A real-time signal control strategy for mitigating the impact of bus stops at urban signalized intersections

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1 Journal of Intelligent Transportation Systems Technology, Planning, and Operations ISSN: (Print) (Online) Journal homepage: A real-time signal control strategy for mitigating the impact of bus stops at urban signalized intersections Celeste Chavis & Eleni Christofa To cite this article: Celeste Chavis & Eleni Christofa (2017) A real-time signal control strategy for mitigating the impact of bus stops at urban signalized intersections, Journal of Intelligent Transportation Systems, 21:5, , DOI: / To link to this article: Accepted author version posted online: 31 May Published online: 31 May Submit your article to this journal Article views: 149 View related articles View Crossmark data Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at Download by: [Universiti Malaysia Terengganu] Date: 22 November 2017, At: 23:01

2 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 2017, VOL. 21, NO. 5, A real-time signal control strategy for mitigating the impact of bus stops at urban signalized intersections Celeste Chavis a and Eleni Christofa b a Department of Transportation and Urban Infrastructure Studies, Morgan State University, Baltimore, MD, USA; b Department of Civil and Environmental Engineering, University of Massachusetts, Amherst, MA, USA ABSTRACT Buses stopping at transit stops reduce the capacity of signalized intersections, which can lead to excessive delays for all users. In order to avoid such phenomena, signal control strategies can be utilized. This article presents a real-time signal control strategy to mitigate the impact of bus stop operations on traffic operations along an undersaturated approach. The objective of the proposed strategy is to ensure that any residual queues due to a bus stopping are fully dissipated as soon as possible by increasing the green time for the bus stop approach as soon as the bus departs. In addition, this strategy ensures that the cross-street approaches do not become oversaturated. Kinematic wave theory is utilized to track the formation and dissipation of queues and determine the green extension (or red truncation) for the subject approach. The benefits achieved from the proposed strategy are illustrated through simulation tests at a single intersection for a variety of bus stop and bus operation characteristics. Average delay and average queue length for the bus stop and cross-street approaches, as well as for the whole intersection, are used to assess the performance of the strategy. The tests performed indicate that the signal control strategy can achieve substantial reductions in delay for the bus stop approaches and the intersection as a whole without adversely affecting the cross street operations, when the demand at those cross streets is low. Introduction Efficient multimodal transportation systems are essential components for maintaining and improving the livability of our cities. However, the presence of multiple modes that differ in their dimensions and performance often complicates traffic operations and leads to underutilization of available capacity. Such an example is the existenceofbusstopsthatarecommoninurbanareas. Ifnobusbaysexist,busstopsblocklanes,reducingthe capacity of signalized intersections, and leading to excessive delays and potentially gridlock. Therefore, a comprehensive evaluation of the impact of bus stops on the capacity of signalized intersections and the development of signal control strategies to reduce this impact are critical for achieving efficient multimodal traffic operations and improving mobility for all users in urban networks. Multiple studies have performed real-time monitoring of traffic conditions on signalized arterials (Skabardonis & Geroliminis, 2008;Zheng,Ma,Wu,&Wang,2013)and other studies have specifically addressed real-time traffic signal control with transit operations (Yao et al., 2009; ARTICLE HISTORY Received 23 November 2014 Revised 17 November 2015 Accepted 2 May 2016 KEYWORDS bus stops; kinematic wave theory; real-time signal control; signalized intersection capacity Christofa & Skabardonis, 2011; Christofa,Papamichail, &Skabardonis,2013; Ma,Liu,&Yang,2013; Ghanim& Abu-Lebdeh, 2015;Christofa,Ampountolas,&Skabardonis, 2016). The impact of bus stops on traffic and transit operations, and in particular on traffic flow at signalized intersections has also been extensively studied (Coeymans & Herrera, 2003; Tang et al., 2009; Teply, Allingham, Richardson, & Stephenson, 2008; Yang, Gao, Zhao, &Si,2009; Zhao, Gao, & Jia, 2007; Zhao, Gao, & Li, 2008; Zhao, Jia, Gao, & Jiang, 2009; TRB,2010). However, several of the studies have not provided explicit formulas for estimating this impact (Tang et al., 2009; Zhao, Gao, & Jia, 2007; Zhao, Gao, & Li, 2008), or have investigated the impact in developing countries where bus stops are commonly located on the non-motorized traffic lane and the behavior of drivers is substantially different than in the United States (Coeymans & Herrera, 2003;Yang,Gao, Zhao, & Si, 2009; Zhao, Jia, Gao, & Jiang, 2009). Other studies have developed analytical formulas to estimate the impact as a function of the bus frequency and dwell time, thenumberoflanes,andthelocationofthesubjectbus CONTACT Celeste Chavis celeste.chavis@morgan.edu Department of Transportation and Urban Infrastructure Studies, Morgan State University, 1700 East Cold Spring Ln., Baltimore, MD 21251, USA. Color versions of one or more of the figures in the article can be found online at This paper was submitted to the Celebrating 50 Years of Traffic Flow Theory meeting in August 2014 in Portland, Oregon. Professor Robert Bertini handled the external review of this paper in accordancewiththe Journal of Intelligent Transportation Systems s peer review guidelines Taylor & Francis

