A Simple Traffic Signal Control Using Queue Length Information
aa r X i v : . [ ee ss . S Y ] J un A Simple Traffic Signal Control Using Queue Length Information
Gurcan Comert a, ∗ , Mecit Cetin b , Negash Begashaw a a Department of Computer Sc., Phys., and Eng., Benedict College, 1600 Harden St., Columbia, SC 29204 USA b Department of Civil and Env. Eng., Old Dominion University, 135 Kaufman Hall, Norfolk, VA 23529 USA
Abstract
Developments in sensor technologies, especially emerging connected and autonomous vehicles, facilitatebetter queue length (QL) measurements on signalized intersection approaches in real time. Currentlythere are very limited methods that utilize QL information in real-time to enhance the performance ofsignalized intersections. In this paper we present methods for QL estimation and a control algorithmthat adjusts maximum green times in actuated signals at each cycle based on QLs. The proposed methodis implemented at a single intersection with random and platoon arrivals, and evaluated in VISSIM (amicroscopic traffic simulation environment) assuming 100% accurate cycle-by-cycle queue length infor-mation is available. To test the robustness of the method, numerical experiments are performed wheretraffic demand is increased and by 20% relative to the demand levels for which signal timing parametersare optimized. Compared to the typical fully-actuated signal control, the proposed QL-based method im-proves average delay, number of stops, and QL for random arrivals, by 6%, 9%, and 10% respectively. Inaddition, the method improves average delay, number of stops, and QL by 3%, 3%, and 11% respectivelyfor platoon vehicle arrivals.
Keywords:
Control, signal control, queue lengths, platoon arrivals, queue length estimation
1. Introduction
In real-world traffic operations, demand at each intersection approach is subject to significant fluc-tuations throughout the day. To adapt these changes, phase lengths need to be adjusted in real-time tominimize delays and maximize throughput. In order to notify the traffic signal controller that a vehicleis calling a green phase (during a red interval) and extend the green time for an approaching vehicle(during a green interval), the common practice is to install fixed detectors (i.e., inductive loops or videocameras) to detect vehicle presence at the stop-bar. The use of vehicle detection to call and extend phasesis commonly referred to as actuated control. A typical actuated control framework operates within theconstraints of minimum (min) and maximum (max) green times for each phase. If the max green timesare not high enough to accommodate the demand for a phase then residual queues can occur during peaktraffic flow. It can sometimes take numerous cycles to fully disperse the residual queue. In this paper wepresent a method to minimize the average delay at an intersection. The method uses queue length (QL)measured in real time on each approach to update the duration of the max green interval.Actuated signal control operates based on a simple binary input from vehicle detectors (vehiclepresence/non-presence). In the paper by Lin ( Lin (1985)), green phases are extended only based onthe detector inputs serving these phases (actuation) and conflicting calls on the competing phases. Thereis no distinction between one vehicle versus tens of vehicles on the conflicting movement.An adaptive max green feature is available in some manufacturer’s traffic signal controllers. Accordingto National Electronic Manufacture Association 1202 (Association (2004)), definition for actuated trafficsignal control is the adaptive green operation that is defined as a cycle-by-cycle max green intervaladjustment within an upper and lower limit. This feature allows the max green time for a phase to be ∗ Corresponding author
Email addresses: [email protected] (Gurcan Comert), [email protected] (Mecit Cetin), [email protected] (Negash Begashaw) . . .
