various levels of turning volumes. A breaking point in otherwise smooth curves occurs at volume of 1300 veh/h. This volume equals the capacity of the bottleneck, thus this is a critical volume above which metering occurs. The results for the volumes below 1300 veh/h reflect the sole effect of filtering. The results obtained with the present HCM method follow the results produced with the proposed method for the case without turning volumes. The largest difference between the two methods is 5 km/h. A quite considerable difference occurs when metering is in effect. It must be stressed, for the fairness of the analysis, that if the input volumes were measured in the conditions close to the evaluated ones, then these differences would be smaller. Nevertheless, the sensitivity analysis demonstrates a danger of considerable underestimation of the travel times if the metering is improperly incorporated. Figure 3 demonstrates a strong effect of turning volumes. The shown case of 1700 veh/h reflects the joint effect of filtering and metering. The current method yields results identical to the results obtained in the proposed method if the through movement is only 10 % of the total stream. It should be emphasized that in the investigated case, the turning volumes entering the arterial are neither filtered nor metered. The full version of the method allows for the consideration of metering of movements other then straight ahead, but this makes the method more complicated. Figure 4 presents (v/c) ratios along the investigated street obtained for the present and proposed methods. The current method does not adjust the input volumes (v 0 = 1800 veh/h shown in the figure), thus (v/c) i = (v 0 /c i ) where c i is the capacity at intersection i. The effect of metering is not incorporated. The most interesting point conveyed by Figure 4 is that overflow can occur even downstream of the bottleneck. If the turning volume is strong and non-metered, then even strong metering along the arterial will not prevent congestion downstream of the intersection with the lowest capacity. It happens when the additional traffic entering the arterial from the side streets exceeds the increase in the capacities along the arterial. 13

Closing Remarks This paper presented a new method of incorporating filtering and metering along signalized arterial streets. The method fits the framework based on fixed volumes rates in periods of analysis. Filtering and metering, and conditions of their occurrence have been clearly defined. The set of equations has been derived using clearly stated assumptions. The paper discusses conditions where adjustments of measured or predicted volumes are not needed and where adjustments are required. The proposed method incorporates the effect of turning volumes, a feature not present in the current HCM method. The sensitivity analysis has indicated the significant effect of turning volumes. The differences in the results obtained from both the methods are considerable. The proposed method tends to produce travel speeds along signalized arterial streets higher than the current method, which addresses the concern raised by some users of HCM that the current method underestimates the travel speed along arterial streets. The filtering equation has been derived with several simplifying assumptions (no dispersion, fixed capacity). Under some conditions, the filtering equation may underestimate I. This can be remedied by adding additional adjustments. It must be noted though that, in most cases, the proposed method produces I estimates higher than in the current HCM method. The proposed method does not incorporate the effect of long queues blocking upstream lane groups. The method should provide a good estimate of the average travel speed along the entire arterial section, although the travel speed estimates along some individual segments may be biased. The effect of long queues can be incorporated by adding an additional constraint on the number of vehicles passing a stop line depending on the length of the downstream queue. This improvement is beyond the scope of this paper. Further research is required to incorporate the effect of vehicle dispersion along long segments, as well as signal actuation. These additional factors increase the variability of traffic streams. It is rather doubtful that a simple and comprehensive model that includes the two mentioned factors can be derived using the theoretical approach. Adjustments of the values obtained in the presented method should be considered as a practical alternative. Such adjustment factors could be quantified using field observations and/or computer simulation. 14

Literature Tarko, A. and Rajaraman G. (1998). "Effect of Traffic Metering, Splitting, and Merging on Control Delays in Signalized Networks," Proceedings of the Third International Symposium on Highway Capacity, Rysgaard (ed.), Vol.1, Copenhagen, published by Ministry of Transport of Denmark, Copenhagen, Denmark, pp.1007-1158. TRANSPORTATION RESEARCH BOARD, (1997). Highway Capacity Manual, Special Report 209, National Research Council, Washington, D.C. VAN AS, S. C., (1991). Overflow Delay in Signalized Networks, Transportation Research, Part A, Vol.25A, No. 1, pp. 1-7. 15