3 350 C. CHAVIS AND E. CHRISTOFA stop with respect to the stop line (i.e., near-side vs. farside). However, some of these studies have not explicitly consideredtheimpactofthebusstop slocation(i.e.,distance from the stop line) on the capacity of the signalized approach (Teply, Allingham, Richardson, & Stephenson, 2008; Transportation Research Board [TRB], 2010). Only a recent analytical method has accounted for the location ofthebusstop,thebusdwelltime,andthebusfrequency when determining the impact of bus stops on capacity (Li, Chen, & Zhang, 2012). Whiletheimpactofbusstopsonthecapacityofsignalized intersections has been extensively studied, the literature on strategies that mitigate the impacts of bus stops on the capacity or delay of signalized intersections is very limited. A recent study by Gu, Cassidy, Gayah, and Ouyang (2013) investigated the impact of near-side bus stop location on the residual queue length and proposed a real-time bus holding strategy that ensures clearanceofthequeuewithinasignalcycle.however,thestudy used predicted arrival times instead of actual arrivals. The study was later extended (Gu, Gayah, Cassidy, & Saade, 2014) to estimate car and bus delays under the presence of bus stops assuming stochastic bus arrivals and both nearside and far-side bus stops. However, the proposed formulas assumed that the car arrival flow is always less than therestrictedcapacityduetothepresenceofabusata busstop.recently,gayah,ilginguler,andgu(2015)used variational theory to quantify the capacity of an isolated intersection when an obstruction is present downstream or upstream of the intersection. They also proposed an adaptive signal control that delays the beginning of the green phase when an obstruction is present in order to achieve minimum capacity loss. This study focused on oversaturated traffic conditions, while the signal control strategy assumed a priori knowledge of bus stop dwell time. In addition, it focused only on capacity, and did not report queue length or delays of the bus stop approach or the impact of the signal control strategy on performance measures of other intersection approaches and the intersection as a whole. Given the limitations of the literature, the objective of this study is to investigate the impact of near-side bus stops on the capacity of signalized approaches as a function of the bus stop s location, bus arrival time at the stop, and dwell times. The study investigates the impacts of those factors for cases where the car arrival flow is higher or lower than the restricted capacity when a bus is present at the bus stop during the green time interval, thus covering a variety of cases that can occur in reality. In addition, this study introduces an intelligent transportation system (ITS) that utilizes information on the bus stop s impact on capacity to implement a real-time signal control strategy after the bus leaves the stop in order to ensure clearance of the residual queue on the bus stop approach within the cycle(s) following the departure of a bus from its stop. The focus is on a well-timed signalized intersection for which all four approaches are undersaturated whennobusispresentatthebusstopandtheintersection approach becomes saturated as a result of a bus stop incident when the demand is higher than the capacity of M 1 lanes, where M isthenumberoftrafficlanesinthe subject approach. In addition, the methodology has been developed for isolated intersections that are not affected by traffic conditions at adjacent intersections, and therefore, no spillbacks from adjacent intersections are considered. Finally, the focus is on the impact of bus stops on the capacityoftheintersectiondownstreamofthebusstop. Research approach The proposed research is based on tracking traffic conditions in the time space domain while bus stops are both occupiedandunoccupiedbyabus.inordertodoso,kinematic wave theory (KWT) (Lighthill & Whitham, 1955; Richards, 1956) is utilized. In particular, it is assumed that traffic operations for an approach that contains a bus stop can be described by a triangular fundamental diagram. Other methods, such as variational theory (Daganzo, 2005;Hans, Chiabaut,&Leclercq, 2015), quantify capacity in a way that is consistent with KWT. In this article, the kinematic waves and time space diagrams areusedtoillustratethecompletequeuingdynamicsat an intersection. By illustrating traffic conditions as states onatime spacediagram,itispossibletoidentifythe formation and dissipation of queues and determine the impact of bus stop operations on traffic conditions (e.g., queue length, delays) in more direct ways than with variational theory. In addition, KWT allows for easily estimating the number of vehicles served under the influence of a bus stop incident and comparing it with when no bus is present at the bus stop in order to determine how many vehicles were left unserved due to the presence of the bus. This value is particularly useful in this study since it is used in the proposed signal control strategy to determine the additional green needed to clear the queues caused by the bus stop incident and to avoid oversaturation as quickly as possible. Once traffic conditions are depicted on a time space diagram, a signal control strategy is introduced. This strategy aims at increasing the green time for the bus stop approach as soon as it can after the bus is detected to have left the bus stop, in order to clear the additional queues created by the presence of the bus and avoid oversaturation of the subject approach as quickly as possible. Iftheimpactofthebusstopissmallandthegreentime interval of the next cycle is sufficient to clear the residual