8% (Smith et al. (2010)).There are numerous research efforts to develop methods to optimize traffic signals (Brian Park & Chang(2002); Liu et al. (2002); Cassidy & Coifman (1998); Abbas & Sharma (2006); Mirchandani & Head (2001);Bullock et al. (2004); Comert et al. (2009b)). However, there is still no accepted methodology for opti-mizing or enhancing the performance of a signalized intersection using QL data. QL is usually utilizedto measure the performance of signalized intersections. It is used to estimate delays and travel times(Gartner et al. (2002); Mirchandani & Zou (2007); Lee et al. (2015); Feng et al. (2015)). It is shown in aneco-signaling application, queue lengths are utilized for speed recommendation which are high negativelycorrelated (Yang et al. (2017)). With known queue lengths, adaptive signal control was also studied ina reinforcement learning scheme (Genders & Razavi (2016); Gao et al. (2017)). If true QLs can be ob-tained as feedback, Comert et al. (2019) showed that QLs for next time interval can be predicted within5 meters ( m ) accuracy. Assuming Poisson arrivals, Zhang and Wang (Zhang & Wang (2011)) developeda method to optimize min green and max green parameters of an actuated control using real-time QLinformation (i.e., utilizing the information in the constraint of the optimization). In our approach, we donot assume Poisson arrivals. Partial information about vehicle arrivals can also be found in queue lengthestimation.Past research also gives detailed insights about the distributions of CV information types that can beutilized for more complex models (e.g., multilane intersections) and estimating delays for signal controlparameters (Comert (2013b); Tiaprasert et al. (2015)). Similar results were used as input for QLs/delayapproximations in new signal control strategies (Comert et al. (2009b); Smith et al. (2010); Goodall et al.(2013)). Accuracy of QL estimation for the traffic signal control under connected vehicle (CV) frameworkwas also investigated by Tiaprasert et. al (Tiaprasert et al. (2015)). Allocating discrete wavelet trans-form, the authors obtained enough accuracy at 30% CV penetration rate. Similar market penetrationrate was observed in (Comert (2013a, 2016)).Connected signal control is one of the priority applications as 80% (250,000) of the Nation’s signalnetwork and 90% of the vehicles are projected to be equipped by 2040 (Wright et al. (2014)). Accurate,real-time, localized, traveler information will be available on at least 90% of roadways. Next-generation,2ultimodal, information-driven, active traffic management will be deployed system-wide. Thus, step-by-step inference based (up to 20% of signals to be equipped by 2025) and fully information based (withsome filtering) need to be developed. Overall, it is necessary to develop signal control algorithms thatfocus on various points of connected systems which vary from communication protocols, use of effectiveand different data types, to security and reliability of such components (Dey et al. (2016)). Adaptiveactuated traffic signal control was introduced by changing unit extensions and max greens using arrivalprofiles. Zhang and Recker (Zheng & Recker (2013)) showed 17 .
3% and 16 .
2% improvements in max QLand delay respectively. In another study under CV framework, Feng et al. (Feng et al. (2015)) proposedan algorithm that outperforms the typical actuated control when the penetration rate is more than50%. When all vehicles are connected, the total delay is improved by 12% on average when minimizingtotal vehicle delay and 11% when minimizing QL. In our proposed simpler method, no cycle-by-cycleoptimization is required.Estimation of queue length problem was discussed in the context of performance rather than cycle-by-cycle control and improvement of signal timing via weighing queues at competing approaches relatively.In this paper, we aim to fill the gap of simple adaptations of signal timing to demand changes shown inqueue lengths. Hence, we propose a queue length-based adaptive signal control. The proposed methodis tested in VISSIM, a state-of-the-art microscopic traffic simulation environment (VISSIM (2012)), foran isolated intersection. This platform is a critical and valuable tool in assessing the benefits of thequeue data on signal operations. It allows testing different scenarios under different assumptions whilerepresenting vehicular movements realistically. The proposed method is tested with both random arrivalsand platoon vehicle arrivals under various demand scenarios. Platoon arrivals are generated with asignalized intersection located 650 m upstream of the intersection where queue lengths are measured.
2. Queue Length-based Signal Control
