Ning Wu Institute for Traffic Engineering Ruhr University Bochum, Germany Tel: ; Fax: ;

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1 MODELLING THE IMPACT OF SIDE-STREET TRAFFIC VOLUME ON MAJOR- STREET GREEN TIME AT ISOLATED SEMI-ACTUATED INTERSECTIONS FOR SIGNAL COORDINATION DECISIONS Donmei Lin, Correspondin Author Center for Advanced Transportation Education and Research and Education (CATER) University of Nevada, Reno N Virinia St, Mail Stop, Reno, NV Tel: --; lindonmei@mail.com Nin Wu Institute for Traffic Enineerin Ruhr University Bochum, Germany Tel: +-0- ; Fax: +-0- ; nin.wu@rub.de Zon Tian Center for Advanced Transportation Education and Research and Education (CATER) University of Nevada, Reno N Virinia St, Mail Stop, Reno, NV Tel: --; Fax: --; zont@unr.edu Dian Mao Center for Advanced Transportation Education and Research and Education (CATER) University of Nevada, Reno N Virinia St, Mail Stop, Reno, NV Tel: --; dmao@unr.edu Word count:,words text + tables/fiures x 0 words (each) =,0 words July, 0

2 Lin, Wu, Tian and Mao 0 0 ABSTRACT Sinal coordination is enerally reconized by traffic enineers as a beneficial stratey for improvin arterial traffic proression and safety. Previous research on the criteria for establishin sinal coordination plans has been focused on more objective factors such as intersection distance, arterial traffic volume, travel time, platoon dispersion and combinations of these factors. They provided useful uidance for sinal coordination decisions, especially durin peak hours. However, as traffic is usually less heavy durin off-peak hours, the number of stops would have more influence on driver perception of traffic efficiency. This paper developed a mathematical relationship between arterial reen time ratio and side-street traffic volume, which can serve as the theoretical foundation for determinin sinal coordination based on number of stops. The paper investiated how side-street traffic volume would affect major-street reen time ratio when an isolated intersection is runnin semi-actuated sinal operation. A probabilistic model was proposed to address this issue. The model was validated aainst simulation results and the upper limit of side-street traffic volume was defined for the model application. Followin the proposed model, the paper briefly introduced how a traffic enineer can use the model results to make sinal coordination decision based on the expected number of stops. A real case study was conducted. It was found that the model can successfully analyze the impact of side-street traffic volume on major-street reen time at isolated intersections where left turns are permitted. The method for sinal coordination decision can be adopted to determine the time periods of runnin sinal coordination plans. The method and the results may be useful to traffic enineers for the effective manaement of traffic sinal networks. Keywords: Traffic volume, Green time ratio, Sinal coordination, Number of stops, Probability

3 Lin, Wu, Tian and Mao INTRODUCTION Sinal coordination has lon been reconized as havin beneficial effects on the quality of traffic flow alon a street or arterial (-). Good sinal coordination can also enerate measurable safety benefits (-) and reduce emissions (, ). Despite the advatanes of sinal coordination, there lack widely accepted standards in traffic aencies for when to implement sinal coordination. Various studies have been conducted reardin the criteria of establishin sinal coordination plans. Intersection distance has been recommended in manuals and research as a criterion to support sinal coordination decision, but these sources do not provide uniform uidelines for aencies to determine whether coordination is necessary. The Manual on Uniform Traffic Control Devices (MUTCD) provides the uidance that traffic sinals within 00 meters (0. miles) of each other alon a corridor should be coordinated unless operatin on different cycle lenths (). The Traffic Sinal Timin Manual (STM) states that when the intersections are in close proximity and there is a lare amount of traffic on the coordinated street, establishin coordination would be easily justified (). Besides considerin intersection distance, traffic enineers may develop their own standards on when traffic volume is substantially hih to coordinate sinals. A number of simple criteria have been developed in previous research that do not directly incorporate a platoon dispersion model to determine whether two intersections should be coordinated. Robertson and Hunt (0) used reduction in queue, a function of travel volume and travel time between intersections, as a coordination criterion. The Traffic Sinal Book introduced a criterion for coordinatin sinals considerin both intersection distance and two-way peak hour volume (). When the ratio of two-way peak-hour link volume (vph) over link lenth (feet) exceeds 0., the intersections should be coordinated. Chan and Messer developed the intercoordination desirability index () incorporatin factors such as travel time, traffic flow and number of lanes, and recommended interconnection for two adjacent sinalized intersections when the index exceeds 0.. These simple criteria can be adopted to uide sinal coordination decisions. They may also be employed to establish boundaries between sections of coordinated sinals. However, adoptin these criteria may still result in conflictin recommendations, so enineerin judment plays a sinificant role in real practice to determine sinal coordination. Some other research incorporated platoon dispersion models for the development of coordination plans. Robertson interated the concept of delay minimization with a formalized platoon dispersion model (). Manar and Baas () studied platoon dispersion under various traffic volumes. Their study provided evidence for sinal coordination needs durin peak hours and suested that further study is necessary for sinal coordination decision durin off-peak hours. Simulation is often used to determine coordination requirements and benefits, particularly when performed in connection with retimin of traffic sinals (). Traffic enineers may employ a eneral model such as CORSIM and VISSIM, toether with a sinal timin proram, or may use the optimizaion features of a sinal timin proram such as Synchro/SimTraffic. In the latter case, coordination requirements and section boundary identification may be directly coordinated with the sinal retimin effort. Typically, sinal optimization software minimizes the total delays and the number of stops at intersections alon the subject arterial street. Usin delay and number of stops is a more perception-based approach to coordination desin compared to the aforementioned methods. A research report () specificly documented number of stops as a criterion for ood coordination plans used by Indiana Department of Transportation. It stated that an arterial sinal plan is acceptable when traffic proression alon the arterial is reasonably smooth and most of the drivers movin alon the arterial street do not stop at two consecutive intersections. Based on the probability of makin a certain number of stops, a model was proposed to determine when to turn on sinal coordination plans and the relationship between reen time ratio and traffic volume was