4 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 351 queue, then no additional green time is provided for that approach. The proposed strategy can be implemented as an early green (i.e., red truncation) or green extension depending on the phase sequence. If green extension or red truncation is possible in the cycle where the bus stop incidentends,thenitisimplementedforaslongasit is allowable in order not to oversaturate the cross-street approaches.ifmoregreentimeisneededtoreducethe impact of the bus stop, then additional red truncation or green extension is implemented in the next cycle. Note also that this strategy is based on the assumption that the cycle length remains constant. However, the strategy could be easily adapted to account for variable cycle lengths. For illustrative purposes throughout this articleitisassumedthatthegreentimeintervalfor the bus stop approach precedes the red in a cycle, and therefore, the signal control strategy implemented corresponds to a green extension. In addition, this study calculates the maximum green extension or red truncation that is allowed so that the cross streets does not get oversaturated. The proposed methodology assumes knowledge of the triangular fundamental diagram, a constant demand level for the subject approach, q A, and a reduced capacity, q I, caused by a bus dwelling at a bus stop; see Figure 1. Itis also assumed that a bus dwelling at a stop would block one lane, which means that the reduced capacity q I is equivalent to the capacity of M 1 lanes, where M is the number of traffic lanes in the subject approach. Note that the proposed equations are applicable for any number of lanes per approach since the number of lanes only affects the capacity of the intersection approach, q A,andthereduced capacity, q I,causedbyabusdwellingatabusstop.Furthermore, the reduced capacity q I can also be adjusted to account for the loss of capacity due to lane-changing maneuvers occurring due to the presence of a bus at the stop. However, in the tests performed in this study, the loss of capacity due to the presence of a bus stop has not been taken into account; that is, it is assumed that the lanes that are not blocked by the presence of the bus operate at their full capacity. In addition, only bus stops that are located upstream of the subject approach are considered in this study and it is assumed that the exact bus stop location as measured from the stop line, X, isknown.notethat X is negative. It is also assumed that detection technologies such as Automated Vehicle Location (AVL) systems exist and can provide information on the bus arrival at the bus stop, T o,anditsdeparturefromthestop,t e,in real time. Note that no prediction of arrival or departure time is necessary since the signal control strategy is always implemented after the bus departs from the stop. It is further assumed that the bus dwell time does not exceed a cycle length, which is a reasonable assumption for most busstops.finally,itisassumedthatvehicledemandis availablethroughsensingtechnologiessuchasloopdetectors placed at upstream locations that are not reached by queues and the initial signal timing parameters of the pretimed signal are known. Green extension estimation In the absence of a bus at the stop the number of vehicles arrived and therefore served in one cycle length, N, is equal to q A C where q A is the demand flow for the subject approach in vehicles per second, and C is the cycle length in seconds, which is the sum of the effective red time, R, and effective green time, G. However, when a bus is present and oversaturation occurs, the number of vehicles served, N i, can be determined by examining the flow rates at the stop line using the equation N i = τ C q C + τ I q I + τ A q A (1) where τ c, τ I,andτ A (seconds) are the total time that the flow rate is q c,q I,andq A,respectively,duringthecycle(s) thatthebusisstoppedatabusstop.giventhatthenumber of vehicles served by the intersection, N i,islessthanthe number of vehicles that arrived, N o,duringthecycle(s) thebusispresentatthebusstop,theamountthatthe Figure 1. Fundamental diagrams.

5 352 C. CHAVIS AND E. CHRISTOFA green time interval is extended is such that the number of vehicles that were unable to go through the intersection due to the bus-stop-induced reduced capacity, N o N i, plus the number of vehicles arriving in the next cycle, N, is equal to the number of vehicles that can be served during the initial effective green time for the bus approach, G, plus the additional green provided, D G.Thiscanbe expressed as follows: { } No N i + N D G = max G, 0 (2) q C where D G is given in seconds and N o and τ c are based on whetherornotthebusdwelltimespansoneortwocycles, yielding { N if Te C N o = (3) 2N otherwise { G τi τ A if T e C τ C = (4) 2G τ I τ A otherwise. All time quantities used are measured from the beginning of the subject cycle, that is, the start of the green, within which a bus starts dwelling at a stop. The equations for τ I and τ A are dependent on the cases defined by thepositionofthebusstop,thearrivalanddeparturetime of the bus from the stop, and the demand levels and signal timings.thederivationoftheseequationsisdescribedin the subsection after the next one, and the equations are presented in Table 2. Cross-street minimum green time constraint The green extension implemented for the bus stop approach, D G, will result in a reduced green for the crossstreet approaches. The proposed signal control strategy implements a green extension that is restricted by the minimum green time required for the cross street to ensure undersaturated traffic conditions. This maximum green extension time, D Gmax,canbecalculatedas D Gmax = G x q AxC q Cx. (5) where q Ax is the arrival rate and q Cx the saturation flow at the cross-street approach x, both in vehicles per second. G x is the effective green time for cross-street approach x when no green extension is implemented for the bus stop approach. When the calculated green extension is greater than the maximumallowed,thatis,d G > D Gmax, additional green extension or red truncation can take place in the following cycle. The green extension for that cycle, D G2,iscalculated based on the following equations: N s = (D G D Gmax ) q C ( G q ) A R (q ) C q A (6) q C q A { } Ns D G2 = max, 0 (7) q C where N s is the number of vehicles along the bus approach not served in the following cycle in the absence of a second green extension. Note that for the purposes of this study, additional green extension is allowed for only one more cycle after the one that that the initial green extension takes place. Furthermore, this additional green extension is also restricted by the minimum green time for the cross street. Identifying the cases Depending on the location of the bus stop, starting time and dwell time of the bus the capacity reduction can be categorized as falling into one of five cases. All other instances that do not fall into one of the five cases do not require green extension, that is, D G = 0, and fall under Case 6. As shown in Eq. 2, Cases1 5maynotrequire green extension, depending upon input parameters. In order to determine which case each bus stop induced capacity reduction incident is under and estimate its associated green extension time, the following critical times have been identified: T 1 = X U AJ R (8) T 2 = X w (9) T 3 = q A R + X q C q A v f (10) T 4 = G + X v f (11) T 5 = v f T o (q A q I ) + X(q C q A ) + v f q A R (q C q I )v f (12) T 6 = T e(q I q C ) + T o (q A q I ) (13) q A q C where T 1, T 2, T 3, T 4, T 5,andT 6 are given in seconds. Thesetimesaremeasuredatthelocationofthebusstop, X (ft). U AJ is the speed of the shock wave between states A and J and ν f is the free-flow speed, both measured in feet per second. T 1, T 2, T 3,andT 4 denotetimeswhenabusisnot present and the effect of past buses has dissipated, and these times are independent of the capacity restriction of adwellingbus.t 1 represents the time the backward wave,

