Efficient Priority Control Model for Multimodal Traffic Signals

Efficient Priority Control Model for Multimodal Traffic Signals Mehdi Zamanipour, K. Larry Head, Yiheng Feng, and Shayan Khoshmagham The paper presents a model for multimodal traffic signal priority control. The approach is based on an analytical model and a flexible implementation algorithm that considers real-time vehicle actuation. The analytical model considers the needs of different modes in a real-time connected vehicle environment. The model provides an optimal signal schedule that minimizes the total weighted priority request delay. The flexible implementation algorithm is designed to guarantee that the optimal signal schedule is applied with minimum negative impact on regular vehicles. The model has been tested in a simulation framework on two networks: San Mateo, California, and Anthem, Arizona. The simulation experiments showed that the model, when compared with fully actuated control, was able to reduce average delay and travel times for priority vehicles without a significant negative impact on passenger cars. The field results of implementing the priority framework in the nationally affiliated connected vehicles test bed in Anthem showed the effectiveness of the model in the real world.

to serve the requesting vehicle as soon as possible with little or no delay (1). Preemption is frequently used for emergency vehicles. In the priority system presented in this paper, a high level of priority includes skipping phases, but does not include termination of pedestrian clearance intervals or violation of minimum green times or change of clearance intervals. TSP systems modify signal operations to favor the movements of transit vehicles through a signalized intersection with less delay, less travel time variability, or both. TSP techniques can be classified as active or passive. Passive TSP techniques involve optimizing signal timing or coordinating successive signals on the basis of historical data to create a green wave for transit along the transit route. Passive techniques do not need any specialized hardware or detection systems (2). Active TSP systems rely on detecting transit vehicles as they approach an intersection. Active TSP systems are usually more effective than passive priority strategies because they can better accommodate uncertain arrival times. Active TSP includes green extension, phase advance, phase insertion, or phase rotation. The research literature addresses the design, implementation, and deployment of active TSP systems (3, 4). It has been shown that active TSP improves the performance of transit vehicles without significant impacts on the traffic on side streets (5–7). Other researchers have emphasized that TSP often has negative impacts on nontransit traffic, can cause confusion for motorists, and in many cases can result in loss of signal coordination (8, 9). Existing TSP strategies do not have an efficient way of addressing the issue of conflicting transit routes because of limited flexibility in granting priority for requests from multiple vehicles (2). Li et al. (10) and Ngan et al. (11) provided conditional priority strategies for vehicles that are behind schedule and whose reliability can be improved. Ahn and Rakha proposed an active TSP strategy that considers only one transit vehicle when there were multiple conflicting candidate transit vehicles (4). Zlatkovic et al. presented an algorithm that uses the ASC/3 logic processor and developed custom TSP strategies for resolving conflicting requests (12). He et al. adopted a fast heuristic algorithm to provide priority to multiple requests in real time (13). Despite the promising progress in previous studies, there is insufficient research on designing effective optimal transit priority signals at coordinated intersections along an arterial (14). The consideration of coordination in TSP control was proposed by Skabardonis (9). The evaluation of the effects of TSP on general traffic demonstrates the importance of incorporating signal coordination into TSP control systems (15). Ma et al. presented a coordinated transit priority control optimization model to generate the optimal priority strategies and reduce bus travel time when priority is necessary (16). Providing priority for multiple modes has been recently considered. A mixed-integer nonlinear program was formulated by Christofa and

There are many users at signalized traffic intersections, including passenger vehicles, commercial trucks, pedestrians, bicycles, transit buses, light rail vehicles, snowplows, and emergency vehicles. In North America, most traffic signal control operations are centered on general flow of traffic, with accommodations for other modes or exceptions for special considerations such as emergency vehicles. Signal priority systems manipulate the traffic signals to favor one or multiple priority vehicles at a time. The literature on traffic signal priority systems can be classified into several categories: • Preemption versus priority, • Active transit signal priority (TSP) versus passive TSP, • One approach versus conflicting approaches, • Single mode versus multiple modes, • Single intersection versus coordinated intersections, and • One request at a time versus multiple requests. Preemption can be considered the highest level of priority. Preemption interrupts normal signal operations, sometimes severely, M. Zamanipour, Department of Systems and Industrial Engineering, College of Engineering, University of Arizona, and Turner–Fairbank Highway Research Center, FHWA, 6300 George Washington Memorial Parkway, McLean, VA 22102. K. L. Head and S. Khoshmagham, Department of Systems and Industrial Engineering, College of Engineering, University of Arizona, 1127 East James E. Rogers Way, P.O. Box 210020, Tucson, AZ 85721-0012. Y. Feng, University of Michigan Transportation Research Institute, 2901 Baxter Road, Ann Arbor, MI 48109. Corresponding author: M. Zamanipour, [email protected]. Transportation Research Record: Journal of the Transportation Research Board, No. 2557, Transportation Research Board, Washington, D.C., 2016, pp. 86–99. DOI: 10.3141/2557-09 86