4 Lin, Wu, Tian and Mao assessed usin simulation tools (). However, to the authors best knowlede, no such research has established a direct relationship between traffic volume and reen time ratio on an arterial. Therefore, coordination decisions based on number of stops may use more valid theoretical evidence. When traffic is usually less heavy durin off-peak hours, number of stops would have more influence on driver perception of traffic efficiency. This is the basis for enineers usin number of stops as a criterion to determine whether to implement sinal coordination durin offpeak hours. This paper aims to develop a mathematical relationship between arterial reen time ratio and side-street traffic volume, which can serve as the theoretical foundation for determinin sinal coordination based on number of stops, especially durin off-peak hours. The remainin of this paper is oranized as follows. Problem statement and model assumption are provided in the next section. A probabilistic model is then proposed to address how side-street traffic volume will affect the reen time ratio of an arterial street at an isolated semiactuated intersection. The model validity is tested aainst simulation results and the upper limit of side-street traffic volume is defined for the model application. Sensitivity analyses are also included and the critical parameters are identified. Followin the proposed model, the paper briefly introduces how a traffic enineer can use the model results to make sinal coordination decisions. The summary and conclusions are provided in the end. PROBLEM DESCRIPTION AND ASSUMPTIONS Durin off-peak hours, especially at low volume conditions, sinalized intersections (with an arterial street and a side street) can run semi-actuated sinal operation. Detectors are placed at the approaches, which usually include side-street movements and in some cases the major-street left-turn movements. Green time will remain on the major-street throuh movements unless there is demand for the movements. A movement is served only when a vehicle demand of that phase is detected. When this phase is in service, it retains the riht of way for a minimum reen time and additional time can be iven in the form of passae time if more vehicles are detected. If there is enouh traffic, extensions will be added to the phase up to some set maximum reen time. However, if another call is not received durin the reen time, the phase will ap out. Under this semi-actuated operation, the reen time of each -movement phase depends on the detected demand of that movement. Because there is no detection for major movements, the reen time of major movements is also determined upon the -movement demand. In order to model the effect of side-street traffic volume on major-street reen time, the followin problem description is provided. Certain assumptions are made to mathematically develop the model. Problem Description At an isolated four-le intersection, the sinal is runnin semi-actuated operation without fixed cycle lenth. The traffic volume is at a relatively low level. Both the major street and the side street have their own minimum reen time. The riht-of way (reen sinal) will remain on the major street unless there is a demand from the side street. Side-street demand will be served after the major street reaches minimum reen plus its yellow and all-red intervals. The model is to calculate the major-street reen time ratio under different volume scenarios. Model Assumptions and Pre-defined Factors The followin assumptions are made so that the model can be mathematically derived. ) The traffic demand on the two side-street approaches is combined. The major street vehicle arrival is independent from any upstream intersections and is considered random.