In the proposed method, the maximum (max) green times in each cycle are calculated based on asimple formula as described in equation (1) below. In a typical actuated signal control, there are three keyparameters for each phase: minimum (min) green, maximum (max) green, and vehicle (unit) extension.For given input volumes, these three parameters are set to fixed values based on the output from asignal optimization program (e.g., Synchro). The max green timer counts down when there is a call onthe conflicting movements. If there is no vehicle on the conflicting phases for some duration then thedisplayed green time can be longer than the preset green timesWhen a phase is extended up to the max green time because of high demand, the phase is said to be maxed out . If one of the phases maxes out many times and the other phases do not then this may be anindication of inefficient allocation of the capacity. A potential solution is to make max green adaptive tothe prevailing traffic conditions. Yun et al. (Yun et al. (2007)) provide an adaptive control feature wherethe max green is adjusted based on the number of max out events that occured in the past few cycles.Alternatively, the max green time for each phase can also be determined adaptively based on QLdata. One approach is to set the max green for each phase based on the QL observed at the end of redinterval that immediately proceeds the green time. For a simple intersection with two one-way streets,the max green for the major and minor streets can be expressed as a function of the QL as follows: G max ,k +1 = max LB , min " U B, β N ,k +1 ( N ,k +1 + N ,k ! (1) G max ,k +1 = max LB , min " U B, β N ,k +1 ( N ,k +1 + N ,k ! (2)where, G max ,k +1 is the max green time of major street at cycle k + 1, G max ,k +1 is the max green time of minor street at cycle k + 1,3 ,k +1 is the queue length (in number of vehicles) on major street at cycle k + 1, N ,k +1 is the queue length (in number of vehicles) on minor street at cycle k + 1, N ,k is the queue length (in number of vehicles) on major street at cycle k , N ,k is the queue length (in number of vehicles) on minor street at cycle k , β is a model parameter, LB is lower bound on green time for major street, LB is lower bound on green time for minor street, U B is upper bounds for max green (the same for major and minor streets)In equations (1) and (2), if there are more than two phases, QLs on other approaches can be includedin the denominators of the fractional expressions. QLs of the conflicting movements in cycle k + 1 areapproximated (predicted) by the QLs observed in the previous cycle. Therefore, there is an element ofrandomness in this method.Eqs. (1) and (2) have three key parameters to be optimized: LB , LB , and β . U B is set to alarge value that represents the maximum allowable time (e.g., 5 minutes in the experiments) that thesignal phase can stay green under extreme demand scenarios. LB , LB , and β are optimized offline forsome given intersection demand scenarios (Comert et al. (2009a)). For completeness, the same randomseed is used in simulating both methods in VISSIM to ensure that the generated vehicles have the sameheadways.The proposed model control parameters are determined after running numerous simulations in VISSIMwith uniform increments. The set of parameters that yield the lowest average delay are given in Table 6.The optimal results of the QL-based method shown in the table provide improvements in average delaysover the typical actuated control. It is found that the value of the parameter β is the same in all threecases. Other β values were tried and there were no improvements. More demand profiles need to betested before one can make any generalizations about β . To choose the parameters in Eqs. (1) and (2), three main tools are used: a microscopic trafficsimulation platform to generate measures of performance (e.g., delay, number of stops, and QLs), aninterface to change traffic signal times, and an optimization algorithm to determine the best parameters.These three components and the flow of information between them are shown in Fig. 1. VISSIM is themain tool that simulates the movements of all vehicles at the intersection. Vehicle Actuated Programming(VAP) interface is a component within VISSIM that allows the user to manipulate the signal times basedon data from the detector. The QLs (i.e., N ,k +1 , N ,k +1 ) are measured in VISSIM on each approach.Enough node evaluation space is covered such that for any demand scenario the QLs never extend beyondthe evaluation area. The average intersection delay calculated by VISSIM is used as the performancemeasure to optimize the parameters. Since delay does not have a closed form solution, in order to ensurethat a good solution is found, a grid search is used where the parameter values are changed by fixedincrements. The parameters that give min delay values were selected for both control methods. In the proposed method, QLs, N ,k , N ,k +1 , N ,k , and N ,k +1 are the dynamical inputs. In case,connected vehicles are utilized for QL information, it is important check at what market penetrationlevel, adequate accuracy can be achieved for given estimators. Control results are given for known ortrue QL information, that is, for best case scenario how much can be saved with proposed control.Errors