Backpressure Traffic Control Algorithms in Field-like

Backpressure Traffic Control Algorithms in Field-like Signal Operations Igor Dakic

Jelka Stevanovic

Aleksandar Stevanovic

Research Graduate Assistant Department of Civil, Environmental and Geomatics Engineering Florida Atlantic University Boca Raton, Florida [email protected]

Research Consultant 2145 NW 3rd CT Boca Raton, Florida [email protected]

Associate Professor Department of Civil, Environmental and Geomatics Engineering Florida Atlantic University Boca Raton, Florida [email protected]

evaluated both in the field and through microscopic simulation, primarily addressing their performance and comparisons to conventional traffic signal controls [5-10]. Studies have presented either positive or negative impacts of these dynamic signal strategies [10]. The challenges of throughput maximization at signalized intersections have triggered the development of methods that have incorporated changes in drivers’ behavior to achieve optimum performance at signalized intersections. One such application is called GLOSA - Green Light Optimized Speed Advisory that is shown to have a significantly positive effect on number of stops and fuel consumption when implemented with fixed-time signal timings [11]. Modeling technique such as Petri Nets has also been analyzed in the field of traffic management and was recognized to provide enough flexibility in modeling traffic control processes [12]. Several decentralized methods, presented as multi-agent problem were applied at independently controlled intersections to provide efficient progression through a network [13-14]. To maximize the travel capacity of a road network, a local traffic control policy is developed [15]. The policy does not require origin-destination information, but rather local information such as traffic flows and queue lengths, which can be obtained from vehicle detectors. For junction delay cases, the theoretical formulations of link-flow definitions of equilibrium and stability, including conditions which guarantee the existence, uniqueness and stability of traffic equilibria, are given [16].

Abstract—Traffic signal control is one of the most common means of traffic management in urban areas. To create an efficient urban transportation network, the optimization of signal control strategy is required. Various methods and tools can be used for that purpose. This study proposes two signal control algorithms that are based on backpressure model, which is originally developed to maximize the throughput in communication networks. Thus, one of the goals was to determine if such control strategies can lead to maximum throughput through an urban traffic network. In addition, the evaluation of the two algorithms included comparison of their performances with the performances of the conventional signal control strategies in microsimulation software. Evaluation results, in terms of various performance measures, demonstrate that backpressure control models are outperformed by conventional (fixed and actuated) signal timings optimized by a genetic algorithm. Keywords—Traffic Signal Control, Backpressure Algorithm, Traffic Signal Timings, Optimization Procedures

I. INTRODUCTION Traffic signal optimization represents one of the common strategies in traffic management that impacts the efficiency of urban transportation network. Traffic signals are considered as one of the vital control elements that directly affect mobility, safety, and environmental parameters of the transportation networks [1]. The optimal signal timing plan provides best urban traffic network performance, i.e. prevents conflicts while minimizing delay and pollution, especially in environment where construction of new road infrastructure would cause even greater demand.

Algorithms presented in this paper represent two modified versions of the traffic signal control strategy introduced in [17], originally based on backpressure routing used for the maximization of the throughput in multihop radio networks [18]. The backpressure algorithm calculates the weight of a link as the maximum “back-pressure” i.e. the queue length or delay difference between the queues at the transmitting and receiving nodes of the link [18]. The link with the maximum weighted link-rate sum is then chosen to transmits packets of the flow. So, the algorithm requires only local information at each node/intersection and provably maximizes throughput [19]. It was demonstrated that the algorithm can stabilize the

Various methods can be used for optimization purposes. Some of them utilize the offline optimization tools such as PASSER, SYNCHRO, and TRANSYT-7F for conventional traffic control (e.g. fixed-time or actuated-coordinated signal timings) [2-4] to optimize cycle length, offsets or splits. Advancements in detection and controller logging capabilities introduced new technologies resulting in the development of adaptive signal control systems that dynamically respond to real time traffic demand variations. Those systems have been 1

queues in arterial traffic systems when testted in simulation environment [20]. Previous research [17] describes the changges that needed to be made within original model for the implementation of a backpressure-based strategy to a transporrtation network. However, those modifications are made on theoretical level since they consider infinity queue length.. Therefore, the proposed study establishes practical models thhat analyze queue length subjected to link capacity and uses data regarding arrival rate to determine which phase should be givven green in the next time step along a corridor in Salt Lake Ciity. Those models are different in terms of computation of the queue length. In order to evaluate the performance of the pressented algorithms that would allow authors to determine if suchh models can lead to maximum network throughput, compaarison with the following conventional traffic control strattegies has been made: fixed-time initial plans (which would opperate in the field based on equivalent actuated controllers), fixeed-time optimized plans, actuated-coordinated initial (plans curreently operating in the field), and actuated-coordinated optimized signal timing plans. II. METHODOLOGY Fig. 1. A typical set of phases of a four-way intersection