5 Lin, Wu, Tian and Mao ) The basic model does not consider major-street left-turn phases, assumin that left-turn movements are permitted durin major-street throuh-movement phases. The model only investiates semi-actuated intersections, so it is assumed that no detection is provided for the major movements. As a result, major-street traffic flow does not influence the majorstreet sinal, so it is not modeled. ) Major-street sinal does not account for extension due to the assumption that no detection is available on major movements, as well as the confiuration that reen time is defaulted to remain on the major street. ) Side-street sinal accounts for reen time extension. Side-street sinal will run for the minimum reen time and, if more demand exsits, can extend in the form of passae time up to maximum reen. Passae time is the maximum allowable headway (MAH) between two vehicles to extend the sinal. It is necessary to point out that the terms minimum initial and minimum reen are used interchaneably in some sinal controllers. However, in this paper, minimum reen equals the sum of minimum initial and passae time. (The MAH can be set to zero if no extension on the side street is considered.) ) Because the analysis is only for low-volume conditions, it is assumed that side-street vehicle demand would not be sufficiently hih to extend the sinal to maximum reen, so the model does not consider maximum reen time for the side street. Model Parameters Based on the problem description and the above assumption, the followin model parameters are defined. q : side-street traffic volume (vph) major_min _min : major-street minimum reen : side-street minimum reen y major : major-street yellow interval y : side-street yellow interval ar : major-street red clearance (all red) interval major ar major : side-street red clearance interval MAH : side-street passae time for sinal extension R : major-street reen time ratio major DEVELOPMENT OF A PROBABILISTIC MODEL Side-Street Vehicle Time Headway Distribution When side-street traffic volume is low, the vehicle arrivals are considered as random events. It is enerally accepted in related research that, when platoon is not considered, the time headway follows an exponential distribution or a shifted exponential distribution if a minimum headway applies. Time headway t follows Cowan s M distribution, as shown in Equation.

6 Lin, Wu, Tian and Mao f () t 0 q 00 t t q q ( ) q t 00 ( ) e t where ( 0) is the minimum safety headway. When equals zero, Cowan s M reduces to an exponential distribution. 0 0 Basic Model Development for Intersections with Permitted Left Turns on the Major Street Cycle Lenth Althouh no fixed cycle lenth applies under the semi-actuated opearation, a cycle of the sinal consists of three roups of intervals, includin reen time on the side street, reen time on the major street, and the clearance intervals between reen intervals. The cycle lenth is the sum of major-street reen time, side-street reen time and clearance intervals in between. C G G T () mean mean_major mean_ interreen Green Time Consumed by Side-Street When side-street sinal accounts for reen extension, the side-street reen time is the sum of minimum reen and extended reen time, G G () mean min ext where G ext is the mean reen extension time. Mean reen time extension on the side street is calculated as q Gext exp MAH MAH q q q Then Equation becomes () () G G mean min ext q exp _min MAH MAH q q q Green Time Consumed by Major-Street The mean reen time on the major street is calculated as ()

7 Lin, Wu, Tian and Mao 00 G ( ) ( Pr( t ) Pr( t ) mean_major major_min major_min major_min major_min q ( ) Pr( t ) major_min major_min q q () ( Pr( t )) major_min major_min q with the probability of ap on side-street bein less or equal to major_min q q Pr( t major_min ) ( ) exp( ( major_min )) () Clearance Time Consumed between Green Intervals Sum of clearance intervals is all the time intervals in between the major-street and side-street reen time, calculated as in Equation. T y ar y ar () interreen major major Major-Street Green Time Ratio The major-street reen time ratio is calculated as the mean reen time on the major street over the mean cycle lenth, Gmean_major Rmajor Cmean () Gmean_major G G T where mean_major mean_ interreen G mean_, G mean_major, and T interreen are shown in Equation,,and, respectively. Upper Limit of Side-Street Traffic Volume for Model Application The proposed model was to analyze the traffic operation under low volume condition, so we did not consider side-street queue dischare, which would happen when side-street volume is hih. When the averae queue dischare time is larer than or equal to the side-street minimum reen time, the model no loner fits. Due to this fact, an upper limit of side-street traffic volume, q, should be defined. An estimation of averae queue (measured in vehicles) when the side-street sinal turns reen is the averae number of arrivin vehicles when the side-street sinal was yellow and red durin last cycle, q Queueav ( major_min Tinterreen ). (0) 00 The queue dischare time is + Queueav Tdis l () s / 00 where l is start-up loss time and s is the saturation flow rate. Then the upper limit of q is derived by