Table 1 Arterial characteristics for the sensitivity analysis 6HJPHQW,QSXW 1 2 3 4 5 6 7 8 &\FOHÃ/HQJKÃ& 60 60 60 60 60 60 60 60 (IIHFWLYHÃJUHHQÃWRÃF\FOHÃOHQJWKÃUDWLRÃJ& 0.4 0.4 0.4 0.3 0.3 0.4 0.4 0.4 &DSDFLW\ÃRIÃODQHÃJURXSÃFÃYHKK 1600 1500 1400 1300 1300 1400 1500 1600 $UULYDOÃW\SHÃ$7 3 5 5 5 5 5 5 5 /HQJWKÃRIÃVHJPHQWÃ/ÃNP 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 $UWHULDOÃFODVVÃ$& II II II II II II II II )UHHIORZÃVSHHGÃ))6ÃNPK 55 55 55 55 55 55 55 55 8QLWÃUXQQLQJÃWLPHÃ75ÃVNP 75 75 75 75 75 75 75 75 3URJUHVVLRQÃDGMÃ)DFWRUÃ3) 1.00 0.33 0.33 0.33 0.33 0.33 0.33 0.33 $GMXVWPHQWÃIRUÃDFWXDWHGÃFRQWUROÃN 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 16

,XÃ Ã 4XÃ ÃÃYHK (4XÃ ÃÃYHK FXÃ ÃÃYHKK ÃÃ FXÃ ÃÃYHKK YXÃ ÃÃYHKK XÃ Ã,XÃ Ã 4XÃ ÃÃYHK (4XÃ ÃÃYHK FXÃ ÃÃYHKK YXÃ ÃÃYHKK XÃ Ã Ã,XÃ Ã 4XÃ ÃÃYHK (4XÃ ÃÃYHK FXÃ ÃÃYHKK YXÃ ÃÃYHKK XÃ Ã ÃÃY[PÃ ÃÃYHKK YHPÃ ÃÃYHKK &\FOH& V YÃ ÃÃ ÃÃYHKK 3HULRGRIDQDO\VLV 7 K ÃÃÃYGÃ ÃÃYHKK ÃÃÃÃ Figure 1 Intersections for example computations 17

Capacities: 1600, 1500, 1400, 1300, 1300, 1400, 1500, 1600 40 Travel Speed (km/h) 30 20 10 Proposed, strong turns Current Proposed, moderate turns Proposed, no turns 0 800 1000 1200 1400 1600 1800 Input Volume (veh/h) Figure 2 The effect of volume on the travel speed along the analyzed arterial street 18

40 Capacities: 1600, 1500, 1400, 1300, 1300, 1400, 1500, 1600 Input volume = 1700 veh/h Travel Speed (km/h) 30 20 10 0 Proposed Current 0 0.2 0.4 0.6 0.8 1 Proportions of Through Traffic p and f Figure 3 The effect of turning volumes on the travel speed along the analyzed arterial street 19

Capacities: 1600, 1500, 1400, 1300, 1300, 1400, 1500, 1600 Input volume = 1800 veh/h 1.60 1.40 1.20 Current Proposed, strong turns v/c 1.00 0.80 0.60 Proposed, moderate turns Proposed, no turns 0 1 2 3 4 5 6 7 8 Signal Figure 4 Values of (v/c) ratio along the analyzed arterial street 20

List of Tables Table 1 Arterial characteristics for the sensitivity analysis List of Figures Figure 1 Intersections for example computations Figure 2 The effect of volume on the travel speed along the analyzed arterial street Figure 3 The effect of turning volumes on the travel speed along the analyzed arterial street Figure 4 Values of (v/c) ratio along the analyzed arterial street 21