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Skabardonis that minimizes the total person delay while assigning priority to the transit vehicles on the basis of their passenger occupancy (2). He et al. proposed a request-based mixed-integer linear program (MILP) that can accommodate multiple priority requests from different traffic users (17). This paper is motivated by the logic in work by He et al. (17) and Zamanipour et al. (18) but presents several enhancements. The MILP in (17) is an NP-hard problem, and the solution time increases exponentially as the number of inputs (e.g., priority vehicles) increases. The model presented in this paper has a polynomial solvable structure so that the solution time increases linearly with the number of inputs. The model allows multiple priority requests to be considered simultaneously. In addition to multimodal users, system-operating principles such as coordination are included as a form of priority requests within the decision framework to make it applicable for coordinated intersections. This paper is part of the Multi-Modal Intelligent Traffic Signal System (MMITSS) project. MMITSS is a U.S. Department of Transportation Cooperative Transportation Systems Pooled Fund project that focuses on connected vehicle dynamic mobility applications. In addition to the signal priority framework presented in this paper, the MMITSS project also includes a real-time performance observer (19) and an adaptive signal control (20). More details about MMITSS development and assessment can be found in work by Ahn et al. (21).

The framework has been developed and tested in simulation with Vissim on a model of networks in San Mateo, California, and Anthem, Arizona. The system has been implemented in the field in a network of six intersections in Anthem in a connected vehicle environment. Both simulation experiments and field results show that the proposed model is able to reduce delay and travel time of vehicles eligible for priority treatment. The remainder of the paper is organized as follows: the mathematical model is presented; the flexible implementation algorithm is described; the framework in which the priority model is applied is described; the simulation and field results are presented; and the major conclusions are explained. Mathematical Model The traffic signal priority control model in this paper builds on a mathematical optimization approach and a flexible implementation algorithm. It is assumed that the sequence of phases in each ring is fixed. Skabardonis noted that phase rotation can cause confusion to the motorist, loss of coordination, and long delay to the traffic stream (9). It is assumed that an existing offline optimized signal coordination plan is available so that a virtual coordination priority request can be generated. Table 1 summarizes the notation of the mathematical model.

TABLE 1   Notation Definitions Type

Symbol

Definition

Sets

K P TM CP Jm k ∈ K p ∈ P m ∈ TM p1, p2 ∈ P jm ∈ Jm p( jm) ∈ P yp rp gminp gmaxp ElapsGrnp1 ElapsGrnp2 Initp1 Initp2 ujm ljm wm α β Ip

Set of cycles K = {1, 2} Set of phases P = {1, . . . , 8} Set of all modes TM = {1, . . . , 10} Set of predefined coordinated phase, e.g., {2, 6} Set of request numbers of mode m Index of cycles Index of phases Index of modes Index of the current phase in Ring 1 and current phase in Ring 2 at the time of solving the problem Index of the jth request of mode m Index of requested phase for the jth request of mode m Required yellow time for phase p Required red clearance time for phase p Minimum green time for phase p Maximum green time for phase p Elapsed green time of the current phase in Ring 1 Elapsed green time of the current phase in Ring 2 Required time to start the next phase in Ring 1 if current phase is in yellow change or red clearance Required time to start the next phase in Ring 2 if current phase is in yellow change or red clearance Latest arrival time of the jth request of mode m at the intersection stop bar Earliest arrival time of the jth request of mode m at the intersection stop bar Weight (e.g., importance) of mode m Weight of priority-eligible vehicles Weight of coordination An indicator that is 1, if at the current time, the signal is in early return to green of coordinated phase p ∈ CP, otherwise 0 A sufficiently large number