8 Lin, Wu, Tian and Mao 0 _min T dis q ( major_min Tinterreen ) _min l 00 + () s / 00 ( _min l ) s q major_min Tinterreen. In Sinal Timin Manual (), a practical estimation of start-up loss time and saturation flow rate is sec and 00 vph. Then the upper limit of q can be estimated as ( _min l ) s 00( _min ) q () major_min Tinterreen major_min. The upper limit of side-street volume is a function of major-street and side-street minimum reen. When the side-street volume exceeds the limit, it is not recommended to use the proposed model to evaluate the impact of side-street volume on major-street reen ratio. MODEL VALIDATION WITH SIMULATION RESULTS A simulation model was developed usin Python script to validate the proposed probablistic model. The model enerated a random vehicle arrival and simulated the correspondin sinal operation process for a period of one hour under various volume scenarios. For each volume scenario, the simulation ran 00 times and the averae major-street reen time ratio was obtained. The results of the simulation model were compared to the calculated results from the proposed model to demonstrate that the proposed analytical model is able to represent the averae major-street reen ratio at semi-actuated intersections. FIGURE Comparison between Model and Simulation Results (Side-street vehicle time headway follows an exponential distribution).

9 Lin, Wu, Tian and Mao 0 0 FIGURE Comparison between Model and Simulation Results (Side-street vehicle time headway follows Cowan s M distribution). Comparison between the proposed model and simulation results is provided. The scenarios of sidestreet vehicle time headway followin both the exponential distribution (Fiure ) and Cowan s M distribution (Fiure ) were tested in the simulation. The rane of side-street traffic volume tested in the simulation was from to 00 vph. The derived upper limit of q under each sinal timin condition was also indicated in the curves. It can be concluded that the proposed model can appropriately estimate the major-street reen time ratio under different side-street volume scenarios. SIGNAL COORDINATION DECISION BASED ON THE PROPOSED MODEL The proposed model established a relationship between side-street traffic volume and major-street reen time ratio at an isolated intersection with semi-actuated sinal operation. It provides a foundation for sinal coordination decision based on number of stops. If the sinals on an arterial street of n intersections are runnin free (semi-actuated) and traffic volume is not hih, the vehicle arrival is assumed as a random process. Thus, the probability of a major-street vehicle hittin a reen liht at an intersection equals the major-street reen time ratio. Let p denote the probability of a major-street vehicle hittin a reen liht at intersection i, i and let ( R ) denote the major-street reen time ratio at intersection i. Then p major i ( R ). () i major i When a vehicle travels alon an arterial with n intersections, the probability of the vehicle makin x stops (0 x n) can be calculated by n Pr( X x) p j ( pk ) x ja kb where ()

10 Lin, Wu, Tian and Mao A a set of (n- x) intersections where the vehicle arrives at reen liht, B a set of x intersections where the vehicle does not arrive at reen liht and stops. If the major-street reen time ratios of the intersections alon the arterial are in close proximity, a ood approximation of Equation is a binomial distribution usin the mean of p. n n x x Pr( X x) ( p ) ( p ) x () n p pi / n i Consequently, the probability of a vehicle makin x or more stops when travellin on an arterial road with n sinals operatin free is determined as x n nm m Pr( X x) Pr( X x ) ( p ) ( p ) m0 x. () Sinal coordination decisions can be made based on Equation. When the probability of makin expected number of stops or more exceeds a certain value, sinals should run coordination; otherwise the sinals can run actuated control. In other words, when Pr( X x) K, sinals should run coordination. The application of this method requires two thresholds to be established. One is the number of stops ( x ), and the other is the probability of makin expected number of stops ( K ). As an example, Fiure depicts the probability of makin or more stops ( Pr( X ) ) alon an arterial with,, and sinals, with respect to various mean major-street reen time ratio ( p ). Assumin an arterial of sinals has a mean major-street reen time ratio of 0., and the thresholds are established as Pr( X ) 0., the probability of a major-street vehicle makin or more stops bein less than 0. will result in a decision not to run sinal coordination Mean major-street reen time ratio ( ) FIGURE Probability of Makin Two or More Stops alon an Arterial Case Study A case study was conducted to demonstrate the application of the proposed model and sinal coordination decision-makin procedure. n= n= n= i