6 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 353 Table 1. Constraints for each case. Case Constraints Table 2. Time spent in state A, τ A,andstateI, τ I. Case τ A τ I 1 T o T 3, T 2 T e T 2 + C, T 5 > T 2 2 T o C, T e T 2 + C, T 5 2 if q A > q I T o T 3, T e T 2 + C, otherwise 3 T 3 < T o C, T 2 + C T e 2C, T 1 T 2, q A q I 4 T 5 T 2, T 6 T 4, T o T 3, q A q I 5 T 5 T 2, T 6 T 4 + C, T o T 3, q A > q I which carries the information that the signal downstream has turned red, U AJ,reachesthebusstoplocation,whichis essentially the time the queue created by the signal reaches the bus stop. T 2 is the time the backward wave that carries the information that the signal downstream has turned green, U CJ (or w),reachesthebusstoplocation,whichis alsothetimethefirstvehiclethatisstoppedatthebusstop location can move at free-flow speed. T 3 is the time the forward wave carrying the information that the queue has dissipated and vehicle discharge at the stopline can occur at a rate equal to the arrival rate, v f,reachesthebusstop location. T 4 isthetimethelastvehiclethatcouldbeserved by the intersection during the given cycle crosses the bus stoplocationundertheabsenceofabusatthestop.t 5 and T 6 are critical times that take into account the maximum 1 0 min{t e, T 4 } max{t o, T 2 } 2 min{t o, T 4 } max{t o, T 4 } T o + T e (T 2 + C) min{t 3, T o } 3 T 4 T 3 min{t e, T 4 + C} (T 2 + C) 4 0 min{t e, T 4 } T 5 5 T 4 T 3 min{t e 4 } T 5 queue length while a bus is present at the stop and are necessary for determining Cases 4 and 5. They are discussed in detail later when these two cases are defined. A dwelling bus may fall into one of six cases.table 1 provides the constraints that are used to identify Cases 1 to 5. All constraints in each case must be satisfied and all cases are mutually exclusive. If the constraints in Table 1 are not satisfied then the case falls into category six which does not require green extension. Figure 2 shows the constraints for the bus stop location for Cases 1 to 3 on time space diagrams for undersaturated conditions and depicts the time stamps of T 1 through T 4 assuming the busstopislocatedatthestopline.notethattheyellow time intervals are not shown in the time space diagrams of Figures 2 and Figures 4 9 (shown later) because they are included in the effective green and red times illustrated in the diagrams. The area with the horizontal lines Figure 2. Illustration of constraints for Cases 1 3.

7 354 C. CHAVIS AND E. CHRISTOFA Figure 3. Test site: San Pablo and University Avenue, Berkeley, CA. in Figure 2 represents the possible locations where T 0 may be located, and the vertical lines the locations where T e may be located for each case (subject to the constraint T e T 0 C). It is not feasible for a bus stop incident to begin at a location in the jam state since a bus cannot proceed to the bus stop if it is within the zero speed jam state. Note that a bus can, however, end its boarding and alighting processinajamstate,butcannotdepartuntilitmovesto thecapacitystate.therefore,forabusstopincidentthat ends in the jam state, its end time is always defined as the timethebackwardwavereachesthebusstoplocation,that is,whenitiscapableofmovingtothecapacitystate. Case 1 represents the case when the bus arrives at the stopanytimebeforethequeuefromthesignalhasreached thestoporafterthequeueatthatlocationhasstarted dissipatingandleavesbeforethequeueofthefollowing cyclestartsdischargingatthebusstoplocation.case2 represents the case when the bus arrives at the stop any time before the queue from the signal has reached the stop or after the queue at that location has started dissipating and leaves the stop after the queue in the next cycle has Table 3. Parameters and green extension for each sample case. X T o T e q A q Ax case (sec) (ft) (sec) (sec) (vph) (vph) case (sec) Case q A > q I 3.4 Case q A > q I 7.0 Case q A < q I 0.0 Case q A > q I 0.0 Case q A > q I 0.0 Case q A < q I 0.0 starteddissipating.case3occursafterthequeuehasdissipated from the bus stop location and leaves the stop after the queue in the next cycle has started dissipating. Cases 4and5occurwhenthedwellingbusisupstreamofthe maximum queue caused by the signal; see Figures 7 and 8, shown later. This event occurs only when demand exceeds capacity, and often this upstream incident starves the initial queue. Note that Case 4 has the same constraint on T 0 as Case 1 and Case 5 the same as Case 3. The critical times T 5 and T 6 are now defined. T 5 is defined as the time that the forward wave carrying the information that the queue has dissipated and vehicle discharge at the stopline can occuratarateequaltothearrivalrate,v f,reachesthebus stop location. T 6 is defined as the time that the forward wave carrying the information that the second queue createdbythepresenceofabusatthestophasdissipated and vehicles can arrive at the downstream queue at a rate equaltothearrivalrate,v f, reaches the bus stop location. T 5 is defined as the time that is a cycle length earlier than the time the forward wave carrying the information that the queue created by the signal has dissipated and vehicle discharge at the stopline can occur at a rate equal to the arrivalratereachesthebusstoplocation.t 5 can be found by substituting T 0 for T 0 in Eq. 12 where T o = T o C and T e = T e C. Table 2 presents the equations for estimating how long the intersection is discharging at rates as defined by states A and I, τ A and τ I,respectively. Application The evaluation of the proposed methodology and realtime signal control strategy has been performed with the use of analytical tests that estimate delays using KWT and through simulation. Simulation tests have beenperformedwiththesoftwareaimsunthroughits Application Programming Interface (API). API allows for implementing the proposed signal control strategy in real time and evaluating its performance through a variety of performancemeasuressuchasaveragedelayandaverage queue length for different approaches. In particular, API allows for estimation of the green extension and/or red truncation while the simulation is running. The decision ismadeassoonasthedwellingbusstopsdwellingand leaves the bus stop. Detection is performed with the use of detectors placed right upstream and downstream of the subject bus stop. In reality, information on the arrival of a bus at a bus stop can be obtained through AVL systems. If green extension or red truncation is possible in the cycle when the bus leaves the bus stop, then it is implemented foraslongasitisallowableinordertonotoversaturate the cross-street approaches. If not, green extension or red truncation is implemented in the next cycle. If more green time is needed to reduce the impact of the bus