A. Traffic Signal Control Problem In this section, the problem of the study is mathematically formulated. Let be the transportation network that is comprised of N links and L signalized inteersections and is presented as a directed graph (ℒ, ). ℒ = ℒ , … , ℒ and = ,…, are sets of all the links and signalized intersections, respectively. Furthermore, eachh intersection can be described by a set of = ( , , ), wheere is a set of all the possible traffic movements through , , is a set of all the possible phases of and is a finite sett of traffic states, each of which captures factors that affect thee traffic flow rate through such as traffic and weather condittions [17]. Given that a vehicle may enter the network at any linnk and leave it at certain link, origin destination pair (ℒ , ℒ ) is allocated to each traffic movement. Each phase ∈ is defined as a combination of traffic movements thhat can be given green time simultaneously. Fig. 1 providees a typical set , , , of phases at four-way intersecction that is given by: a) b) c) d)

= = = =

(ℒ (ℒ (ℒ (ℒ

,ℒ ,ℒ ,ℒ ,ℒ

), (ℒ ), (ℒ ), (ℒ ), (ℒ

,ℒ ,ℒ ,ℒ ,ℒ

This means that variable ( , ℒ , ℒ , ) would be equal to zero if phase that controls movement from ℒ to ℒ was not given green. Finally, traffic signal controll problem can be defined as a decision analysis made by a trafffic controller, which phase ( ) ∈ should be activated durin ng each time slot ∈ for each intersection , with objectivee function to maximize the network throughput [17]. Howeverr, in order to achieve this goal, various sensors that would provide information about val rate at the beginning of queue length, traffic state and arriv each time slot need to be implementted in the network. B. Backpressure-based Traffic Sign nal Control Strategy This section contains descriptio on of the proposed models that closely follow the strategy established in [17] with certain modifications. Those modifications,, arising from practical field conditions and limitations, includee knowledge about traffic arrival rate and constrains regarding g finite buffer storage space for forming the queues and presencee of protected/permitted left turn phases. In addition, it should be b emphasized that the rates with which vehicles flow through intersections, i.e.-variable ( , ℒ , ℒ , ) are assumed to be the same for every intersection (also a very reasonable practical constraint). Furthermore, the two models pressented in this paper, differ between themselves only in terms of o computation of the queue length, which is formulated with equations e (1) and (2). The first backpressure model computes the t queue as the sum of the number of vehicles that have stop pped ( ) and the ones that are currently discharging ( ) at given d, the second backpressure time step (1). On the other hand model computes queue as a sum off all of the vehicles that are approaching the intersection (2).

), (ℒ , ℒ ), (ℒ ℒ ,ℒ ) ) ), (ℒ , ℒ ), (ℒ ℒ ,ℒ ) )

Models assume that the traffic signal syystem operates in slotted time ∈ and that during each tim me slot vehicles may enter the network at any link [17]. Numbber of vehicles on ℒ and the traffic state for are definedd as and respectively, while a function : such that ( , ℒ , ℒ , ) gives the rate (i.e. the numbeer of vehicles per unit time) at which vehicles can travel from ℒ to ℒ through intersection under traffic state if phase p is activated [17].

( )=

( )+ ( )=

2

( ) ( )

(1) (2)

Step 0: Initializing M, Set of all movements (ℒ a, ℒ b) for current intersection P, Set of all phases for current intersection M, Number of all movements (ℒ a, ℒ b) for current intersection Stoppeda(t), Number of vehicles stopped on link ℒ a Discharginga(t), Number of vehicles discharging from link ℒ a ( , ℒ , ℒ , ( )), Factor that affects the traffic flow rate with which vehicles flow from link ℒ a to ℒ b P, Number of all phases for current intersection Sp(t), Throughputs per each phase to be calculated p*, Phase which will be selected for activation p* = 0 Sp* = 0 m=0 p=0 Step 1: Calculation of flow weight for each movement m = m+1 IF M < m GO TO Step 2 ELSE Qa(t) = Stoppeda(t) + Discharginga(t) Qb(t) = Stoppedb(t) + Dischargingb(t) Wab(t) = max{ Qa(t)- Qb(t), 0} GO TO Step1 Step 2: Selection of phase to be activated p = p+1 IF P < p Activate Phase p* ELSE