Indices

Parameters

Decision  variables

M t pk ∈ R g pk ∈ R

Starting time of phase p in cycle k Green time for phase p in cycle k Duration of phase p in cycle k, including clearance time

v pk ∈ R

 g k + y p + rp v kp =  p 0,

θjm ∈ {0, 1} d jm c pk

0, if the jth priority request of mode m is served in Cycle 1, otherwise 1 Delay of the jth priority request of mode m Delay of coordinated phase p in cycle k

g kp < 0 g kp = 0

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(Figure 1b). Although the model is based on the dual-ring, eight-phase structure, it is possible to reformulate the model to deal with missing phases that occur at T-intersections and other structures. The dualring controller can be modeled by a precedence graph, as depicted in Figure 1c. Arcs in the precedence graph represent the duration of phases, and nodes represent the phase transitions. Phase intervals can be visualized in the precedence graph by decomposing each arc into its respective interval precedence graph (22). The precedence graph defines the phase precedence relationships and green time feasible region. Traditionally, a signal plan is modeled by preallocated splits vpk, where vpk = gpk + yp + rp. However, in the proposed model, the allocated green time (gpk ) and the splits (vpk ) are decision variables, and the clearance times (yp + rp) are a predefined fixed value for each phase. Constraints 1 through 13 modeled the precedence graph of the dual-ring, eight-phase controller in Figure 1c.

The main structure of the mathematical model is as follows: minimize priority-eligible vehicle request delay + coordination request delay subject to • Precedence constraints, • Phase duration and interval constraints, and • Priority request delay evaluation constraints. The objective of the mathematical model is to minimize the total weighted delay for priority-eligible vehicles and virtual coordination requests. There are three sets of constraints: precedence, phase duration and intervals, and priority vehicle delay and coordination delay evaluation constraints. This mathematical model is designed to be solved over a rolling horizon. When a priority-eligible vehicle enters the range of the dedicated short-range communications (DSRC) channels, its arrival time is estimated and the model is solved. When the vehicle changes its status (e.g., joins the queue, leaves the queue, or leaves the intersection), the model is solved again. Because the standard DSRC range is 300 m (∼1,000 ft), the estimated arrival time of a priority-requesting vehicle will probably not exceed the time to serve two cycles. Therefore, the rolling horizon in this model is set to two cycles.

v pk = g pk + y p + rp t pk1+1 = t pk1 + v pk1

∀p, k

(1)

∀k

(2)

t pk1 + 2 = t pk1 +1 + v pk1 +1

∀k

(3)

t pk1 +3 = t pk1 + 2 + v pk1 + 2

∀k

(4)

t pk2 +1 = t pk2 + v pk2

∀k

(5)

Precedence Constraints The standard dual-ring, eight-phase structure specified by the National Electrical Manufacturers Association is considered in this paper, as shown in Figure 1. Each ring in the controller contains four phases

8

t pk2 + 2 = t pk2 +1 + v pk2 +1

∀k

(6)

t pk2 +3 = t pk2 + 2 + v pk2 + 2

∀k

(7)

3 Group 2

Group 1 6

Ring 1

1

5

Ring 2

2

2

1 5

4

3 7

6

8

Barrier

Barrier

(b) 7

4

(a)

5

4

3

2

1

7

6

2

1 8

5

Cycle 1

3 7

6 Cycle 2

(c) FIGURE 1   Dual-ring, eight-phase controller and precedence graph.

4 8

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∀k; (( p1 + p2 ) mod 9 ) = 0

t pk1 = t pk2 + v pk2

(8)

t pk1+1 = t pk1 +3 + v pk1 +3

∀k

(9)

t pk1+1 = t pk2 +3 + v pk2 +3

∀k

(10)

t pk2+1 = t pk2 +3 + v pk2 +3

∀k

(11)

t pk2+1 = t pk1 +3 + v pk1 +3

∀k

(12)

v pk = g pk + y p + rp

∀p, k

(13)