8 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 355 Figure 4. Case 1 time space diagram (control needed). stop, then additional green extension or red truncation is implemented in the cycle following the one that implemented the first green extension. The background signal settings are known a priori, while the average values of demands over the hour are used as input. In the real world, detectors placed at upstream locations that are not reached by queues so that the actual arrival flow can be measured, can be used to estimate the demand in real time. Test site The test site used for the application of the proposed signal control strategy is the intersection of San Pablo and University Avenues in Berkeley, CA; see Figure 3. The intersection operates with a four-phase signal and a cycle length of 80 seconds. Six bus routes with headways that vary between 10 and 30 minutes on each route travel through the intersection and stop at six bus stops located at different distances from their corresponding stop lines. Figure 5. Case 2 time-space diagram (control needed).

9 356 C. CHAVIS AND E. CHRISTOFA Figure 6. Case 3 time space diagram (no control needed). The focus of this study is on the eastbound approach of University Avenue, which has a near-side bus stop where buses of three different bus lines stop with an overall frequency of 10 buses per hour. The demand levels of both approaches were set in such a way so that the test site represents traffic conditions at the intersection of a major with a minor roadway. This was essential since theproposedsignalcontrolstrategyhasbeendesigned under the assumption of undersaturated conditions and performs best when the cross-street approach is not operating close to saturation. The car demand for the cross street was set to veh/sec (250 vph). Two scenarios were created for the bus stop approach (eastbound approach of University Avenue) and the opposite direction of University Avenue: (a) when the demand, q A,ishigherthanthecapacitywhenonelaneisblocked by a bus stopped at the bus stop, q I, and (b) when the arrival demand is lower than the capacity when one lane is blocked by a bus stopped at the bus stop. The high demand was set to veh/sec (2000 vph) Figure 7. Case 4 time space diagram (no control needed).

10 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 357 Figure 8. Case 5 time space diagram (no control needed). and the low to veh/sec (1000 vph) with turning ratiosof10%forrightand5%forleftforbothdemand scenarios. The same turning ratios were used for the cross-street demands. Thus, the demand for the lane group of the mainline through and right movements, q A, was equal to veh/sec (1900 vph) and veh/sec (950 vph) for the high and low demand scenarios, respectively, and the demand for the lane group of the cross-street through and right movements, q Ax, was equal to ft/sec (238 vph). In other words, only the through and right-turn demands are taken into account in the control design since the left-turn pockets are long enough to accommodate the left-turning vehicles and the left-turn movements are served by separate phases. Traffic operations of all intersection approaches for both scenarios can be described by a fundamental diagram with the following characteristics: q C = 1veh/sec, q I = 0.5 veh/sec, w = 17.6 ft/sec (12 mph), and vν f = 44 ft/sec (30 mph). For the low-demand scenario the green time for the phase that serves the University Figure 9. Case 6 time space diagram (no control needed).