Therefore, in both versions of the algorithm, the number of vehicles in the queue will not be larger than the difference between the arrival and the departure rates at any second of the simulation (Fig. 2.). It should be noted that the position of the arriving, stopped, and discharging vehicles is retrieved using the similar-to-wireless communication between vehicles and road infrastructure. This communication is enabled by Car2X Module, the tool included in VISSIM traffic simulation software. The application that implements backpressure algorithm using this tool to track each vehicle position (and destination) for each simulation time step, is written in C++. Signal control strategy is comprised of a set of local that are associated with ,…, controllers = . These local controllers are intersections = , … , constructed and implemented independently of one another and each of them requires only information that is local to the intersection with which they are associated [17]. Furthermore, local controller computes the phase ∈ that should be during time slot as given green time at intersection presented in pseudo code in Fig. 3. The given pseudo code corresponds to the first version of backpressure-based algorithm i.e. the queue is calculated as the sum of the number of vehicles that have stopped and the ones that are currently discharging. Model operates in a way that at the beginning of time slot it first computes weight ( ) for each traffic movement (ℒ , ℒ ) ∈ (3) and the throughput ( ) for each ∈ (4) in order to activate phase ∈ such that ,∀ ∈ during time slot . ( )= ( ) = ∑(ℒ

,ℒ )∈

( )−

( ), 0

( ) ( , ℒ , ℒ , ( ))

∑ W ab ( t ) * ξ i ( p , La , Lb , z ( t ))

Sp(t) = ( L , L )∈Ρ a b IF Sp > Sp* p* = p Sp* = Sp GO TO Step 2

(3) (4)

Once the control module determines which phase needs to be activated, it places demand on a specific detector associated with that phase. At the same time the actual controller (RingBarrier Controller) in VISSIM, which resembles field controllers, operates in free/actuated mode. This means that the controller operates in First-Come-First-Served mode and it serves only the phase selected by the backpressure control module. Since the backpressure control always activates only one phase at the time, this approach ensures implementability and practicality of this concept in the field. Several other adaptive control software, such as RHODES and InSync, use a similar method to place demand calls on the controllers in the field.

Fig. 3. First version of Backpressure Algorithm – Pseudo code for one intersection

C. Optimizations of Signal Timings To determine whether backpressure algorithms can lead to the best results when implemented on a traffic network, theoretically achieved in [17-18], the performance comparison between the proposed model and four different signal timings, is given. The performance description, in terms of number of stops, delay, travel time and throughput, is given in the following section. The four timing plans consist of fixed, actuatedcoordinated, optimized fixed and optimized actuatedcoordinated timing plans. Both fixed and actuated-coordinated (field) signal timings were retimed by VISGAOST, a Genetic Algorithm Stochastic Optimization tool based on VISSIM evaluations [21]. Cycle lengths, offsets and splits were optimized during 120 generations, which included 20 signal timing plans per generation. As a fitness function, performance index, i.e. a linear combination of delay and stops, was used (5).

PI = Total delay [h] + 10 ⋅

Fig. 2. Cumulative Arrival/Departure Curves at 4000W intersection

3

Number of stops 3600

(5)

Purpose of the optimization was to evaluatte performance of the proposed algorithm when compared to thee best-case signal timings. Algorithm used for VISGAOST optimization is presented in Fig. 4. Step 0:Initializing , Total number of generations , Total number of timing plans per geeneration , Convergence threshold , Current number of population =0 t plan Generation of initial population of timing ∀ ∈ 1, … • Read 1 from database , ∀ ∈ 2, … • Generate Step 1: Evaluating Population ∈ , ∀ ∈ 1, … Evaluation of • Encode and write 1 to database • Simulate and evaluate • Calculate Step 2: Testing Termination Criteria ) = max( ,… ) = average( ,… (( = ) − < ) Stop and RETURN ∈

ELSE

VISGAOST was used to en nsure that there are no inconsistencies that occur when a tool with different traffic model (e.g. Synchro or TRANSYT-7F) is used to optimize signals which run in VISSIM. Fig. 6 shows results of stochastic VISGAOST optimization processes. It can be seen how performance index decreases ass number of generations increases. Actuated signal timings (both ( initial and optimized) outperformed fixed timings by abou ut 18% [11]. 140

Fixed Timin gs

130

,

120 110 100 90 80 70 60

20

40

60

80

100

120

140

160

180

200

220

240

260

Number of Generations G

Fig. 6. Evolutions of signal timings duriing stochastic VISSIM-based optimization ns

To illustrate how much queue (the ( sum of the number of vehicles that have stopped and th he ones that are currently discharging) is present in the en ntire network, the authors graphed queue lengths for EB and WB W approaches for all five intersections. Fig. 7 shows moderatee queue lengths.

GO TO Step3

Step 3: Generating New Population i= + 1 Generation of initial population • Select best ranking timing planss from • Generate through GA-operattions GO TO Step 1

Actuated Timings

−1

Fig. 4. VISGAOST Algorithm – Pseudo ccode

D. Experiments Evaluation of the proposed control strateggies is performed along 3500 South Street corridor segment inn Salt Lake City, Utah (Fig. 5) by using VISSIM microsimulation software [22]. A VISSIM model was built, calibrated, and vaalidated based on the field data: signal timings, speed limits, pp.m.-peak 15-min turning-movement counts, and queue leengths at some intersections. To validate the model, travel tim mes (floating car with Global Positioning System device) alongg the arterial were measured while passing times at each inntersection were recorded. High coefficients of determination (R2) for the two pairs of data sets (0.988 for calibration and 0.986 for validation) show that a reliable model of thhe current traffic conditions on this arterial segment was achieveed [11] .