11 Side-street traffic volume (vph) Lin, Wu, Tian and Mao Study Location Fourth St (SR) is one of the arterials in the city of Reno, Nevada that connects the Western and Eastern part of Reno. The study sement is a portion of the street in the downtown area with four sinals. All of the four sinals operate the way that matches the model assumptions. At each intersection, two major-street phases run concurrently with permitted left turns, and the same with two side-street phases. Hourly side-street traffic volume can be obtained for two of the intersections, i.e. the intersections at Arlinton and Ralston. The sinal timin confiurations required by the model for the two intersections are summarized in Table. The -hour volume profile is plotted in Fiure. TABLE Basic Sinal Timin Confiurations at the Study Location Intersection Major-street Major-street Major-street red Side-street Side-street minimum yellow clearance minimum yellow reen (sec) interval (sec) interval (sec) reen (sec) interval Side-street red clearance interval (sec) (sec) th /Arlinton th /Ralston Arlinton Ralston Hour FIGURE Side-Street Traffic Volume Profiles of the Two Intersections alon SR Analysis and Sinal Coordination Decisions The sinal coordination decision is based upon an established threshold. For the case study, the followin to thresholds are considered in the analysis: Pr( X ) 0. Pr( X ) 0. The first threshold describes the scenarios that more than 0% of the drivers make or more stops alon the study sement. The second threshold describes the scenarios that more than 0% of the drivers make or more stops. Once the threshold is established, the associated cut-off point of p can be obtained accordin to Equation. For the iven case, the two associated p values are 0. and 0., respectively. The proposed model can produce the major-street reen time ratio based on the traffic volume and basic sinal timin parameters at each intersection. Both the major-street reen time ratio ( R major ) and the upper limit of side-street traffic volume ( q ) need to be calculated. Obtainin the upper limit of q is used to verify if the model applies under the specific volume

12 Mean Major-Street Green Time Ratio Lin, Wu, Tian and Mao condition. The upper limits of q for the two intersections are indicated in Fiure. Ideally, data for each intersection alon the study arterial should be collected and then the proposed model can be applied to obtain each R. Due to the limit of data availability, only two major intersections have hourly traffic volume. For the demonstration of the decision-makin procedure, the author assumed that the four intersections have close major-street reen time ratios, and substituted the averae of R at the two intersections for the averae of all four intersections. The resultin -hour 0. major p and the two thresholds are illustrated in Fiure Hour FIGURE Hourly Mean Major-Street Green Time Ratio alon the Study Sement if Sinals Run Free For the case study, the time periods when the sinals should run coordination plans were determined based off Fiure and are summarized in Table. TABLE Recommended Time Periods to Run Sinal Coordination Plan alon the Study Sement Time period Threshold Peak Hour Off-Peak Hour (Run coordination) (No coordination) Pr( X ) 0. :-: 0:00-:, :-0:00 Pr( X ) 0. :-:0 0:00-:, :0-0:00 SUMMARY AND CONCLUSION The number of stops is one of the important criteria in sinal optimization and has been adopted in some jurisdictions as a criterion for a ood coordination plan. However, the factors that may impact number of stops have been researched less commonly in previous literature. This paper attemped to find the relationship between traffic volume and number of stops as the round of sinal coordination decisions. The paper first developed a mathematical model to establish the relationship between side-street traffic volume and the probability of a major-street vehicle arrivin at reen at an isolated intersection where the sinal is operatin semi-actuated. The model was developed for

13 Lin, Wu, Tian and Mao 0 low traffic volume conditions, so the upper limit of side-street traffic volume for the model to apply was derived. The model was validated aainst simulation results, and it can be concluded that the model can appropriately evaluate the major-street reen time ratio under low-volume scenarios. Based on the model, the probability of a major-street vehicile makin a certain number of stops or more was predicted by a probabilistic method. In order to determine the time periods for coordination plans, two thresholds need to be established: the expected number of stops, and the probability of expected number of stops. A case study was conducted for a arterials sement with four sinals, located in Reno, Neveda. The case study considered two criteria. One indicated a lower tolerance of number of stops, and the other hiher. It was found that a lower tolerance of number of stops would lead to a loner period of sinal coordination. The decision-makin method may be adopted by traffic enineers for the effective manaement of traffic sinal networks. The mathematical model proved a direct relationship can be established between side-street volume and major-street reen time ratio. However, this model is limited to intersections where left turns are under permitted operation. If left turns are protected, left-turn volume will also impact the throuh-movement reen time. To apply the method in more sinal operation conditions, it is worthwhile to develop a model that accounts for protected left turns. Discussion on this topic will be addressed in future studies.

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