11 358 C. CHAVIS AND E. CHRISTOFA Avenue through and right movements was set to 37 seconds, and the one for the cross-street through and right movements to 19 seconds. For the high-demand scenario, these green times were set equal to 44 seconds and 12 seconds, respectively. The other two phases that serve the left-turning vehicles had a constant green time of 5 seconds allocated to them for both scenarios. Due to the short green interval the left-turn phases have, their split is not affected by the control strategy; that is, all the green time is taken from the cross-street phase that serves the through and right-turning vehicles. Therefore, the green extension for the bus stop approach is translated to green truncation for the phase that serves the through and right-turn cross-street movements for this specific example. In addition, the lost time, which is assumed to be equal to the total yellow time, was kept constant and equal to 14 seconds, 4 seconds after each of the through phases and 3 seconds after each of theleft-turningphases.itisassumedthatcarswillcontinue through the intersection for 2 seconds of the yellow interval, and thus an extra two seconds was added to the green time to obtain the effective green time, with the remaining time in the cycle denoted as the effective red time. This resulted in an effective green time for the phase that serves the mainline movements of 39 seconds and the effective red time of 41 seconds for the low-demand scenario. For the high-demand scenario, these times were set equal to 46 seconds and 34 seconds, respectively. A minimum green time of 5 seconds was also imposed on all phases. Based on this information, the degrees of saturation for the University Avenue through movements were 0.57 and 0.96 for the low- and high-demand scenarios and for the San Pablo approaches equal to 0.28 and 0.44 for the lowand high-demand scenarios, respectively. Results A sample scenario for each of the six cases is provided. The characteristics of bus stop operations, the demands for each lane group, and the required green extension for each are presented in Table 3.Once the case has been determined, the green extension time, D G,canbecalculated using the equations in Table 2,whichshowhowlong theintersectionisdischargingatratesasdefinedbystates A and I and Eqs Figures 4 to 9 show example time space diagrams for each case and depict the critical times defined in the preceding section. Each figure shows in solidblacklinesthepropagationanddissipationofqueues if no signal control strategy is implemented and in dashed lines how the queue dissipates when the red truncation strategy is in place. The gray dotted lines represent the formation and dissipation of queues in the absence of a bus at the bus stop. The bold line in yellow represents the presence of a stopped bus. Note that each figure contains two time axes. The lower time axis is the time used in the KWT calculations and the upper the time used in simulation. The KWT tests were created under the assumption that the beginning of the cycle (i.e., beginning of the green phase)whenthebusstopsatthebusstopiszero,whilethe simulation tests present consistent test cases that occur at cycles that could be starting later. Table 4 shows the resulting average vehicle delays for the lane group of the through and right movements for the bus stop approach, and for both cross streets weighted by their flows for each of the sample cases presented in Figures 4 9 obtained through both KWT and simulation. Table 4 also shows the average vehicle delays for the lane group of the through and right-turning movements for all approaches weighted by their flows for the same sample cases. Recall that left-turning vehicles are served by separate phases and their green is not truncated when green extension is provided to the bus stop approach. For comparison purposes, the average delays are shown with and without control calculated both through KWT and through 10 simulation replications of bus stop incidents of similar duration and starting times; see Table 4. Note that the delays presented here are reported for all cycles affected by the bus stopping: the cycle that the bus arrives at the stop, the cycle it leaves the bus stop (if different), and any cycle that follows until the bus stop approach returns to undersaturated conditions without control. These cycles are shown in Figures 4 to 9. The delay for the analytical tests is calculated constructing a cumulative diagram of the arrivals and departures at the intersection for each approach and is consistent with KWT. When demand is low (Case 3 in Figure 6 and Case 6 in Figure 9) no green extension is needed. In fact, if the bus is not present at the bus stop while the signal is discharging (Case 6), there is no increased delay due to the bus dwelling. Under other conditions, for example, signal timings resulting in the approach nearing saturation, case 3 may require green extension. In sample cases 4and5,thepresenceofabusatthebusstopincreases delays slightly; however, queues dissipate within the cycle that follows the departure of the bus from the bus stop without control. At this stop location, which corresponds to sample cases 4 and 5 and with the assumption that a bus cannot dwell longer than a cycle length, control is not needed regardless of when the bus arrives. However, for a different combination of signal timings and incident characteristics. control may be warranted. Sample cases 1 and 2 demonstrate scenarios that require green extension. As expected, the proposed signal control strategy improves the average delay along the bus stop approach

12 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 359 Table 4. Average delay for Case 1 6 examples. Kinematic wave theory Simulation Average delay for intersection (sec/veh) Average delay for bus stop approach (sec/veh) Average delay for cross-street approaches (sec/veh) Average delay for intersection (sec/veh) Average delay for bus stop approach (sec/veh) Average delay for cross-street approaches (sec/veh) No control Control No control Control No control Control No control Control No control Control No control Control Case Case Case Case Case Case Figure 10. Average vehicle delay for various bus stop locations with and without control.

13 360 C. CHAVIS AND E. CHRISTOFA and slightly increases delays along the cross streets resulting in an delay reduction. Note that even though the bus stops at the stop for only 15 seconds in sample case 1, there isstillaneedforcontrolbecauseofthehighimpacton capacity caused by the short distance between the bus stop location and the stopline and the bus arriving during the discharge period. The average delay values are higher in simulation than KWT due to the stochasticity in arrivals in the simulation tests. In addition, the percent reduction in average delay achieved in simulation is lower than the one for the KWT. This is again due to the variability in traffic operations associated with the ten runs performed in simulation. Sensitivity analysis Several scenarios were run to evaluate the impact of incident location using the microsimulation software AIMSUN as described in the preceding, and the results were evaluated primarily through two performance measures: average vehicle delay and average queue length for the bus stop approach and the cross streets (an average of the performance of the two cross-street directions is presented here), as well as the intersection as a whole. Ten replications were run for each scenario to account for the stochasticity in bus and vehicle arrivals as well as bus dwell times, and the averages, as well as the 90% confidence Figure 11. Average queue for various bus stop locations with and without control.