Fig. 5. Study corridor along 3500 South Street inn SLC, Utah

Fig. 7. Queue Profiles along th he 3500 S Corridor

4

III. RESULTS AND DISCUSION

16000

All of the scenarios were evaluated through five randomly seeded runs in VISSIM 5.3. Each simulation run was one hour and 15 minutes (warm up time) long. Overall, four signal timing (two for each of the fixed-timings and actuated-timings options) and two backpressure algorithm scenarios were evaluated in the following way:

¾ ¾

Number of Stops

¾

14000

Initial timings – these were scenarios with signal timings either taken from the field (actuated) or developed equivalently (fixed)

12000 10000 8000 6000 4000 2000 0 IF

Optimized – signal timings which resulted from VISGAOST optimizations (Fig. 6)

IB

MB

IB

MB

IB

MB

120.0 Total Delay Time (h)

100.0 80.0 60.0 40.0 20.0

On network level, optimized actuated signal timings yielded best results. Compared to backpressure algorithm, number of stops, total delay time and total travel time was reduced by 24%, 50% and 16% respectively. Also, throughput was increased by 1.5%. Optimized fixed signal timings also provided benefits compared to backpressure model, but lower than optimized actuated timings.

0.0 IF

IA OF OA Signal Control Strategy

b) Total Delay Time

Total Travel Time (h)

380.0

Number of stops, total delay time and total travel time were reduced by 15%, 38% and 12%, while throughput was increased by 1.4%. The only benefit of the implementation of backpressure algorithm was achieved in terms of number of stops by 5% and 28%, compared to initial actuated and initial fixed timings respectively (Table I). Graphical interpretations of the comparison of the results from Table I between observed control strategies are presented in the Fig. 8.

360.0 340.0 320.0 300.0 280.0 260.0 IF

IA OF OA Signal Control Strategy

c) Total Travel Time

NETWORK PERFORMANCE MEASURES 6000

Number of Stops

Total Delay Time (h)

Total Travel Time (h)

Throughput

14003

96.9

344.0

5935.0

10520

81.6

328.4

5941.8

8549

68.6

314.9

5931.4

7588

55.0

301.8

5941.6

10005

111.1

357.7

5851.4

10530

113.3

359.8

5854.2

Throughput (veh/h)

Performance Measures

Initial Fixed (IF) Initial Actuated (IA) Optimized Fixed (OF) Optimized Actuated (OA) Initial Backpressure (IB) Modified Backpressure (MB)

MB

140.0

Evaluation focuses on a four conventional performance measures that are compared between observed signal control strategies on a network-wide level (Table I). Given that initial backpressure algorithm performed better than modified backpressure model in all terms, the following discussion is only related to the comparison between initial backpressure model and conventional signal timings.

Control Strategy

IB

a) Number of Stops

Backpressure algorithms – described in previous sections

TABLE I.

IA OF OA Signal Control Strategy

5950 5900 5850 5800 5750 IF

IA OF OA Signal Control Strategy

d) Throughput Fig. 8. Results – a) Number of Stops, b) Total Delay Time, c) Total Travel Time, d) Throughput

5

[9]

IV. CONCLUSIONS AND FUTURE RESEARCH The study proposed two signal control algorithms based on backpressure model, originally established for the maximization of the throughput in communication networks. Given that previous research mostly described theoretical effects of such systems assuming infinite queue length, authors developed microsimulation model of real traffic corridor in Salt Lake City to evaluate practical effects. The goal was to determine if such control strategy can provide best results when implemented in the field-like scenario. Evaluation was performed by comparing the results with conventional signal control practices.

[10] [11]

[12]

[13]

Results demonstrated that proposed models are outperformed by both fixed and actuated signal control strategies. The greatest benefits were achieved with actuated signal timings optimized by VISGAOST in terms of all performance measures: number of stops, total delay time, and total travel time, which also led to maximal network throughput. Maximal throughput which was achieved in previous research can be explained by hypothesis that queues do not have any constrains regarding their length. However, in field-like conditions, where queue are constrained by the link capacity, such results cannot be achieved and optimized signal timing plan would provide greatest performance.

[14]

[15]

[16] [17]

ACKNOWLEDGEMENT

[18]

This research is partially supported by the National Science Foundation under Grant No. 1229616, MRI: Development of Instrumentation to Support Multi-Technology Vehicular Networking Systems Research. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

[19] [20]

[21]

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