of the adopted estimators are calculated using VISSIM simulations. Queue length estimation withknown and unknown hyper parameters (i.e., arrival rate λ and probe percentage p ) are given in Table 1.These estimators are the best performing combinations obtained from Comert (2016). Estimation errorsobtained from simulations are presented in tables and figures below.4 ig. 1: Parameter optimization frameworkTable 1: Estimators for p and λ Information ˆ p Information ˆ λM, L ˆ p = m/l L ˆ λ = l/RM, L, T ˆ p = mt/ ( mt + ( l − m ) R ) L, T, M ˆ λ = ( l − m ) /t + m/R Q = 0Estimator of the total QL at the end of red duration given location ( L = l ), queue joining time of thelast CV ( T = t ), and number of CVs in the queue ( M = m ) is written as sum of two random variables N ′ and N ′′ . Random variable N ′ is the queue up to the last CV and N ′′ is the queue after the lastprobe vehicle (Eq. (3)). When time index i is the cycle number then the estimator is cycle-to-cycle queueestimator. For an alternative time interval, scanned ( L, T, M ) can be used for estimation. Certainly,this is a lower bound as some probes may have already left the intersection. Incorporating the counteddischarged vehicles, the problem can be alleviated (Hao et al. (2014)). For implementation, QL estimatedat the end of red can be used for timing the green duration for the signal and a lower bound to the averageQL for broader signal performance measures. Under the Poisson assumption with known parameters,estimator can be expressed as in Eq. (4). Note that for a multilane formulation, the following estimatorscan be used for signal timing as max QLs for each lane. E ( N | L = l, T = t, M = m, Q i = 0) = E ( N ′ | L = l, T = t, M = m ) + E ( N ′′ | L = l, T = t, M = m ) (3) E ( N | L = l, T = t, M = m, Q i = 0) = l + (1 − p ) λ ( R − t ) (4)Without overflow queue, the total QL with unknown arrival rate and probe proportion can be esti-mated using Eq. (5). Pairs of the estimators that are considered in the numerical examples are given inTable 2. E ( N | l, t, m, Q i = 0) = l + (1 − ˆ p )ˆ λ ( R − t ) (5) Table 2: Estimators in queue length estimation
Estimator Combinations E ( N | l, t, m, Q i = 0Est. 1 p, λ l + λ (1 − p )( R − t )Est. 2 ˆ p , ˆ λ l + ( l − m )(1 − t/R )Est. 3 ˆ p , ˆ λ l + (1 − mtmt +( l − m ) R )(( l − m ) /t + m/R )( R − t ) Table 3 shows the QL estimation errors obtained from VISSIM evaluations for demand levels of 600,700, 800, 900, and 985 vph. In the table, root mean squared errors (RMSE) and %
RM SE/Est i are alsogiven. Average QL will depend on VISSIM queue definition. In the numerical experiment, default in ueue = I ( speed ≤
10 kilometers per hour) was adopted. From the table, at 500 vehicles per hour, 6 . . , . , . , .
25, and 12 . ρ > .
80. On theaverage, we observe queue length of 1 .
25 for ρ = 0 .
88 and queue length of 5 .
70 for rho = 0 .
98. Accuracy ofthe estimators change from ± . ± .
45 vehicles after ρ > .
88. Overall, estimator 2 provide accuracybetween 12% to 19% of the true average QLs.
Table 3: Cycle-to-cycle % √ CV ( RM SE ) and % EN i differences of the QL estimators with/without unknownparameters and true QLs at p = 50% True QL Est. 1 Est. 2 Est. 3 RMSE 1 RMSE 2 RMSE 3 % √ CV /EN i % √ CV /EN i % √ CV /EN i ρ =0.50 5.65 5.83 5.98 6.36 1.30 0.72 1.33 23% 13% 24% ρ =0.60 7.18 7.08 7.32 7.59 1.43 1.04 1.28 20% 15% 18% ρ =0.70 8.39 8.27 8.58 8.87 1.73 1.02 1.19 21% 12% 14% ρ =0.80 10.31 10.29 10.67 10.93 1.56 1.39 1.67 15% 14% 16% ρ =0.88 12.52 12.73 12.99 13.14 2.06 1.60 1.72 16% 13% 14% ρ =0.985 18.01 18.81 19.15 19.26 3.45 3.37 3.45 19% 19% 19% VISSIM generates vehicles with exponential interarrival times at the origin that move and queuerealistically. The arrival profile changes as vehicles move along the network based on vehicle composition,vehicle characteristics, driving behavior, number of lanes, and other network settings. Figs. 2 and 3show the behavior of QL estimators and arrivals within red duration when Poisson (random) arrivals areassumed. The figures were obtained for different volume-to-capacity ratios ( ρ ) at p =50%. Queue lengthsare closely followed by the estimators with ± ρ ≤ .
88. Up to ρ = 0 .
88, the histograms fromVISSIM arrivals are close to the simulated distribution of Poisson random values and therefore Poissonarrival assumption is approximately valid up to ρ = 0 . Q >
Q > I ( l ∈ Q ) is an indicatorfunction for the case of last CV in overflow queue, I ( l ∈ A ) indicates the last CV in new arrivals, and I ( l = 0) indicates that no CV is present in the queue. At any given cycle, the three terms on the righthand side of equation (6) represent disjoint events. Hence, only one of the three terms will be positiveand the remaining two terms will be zero. E ( N i | L = l, T = t, Q i ≥
0) = I ( l ∈ Q )[ l + ˆ θ ( C − t ′ ) + ˆ θR ] + I ( l ∈ A )[ l + ˆ θδ ] + I ( l = 0)[(1 − ˆ p )( E ( Q i ) + ˆ θR )](6)Cycle-by-cycle overflow queue can be given as E ( Q i ) = Xi (ˆ ρ − r (ˆ ρ − + 12(ˆ ρ − ρ o ) Xi where, ρ o =0 .