14 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 361 intervals of those replications, are presented here. Bus stop locations of 30, 100, 200, and 500 ft from the stop line were tested. The dwell times were generated based on a normal distribution with a mean value of 40 seconds with a standard deviation of 30 seconds. These ensured that several different cases of bus stop obstruction were captured. Tests were performed for both a high bus stop approach demand, which exceeds the reduced capacity due to the busdwelling,andforalowdemand.theresultsforthe low arrival rate along the bus stop approach show that there is no need for green extension since even with reduced capacity the intersection approach is still capableofservingallvehicleswithinonecycle,thusmaintaining undersaturated conditions. It is possible that green extension is needed when the arrival rate is lower than the reduced capacity of intersection as the presence of the bus may impede the discharge rate when a signal turns green. However, if the incident is sufficiently upstream and/or thedegreeofsaturationislow,theblockagecausedbythe bus dwelling at the stop does not greatly restrict the flow of arriving vehicles. Figures 10 and 11 show the changes in average vehicle delay and average queue length for the bus stop approach, the cross streets, and the whole intersection, as well as the 90% confidence intervals, when q A q I.Thevalues for the cross streets and overall intersection are presented as a weighted average by the respective flows of the corresponding through and right-turning lane groups. The results indicate that the proposed signal control strategy can significantly reduce average vehicle delay for all through and right-turning movements at the intersection for all bus stop location scenarios. As the distance of the busstopfromthestoplineincreases,theimpactofthebus stop on traffic operations diminishes and so does the ability of the real-time signal control strategy to reduce the delaysalongthebusstopapproachandattheintersection asawhole.asaresult,evenwhennocontrolisinplace, thedelaysofvehiclesonthebusstopapproachareonaveragelowerwhenthedistanceofthebusstopfromthestop line is longer compared to when the bus stop is located closetotheintersectionstopline.thisisconsistentwith findings from recent studies on oversaturated conditions (Gayah, Ilgin Guler, & Gu, 2015). While the average vehicle delay for the cross streets increases, the amount by which it increases is very low, on the order of 2 seconds pervehicle.takingintoaccountthatthecrossstreetisless heavily traveled than the main street, and the approach that is served by the same phases as the bus stop approach also benefits when green extension is provide, the strategy resultstoanoverallreductionofdelayofabout7%forthe case when the bus stop is located directly upstream of the intersection stop line (X = 30 ft). Similar trends are observed for the average queue length at the bus stop and the cross-street approaches. The reduction of average queue length at the bus stop approach diminishes as the distance of the bus stop from the intersection stop line increases. At the same time the increase in average queue length observed at the crossstreet approaches is minimal. This happens because for the tests performed the cross streets were far from reaching saturation. Conclusions This study presents the development of a real-time signal control strategy that utilizes information on the location ofabusstop,aswellasthebusdwelltime,trafficdemand levels, and signal timings, to mitigate the impact of bus stop operations on intersection capacity. The proposed bus stop mitigation strategy utilizes kinematic wave theory to track the formation and dissipation of queues and to estimate the amount of green that needs to be added to the subject approach so that residual queues are cleared within one cycle after the bus departs from the bus stop. Several tests were performed for a variety of bus stop locations,dwelltimes,andfortwolevelsofbusstop approach demands through microsimulation. The outcomesofthetestsindicatethatforthescenariostested there is no need to implement the real-time signal control strategy when the capacity of the approach when a bus is present is higher than the demand of the incoming traffic to the subject approach. On the other hand, when the arrivaldemandatthebusstopapproachexceedsthelower capacity caused by a bus dwelling at the bus stop, the proposed mitigation strategy can achieve average delay and average queue length reductions of up to 17% for the bus stopapproachand7%forthewholeintersection.the17% reduction in average delay corresponds to about 3 seconds per vehicle average delay savings. At the same time, the mitigation strategy only slightly increases the average of delay for cross-street vehicles, on the order of 2 seconds per vehicle. The mitigation strategy is most beneficial when the bus stop is located very close to the stop line of the signalized approach. Regarding the impacts of traffic signal settings on the capacity and delay results, it is expected that the larger the proportion of the cycle time dedicated to the green signal for the subject approach, the higher is the impact on the capacity loss and delay increases since the probability of a bus dwelling during green becomes higher. Note that the proposed strategy is applicable for cases where all intersection approaches are undersaturated and is most beneficial in terms of reducing overall delay when implemented at intersections where the bus stop approach has a much higher demand than the cross street.