67 + X/ X = 24 vehicles per cycle, ˆ ρ = ˆ λC/X is adopted from Ak¸celik (1980). For allnumerical examples in this paper, i = 1 , , ... denotes the cycle index .Another form of cycle-by-cycle overflow queue is given E ( Q i ) = E ( Q )(1 − e − βi ) where E ( Q ) = 3(ˆ ρ − ρ o )2(1 − ˆ ρ )from Viti (2006) can also be used and this gives very close results with Comert (2013b). Cycle-to-cycleerror of the estimator in Eq. (6) (i.e., V ( D i ) with V ( Q i ) = [ E ( Q )(ˆ ρ + (1 − ˆ p ) / .
15) + ( p ˆ ρXi − σ Q e ) e − βi ]
10 20 30 40 50 60 70 80 90 100
Cycle Number Q ueue Leng t h [ N u m be r o f V eh i c l e s ] Volume=500 [vph] p=50%
True QLEstimator1Estimator2Estimator3 (a) Estimation at ρ =0.50 Number of Arrivals Volume=500 [vph]
Arrivals per Red=45 [s] F r equen cy VISSIMPoisson(6.25) (b) Distribution at ρ =0.50 Cycle Number Q ueue Leng t h [ N u m be r o f V eh i c l e s ] Volume=600 [vph] p=50%
True QLEstimator1Estimator2Estimator3 (c) Estimation at ρ =0.60 Number of Arrivals Volume=600 [vph]
Arrivals per Red=45 [s] F r equen cy VISSIMPoisson(7.5) (d) Distribution at ρ =0.60 Cycle Number Q ueue Leng t h [ N u m be r o f V eh i c l e s ] Volume=700 [vph] p=50%
True QLEstimator1Estimator2Estimator3 (e) Estimation at ρ =0.70 Number of Arrivals Volume=700 [vph]
Arrivals per Red=45 [s] F r equen cy VISSIMPoisson(8.75) (f) Distribution at ρ =0.70Fig. 2: Cycle-by-cycle QL estimation for different ρ < .
80 values at p = 50% where σ Q e can be calculated from σ Q e = E ( Q )(ˆ ρ + (1 − ˆ ρ ) / .
10 20 30 40 50 60 70 80 90 100
Cycle Number Q ueue Leng t h [ N u m be r o f V eh i c l e s ] Volume=800 [vph] p=50%
True QLEstimator1Estimator2Estimator3 (a) Estimation at ρ =0.80 Number of Arrivals Volume=800 [vph]
Arrivals per Red=45 [s] F r equen cy VISSIMPoisson(10.00) (b) Distribution at ρ =0.80 Cycle Number Q ueue Leng t h [ N u m be r o f V eh i c l e s ] Volume=900 [vph] p=50%
True QLEstimator1Estimator2Estimator3 (c) Estimation at ρ =0.88 Number of Arrivals Volume=900 [vph]
Arrivals per Red=45 [s] F r equen cy VISSIMPoisson(11.25) (d) Distribution at ρ =0.88 Cycle Number Q ueue Leng t h [ N u m be r o f V eh i c l e s ] Volume=985 [vph] p=50%
True QLEstimator1Estimator2Estimator3 (e) Estimation at ρ =0.98 (f) Distribution at ρ =0.98Fig. 3: Cycle-by-cycle QL estimation for ρ ≥ .
80 values at p = 50% can be given as follows (Viti (2006)), V ( D i | Q i ≥
0) = P ( l ∈ Q )[ˆ θ ( C − E ( T ′ ))+ˆ θR ]+ P ( l ∈ A )[(1 − ˆ p )(1 − e − p ˆ λR ) / ˆ p ]+ P ( l = 0)[(1 − ˆ p )( V ( Q i )+ˆ θR )](7)8able 4 summarizes the queue length estimation errors when overflow queue is included. The errorsare expressed in %∆ CV i and %∆ EN i where, CV i = p V ( D i ) /E ( N i ). Since estimators are able to captureoverflow queue, errors are declining to zero as CV penetration rate increases. Results from literaturereviewed confirm that p ≥
30% queue length can be predicted within ±
10% across all all ρ levels. At p = 50%, queue length can be predicted within ±
2% in %∆ CV i and %∆ EN i . In section 3, we presentnumerical results for queue length-based signal control when queue length estimation errors are ignoredwith p ≥ Table 4: i =2 cycle-to-cycle % CV i and % EN i differences of the QL estimators with unknown parameters and trueQLs %∆ CV i ˆ p ˆ λ %∆ CV i ˆ p ˆ λ %∆ EN i ˆ p ˆ λ %∆ EN i ˆ p ˆ λ probe ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . ρ = 0 . E ( N | l, t, m, Q i = 0) = l + ( l − m/l )( l/R )( R − t ) = l + ( l − m )(1 − t/R ) (8) E ( N | l, t, m, Q i = 0) = l + (1 − mtmt + ( l − m ) R )(( l − m ) /t + m/R )( R − t ) = m + R ( l − m ) t (9)
3. Numerical Experiments
Numerical experiments are conducted at randomly selected demand levels to investigate how β , LB ,and LB interact and to evaluate the benefits of using 100% accurate QL information (i.e., at p = 100%CV market penetration level) in the proposed signal control as compared to the typical actuated control.A simple intersection where a one-way major road intersects with a minor street as shown in Fig. 4, isdesigned in VISSIM. Two signal control methods are designed and evaluated. A typical actuated signalcontrol is utilized with fixed max green. The proposed queue-length based method (i.e., QL-based) isgiven with max green times that are determined based on Eqs. (1) and (2). It is assumed that there arestop bar loops on both approaches (i.e., fully actuated control). Real-time data from these loops are usedin both signal control methods to extend the greens.Parameters are chosen as described in section 2.1 for three different base demand profiles for bothsignal control methods over one-hour period. Table 5 shows these demand profiles for each approach.These demand scenarios and the respective optimum signal control parameters for them are adopted fromComert et al. (2009b). For profile 1, the demand exhibits a steep increase in the second quarter and adecrease in the last quarter for major and minor streets. Demand profile 2 has rather high demand anda large disparity between major and minor streets. Demand profile 3 has larger jumps in demands thanthe other two profiles. Table 5: Three base demand profiles
Profile −
15 800 300 1200 100 800 30016 −
30 1350 400 1400 200 1500 40031 −
45 1350 400 1500 300 900 20046 −
60 800 300 1100 100 500 100 ig. 4: Intersection used in the experiments The volumes in Table 5 are assigned to 15-minute intervals for a total of one hour simulations. Thesebase volumes are used to determine the parameters of both typical actuated signal (i.e., gmax gmax β , LB
1, and LB gmin gmin allred =1 s, yellow =2 s, gapout =3 s). The same random seedis used in simulating both methods in VISSIM to ensure that the same vehicle patterns are generated.The optimal parameter values for all the three demand profiles are shown in Table 6. It is observed thatthere isn’t a very significant difference between gmax and LB and also between gmax and LB . The β values are the same for these demand profiles. Table 6: Optimum parameters for the three demand profiles
Typical QL-BasedDemand Profile gmax (s) gmax (s) β LB (s) LB (s)1 75 15 2 . . .
4. Sensitivity Analysis
In this section, we compare the robustness of the QL-based and typical actuated methods to demandfluctuations by changing the base volumes on the minor and major streets by ±
20% but keeping thecorresponding optimal parameters shown in Table 6 constant. Two arrival types are considered: (i)random and (ii) platoon arrivals where an upstream signal with sufficiently large capacity is introducedin the upstream of the major intersection. This signal has a fixed cycle length of 92 seconds and 60seconds phase lengths for the major street. The major road has two lanes at the upstream signal locationwhereas it narrows to one lane between the upstream and subject intersection. It is designed this way toensure that the upstream signal does not form a bottleneck but only serves to generate platoon arrivals.The results for the random arrivals and platoon arrivals are presented in Table 7 and Table 8 re-spectively. It should be noted that the optimal parameters given in Table 6 for both the actuated andproposed method are