15 362 C. CHAVIS AND E. CHRISTOFA The benefit of the proposed real-time signal control strategy is that it can be implemented for any bus stop location and dwell time, and can be used both when the vehicle demand is higher than the reduced capacity induced by a bus stopping at bus stop and when it is lower. Therefore, in addition to investigating and mitigating the impact of bus stops on capacity and delay, the equations presented here and the mitigation strategy are applicable to any type of incident that can occur in signalized arterial networks, such as freight deliveries, accidents, and so on. Thus, under the assumption that the characteristics of the incident are known in real time (after the incident has been removed, so no prediction of incident characteristics is needed), the proposed strategy can be implemented to mitigate the impact of that incident on traffic operations of that approach. Overall, the proposed strategy can be used for real-time mitigation of bus stop or incident-induced reductions of capacity to improve traffic and transit operations in urban signalized arterials. Next steps include improving the mitigation strategy so it can handle bus stop events that occur within the same cycle or consecutive cycles and cases when a bus is stopping for longer than one cycle length at a stop. In addition, we plan to extend the focus of the strategy to include cases where vehicle demand varies from cycle to cycle. We are currently extending the methodology to account for the impact of bus stops on the capacity of the signalized intersection right upstream of the stop, that is, measuring the impact of a far-side stop on intersection capacity. Future steps include extensions to signalized arterials where queue spillback phenomena will be taken into account. Funding This research was sponsored by the University of Massachusetts STEM Diversity Faculty Exchange Program, funded by NSF grant References Christofa, E., Ampountolas, K., & Skabardonis, A. (2016). Arterial traffic signal optimization: A person-based approach. Transportation Research Part C: Emerging Technologies, 66, Christofa, E., Papamichail, I., & Skabardonis, A. (2013). Personbased traffic responsive signal control optimization. IEEE Transactions on Intelligent Transportation Systems, 14(3), Christofa, E., & Skabardonis, A. (2011). Traffic signal optimization with application of transit signal priority to an isolated intersection. Transportation Research Record, 2259, Coeymans, A J. E., & Herrera, M J. C. (2003). Estimating values for traffic parameters in turning lanes. Transportation Research Record, 1852(1), Daganzo, C. F. (2005). A variational formulation of kinematic waves: Basic theory and complex boundary conditions. Transportation Research Part B: Methodological, 39(2), Gayah, V. V., Ilgin Guler, S., & Gu, W. (2015). On the impact of obstructions on the capacity of nearby signalised intersections. Transportmetrica B: Transport Dynamics, Ghanim, M. S., & Abu-Lebdeh, G. (2015). Real-time dynamic transit signal priority optimization for coordinated traffic networks using genetic algorithms and artificial neural networks. JournalofIntelligentTransportationSystems, 19(4), Gu, W., Cassidy, M. J., Gayah, V. V., & Ouyang, Y. (2013). Mitigating negative impacts of near-side bus stops on cars. Transportation Research Part B: Methodological, 47, Gu, W., Gayah, V. V., Cassidy, M. J., & Saade, N. (2014). On the impacts of bus stops near signalized intersections: Models of car and bus delays. Transportation Research Part B: Methodological, 68(1), Hans, E., Chiabaut, N., Leclercq, L. (2015). Applying variational theory to travel time estimation on urban arterials. Transportation Research Part B: Methodological, 78, Li, M., Chen, H., & Zhang, Y. (2012). Capacity analysis of roadsegmentnearbusstopaffectedbysignalizedintersection. CICTP 2012: Multimodal Transportation Systems Convenient, Safe, Cost-Effective, Efficient, ASCE, pp Lighthill, M. J., & Whitham, G. B. (1955). On kinematic waves. II.Atheoryoftrafficflowonlongcrowdedroads.Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 229(1178), Ma, W., Liu, Y., & Yang, X. (2013). A Dynamic programming approach for optimal signal priority control upon multiple high-frequency bus requests. Journal of Intelligent Transportation Systems, 17(4), Richards, P. I. (1956). Shock waves on the highway. Operations Research, 4(1), Skabardonis, A., & Geroliminis, N. (2008). Real-time monitoring and control on signalized arterials. Journal of Intelligent Transportation Systems, 12(2), Tang, T. Q., Li, Y., & Huang, H. J. (2009). The effects of bus stop on traffic flow. International Journal of Modern Physics C, 20(06), Teply,S.,Allingham,D.I.,Richardson,D.B.,&Stephenson,B. W. (2008). Canadian capacity guide for signalized intersections. Toronto, Ont.: Institute of Transportation Engineers, District 7, Canada, Transportation Research Board. (2010). Highwaycapacitymanual. Washington, DC: Special Report, National Research Council. Yang, X., Gao, Z., Zhao, X., & Si, B. (2009). Road capacity at bus stops with mixed traffic flow in China. Transportation Research Record, 2111(1), Yao, D., Su, Y., Zhang, Y., Li, L., Cheng, S., & Wei, Z. (2009). Control strategies for transit priority based on queue modeling and surrogate testing. Journal of Intelligent Transportation Systems, 13(3),

16 JOURNAL OF INTELLIGENT TRANSPORTATION SYSTEMS 363 Zhao, X. M., Gao, Z. Y., & Jia, B. (2007). The capacity drop caused by the combined effect of the intersection and the bus stop in a CA model. Physica A: Statistical Mechanics and Its Applications, 385(2), Zhao, X. M., Gao, Z. Y., & Li, K. P. (2008). The capacity of two neighbour intersections considering the influence of the bus stop. Physica A: Statistical Mechanics and Its Applications, 387(18), Zhao, X. M., Jia, B., Gao, Z. Y., & Jiang, R. (2009). Traffic interactions between motorized vehicles and nonmotorized vehicles near a bus stop. Journal of Transportation Engineering, 135(11), Zheng, J., Ma, X., Wu, Y. J., & Wang, Y. (2013). Measuring signalized intersection performance in real-time with traffic sensors. JournalofIntelligentTransportationSystems, 17(4),