determined under the assumption of random arrival distributions. These optimalparameters are kept the same in all simulation runs.For each of the three demand profiles, four different scenarios are modeled and run based on the ± able 7: Performance measures for each demand scenario for random arrivals AvgDelay(s) NStops AvgQueue(m)Typ QL-B %Imp Typ QL-B %Imp Typ QL-B %ImpProfile1 1-1 +20%+20% 39.94 21.98 45% 3.84 1.80 53% 66.96 20.76 69%1-2 +20%-20% 15.88 15.59 2% 1.11 1.12 -1% 12.59 10.94 13%1-3 -20%+20% 12.20 1.17 0% 0.75 0.75 0% 8.85 8.76 1%1-4 -20%-20% 9.80 9.45 4% 0.62 0.59 5% 5.47 5.22 5%Profile2 2-1 +20%+20% 15.34 15.45 -1% 1.21 1.12 7% 12.04 12.82 -6%2-2 +20%-20% 12.18 11.52 5% 0.88 0.79 10% 7.68 7.35 4%2-3 -20%+20% 9.45 8.52 10% 0.61 0.55 10% 5.71 4.80 16%2-4 -20%-20% 7.24 7.07 2% 0.47 0.45 4% 3.66 3.46 5%Profile3 3-1 +20%+20% 16.48 16.43 0% 1.27 1.27 0% 11.42 11.88 -4%3-2 +20%-20% 12.83 12.32 4% 1.00 0.89 11% 7.23 6.73 7%3-3 -20%+20% 11.14 10.95 2% 0.71 0.70 1% 6.50 6.40 2%3-4 -20%-20% 8.74 8.55 2% 0.58 0.56 3% 4.03 3.83 5%
Table 8: Performance measures for each demand scenario for platoon arrivals
AvgDelay(s) NStops AvgQueue(m)Typ QL-B %Imp Typ QL-B %Imp Typ QL-B %ImpProfile1 1-1 +20%+20% 39.18 32.07 18% 4.89 4.09 17% 25.54 13.14 49%1-2 +20%-20% 29.83 29.17 2% 4.14 4.13 0% 7.71 6.80 12%1-3 -20%+20% 14.38 13.90 3% 1.04 0.99 5% 6.43 5.97 7%1-4 -20%-20% 12.90 12.71 1% 0.97 0.94 3% 3.89 3.69 5%Profile2 2-1 +20%+20% 37.38 36.94 1% 5.98 5.98 0% 7.02 6.46 8%2-2 +20%-20% 36.35 36.05 1% 6.16 6.14 0% 4.04 3.79 6%2-3 -20%+20% 14.55 14.26 2% 1.18 1.16 2% 3.95 3.69 7%2-4 -20%-20% 13.44 13.30 1% 1.13 1.12 1% 2.55 2.44 4%Profile3 3-1 +20%+20% 27.09 26.80 1% 3.55 3.55 0% 7.99 7.55 5%3-2 +20%-20% 25.53 25.04 2% 3.66 3.62 1% 4.49 4.07 9%3-3 -20%+20% 13.23 12.95 2% 1.01 0.99 2% 4.41 4.16 6%3-4 -20%-20% 12.06 11.73 3% 0.97 0.94 3% 2.71 2.48 9%
From Scenario 1 of demand profile 1 in Table 7, where the volumes are increased by 20% for eachdirection, we see that the improvements reach up to 69% in average QL, 53% in average delay and, 45%in number of stopsCompared to profiles 2 and 3, the traffic demand stays at the peak level for 30 minutes in profile 1 asopposed to 15 minutes in the other two profiles. Therefore, increasing demand on both major and minorstreets by 20% pushes the system to operate at oversaturation level for 30 minutes. For this scenario thesignal is maxing out mostly for the minor street as can be observed in Fig. 7. The improvements forplatoon arrivals (on the major street) in Table 8 reach up to 49% in average QL, 18% in average delayand, 17% in number stops. Scenario 1 of demand profile 1, where the volumes are increased by 20%for each direction, shows these exceptional results. The results in both tables show that the QL-basedmethod performs better for both types of arrivals.Compared to random arrivals, when the arrivals on the major street are random, the relative im-provements are somewhat smaller. This is expected as the control parameters are optimized based on therandom arrivals. It is observed that the number of max-outs decrease significantly for the major streetwhen arrivals are platoon (e.g., on average 1 max-out for the one-hour simulation period for platoon11rrivals, 17 for random arrivals for scenario 1-1). On the other hand, number of max-outs remains similaron the minor street (e.g., 33 for platoon, 30 for random arrivals for scenario 1-1). Overall, both the typicalactuated and QL-based methods perform similar on the major street when the arrivals are platoon.In order to see how the two signal control methods compare in terms of performance metrics andallocating the capacity, green distributions and performance measures over the one-hour simulation timeare plotted for two selected scenarios: Scenarios 1-1 and 3-1. These two scenarios are chosen to analyzethe differences between the typical actuated signal operations and the QL-based operations when theQL-based method performs significantly better (as in Scenario 1-1) and when they perform comparably(as in Scenario 3-1). These comparisons are presented only for the case when arrivals on the major streetare platoon. The results for the random arrivals are very similar.Figs. 5-a and 5-b show the variation in average delay on major and minor streets, respectively, for bothcontrol methods. Clearly, the QL-based method produces much lower delays than the typical actuatedmethod, particularly on the Minor Street. Likewise, Figs. 5-c to 5-f show the variation in average QLand number of stops. It can be seen that the queue on the minor street grows dramatically under thetypical actuated control. The average delay and QL on the minor street increase dramatically since themax green under the typical actuated control for the minor street (i.e., 15 s) is not sufficient to deal withthe increase in demand.
Fig. 5: Performance measures for both major and minor streets obtained with the typical actuated control andQL-based control for scenario 1-1 for platoon arrivals
Fig. 6: Performance measures for both major and minor streets obtained from the typical actuated control andQL-based control for scenario 3-1 for platoon arrivals
Figs. 7 and 8 show the actual green times by cycle number for both control methods. Under thetypical actuated control, the minor street is maxing out many times, especially between cycles 26 and 50when the volumes are larger. Note that at some cycles the green time of the minor street exceeds themax green of 15 seconds. This happens since the max green timer counts down when there is call onthe opposing phase. The QL-based method changes the max green between lower and upper bound. Forthe minor street, the green times are larger than the lower bound (10 seconds) in a number of cycles toaccommodate the large volumes.Fig. 7 shows the total green times for both methods for scenario 1-1. It can be observed that the cyclelengths in the QL-based method and the typical actuated control are quite similar. However, the greendistributions to major and minor streets differ significantly as shown in Fig. 7. The QL-based methodtakes away the green from the major street to allocate more time to the minor street to prevent the queue13 ig. 7: Green times and cycle lengths for scenario 1-1 for platoon arrivals to grow substantially. It is clear that the proposed method is effective in accommodating imbalances inthe queues on the two approaches as illustrated in Fig. 5 for this scenario. In conclusion, the QL-basedmethod adjusts the greens more efficiently to adapt to changes in demand for the two conflicting signalphases.
Fig. 8: Green times and cycle lengths for scenario 3-1 for platoon arrivals
Fig. 8 demonstrates the green times and the cycle times for scenario 3-1. The performance of bothcontrol types are quite similar for this particular scenario. Consequently, the major and minor streetgreen distributions produced by the two control methods are also similar.
Table 9: Average improvements over the typical actuated control
Random Arrivals Platoon ArrivalsOverall Major St. Minor St. Overall Major St. Minor St.AvgDelay 6% 3% 7% 3% 1% 5%NStops 9% 6% 3% 3% 2% 3%AvgQueue 10% 6% 8% 11% 9% 7%
The overall results for all the 12 scenarios are summarized in Table 9 for both random and platoonarrivals. Since each scenario is run 30 times and there are a total of 4 cases to be considered (two controltypes and two arrival types), the total number of simulation runs for the complete analysis is 1 , . Conclusions This paper presents a new queue length based control method for signals where max green times arecalculated in each cycle based on the measured QLs. By varying max green times from cycle to cyclebased on a simple formula, the intersection capacity is allocated more efficiently when traffic demandfluctuates. The proposed method is implemented for a single intersection with random and platoonvehicle arrivals and its performance is evaluated in a microscopic traffic simulation environment (i.e.,VISSIM). To assess the robustness of the proposed method, various numerical experiments are conductedwhere traffic demand on the intersection approaches is increased and decreased by 20% relative to thedemand levels for which signal timing parameters are optimized. Compared to the typical fully-actuatedsignal operations, the proposed queue-length-based method provides significant improvements in efficiencyin terms of average delay, number of stops, and queue size. The results show significant potential benefitsof using QL information. Overall, when all scenarios are considered, the average delay of the isolatedintersection was improved by 3%, number of stops by 3%, and average QL by 11%. For individualscenarios, much larger improvements ranging from 50 to 60% are observed. Future research is needed toanalyze more complicated intersections with more than two phases.
Acknowledgments
This study is supported by the Center for Connected Multimodal Mobility ( C M ) (USDOT Tier 1University Transportation Center) Grant headquartered at Clemson University, Clemson, South Carolina,USA. The authors would also like to acknowledge U.S. Department of Homeland Security (DHS) SummerResearch Team Program Follow-On, U.S. Department of Education Minority Science Improvement Pro-gram (MSIEP-Benedict College Creating Achievers in STEM through Academic Support, Mentoring, andResearch), and U.S. National Science Foundation (NSF, Nos. 1719501, 1436222, and 1400991) grants.Any opinions, findings, conclusions or recommendations expressed in this paper are those of theauthor(s) and do not necessarily reflect the views of ( C M ), U.S. DOT, U.S. DHS, U.S. Department ofEducation, or NSF and the U.S. Government assumes no liability for the contents or use thereof. References
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