Phase Duration and Interval Constraints Because priority requests can be received at any point in the cycle, the optimization problem may be formulated at any time during any phase. Hence, it is necessary to capture the elapsed green time of the current phase. Constraints 14 and 15 address this need. If the phase is in the clearance interval, it is important to know how long it will take to start the next phase in the ring. This information is modeled by Constraints 16 and 17. The minimum and maximum green times are adjusted on the basis of the elapsed time by Constraints 18 and 19. If the phase is a coordinated phase and has returned to green early, the maximum green time limit is relaxed in Constraint 20. Otherwise, there is a maximum green time for each phase. t = ElapsGrn p1

if p1 is not in clearance

t = ElapsGrn p2

if p2 is not in clearance

1 p1

1 p2

(15)

if p1 is in clearance

(16)

t 1p2 = Init p2

if p2 is in clearance

(17)

max {0, gmin p1 − ElapsGrn p1 } ≤ g ≤ gmax p1 − ElapsGrn p1 1 p1

if I p1 = 0 (18) max {0, gmin p2 − ElapsGrn p2 } ≤ g1p2 ≤ gmax p2 − ElapsGrn p2 if I p2 = 0 (19) gmin p ≤ g1p

d jm ≥ t pk( jm ) − l jm

∀m, jm , k = 1

Mθ jm ≥ u jm − ( t pk ( jm ) + g pk( jm ) ) g pk( jm ) ≥ (u jm − l jm ) (1 − θ jm )

∀m, jm , k = 1 ∀m, jm , k = 1

(22) (23) (24)

(14)

t = Init p1 1 p1

phase in the current cycle (t 1p( jm) + g1p( jm)) should be larger than the latest arrival time of the request to the intersection (ujm) (right side of Constraint 23). In this case, the time between the starting time of the requested phase in the current cycle and the earliest arrival time of the request (right side of Constraint 22) is smaller than the time interval between the starting time of the requested phase in the next cycle and the earliest arrival time of the request constraint (right side of Constraint 25). Because djm is being minimized in the objective function, from Constraint 25, θjm is forced to be zero. Therefore, Constraints 25, 26, and 27 are relaxed. The delay of the priority request is calculated by Constraint 22. If the request is to be served in the next cycle, the requested phase in the current cycle should be terminated before the latest arrival time of the request (right side of Constraint 23). Therefore, Constraint 23 forces θjm to be 1, and Constraint 24 is relaxed. Constraint 26 ensures the allocated green time to the requested phase in the next cycle is at least more than the time interval between the latest arrival time of the request and the earliest arrival time of the request. Constraint 27 guarantees that the end of the requested phase in the next cycle is more than the latest arrival time of the priority request. Constraint 25 calculates the delay of the priority request.

∀p, p ∈ CP; I p = 1

d jm ≥ ( t pk( jm ) − l jm ) θ jm

∀m, jm , k = 2

(25)

g pk( jm ) ≥ (u jm − l jm ) θ jm

∀m, jm , k = 2

(26)

t pk( jm ) + g pk( jm ) ≥ u jm θ jm

∀m, jm , k = 2

(27)

In Constraint 25, the term t pk (jm)θjm is a multiplication of a real and a binary decision variable. To linearize this term, an intermediate variable (xjm = t pk (jm)θjm), is introduced and Nonequalities 29, 30, and 31 are added to the constraints. These four constraints ensure that xjm is either 0 (when θjm = 0) or t pk (jm) (when θjm = 1). In addition, Constraint 25 is replaced with Constraint 28. d jm ≥ x jm − l jm θ jm

∀m, jm

(28)

(20)

Mθ jm ≥ x jm

(21)

x jm ≥ t pk( jm ) − M (1 − θ jm )

∀m, jm , k = 2

(30)

Priority Request Delay Evaluation Constraints

t pk( jm ) + M (1 − θ jm ) ≥ x jm

∀m, jm , k = 2

(31)

Because there is uncertainty about traffic in front of the priority vehicle, the arrival time to the stop bar is considered a range (latest to earliest arrival time) to increase the robustness of the model. The range is calculated on the basis of the speed of the vehicle, the distance to the stop bar, and the vehicle mode. Constraints 22 through 27 calculate the delay of priority-eligible vehicle requests. If the request can be served in the current cycle, the end of the requested

In this model, coordination is considered a form of priority through the use of virtual coordination requests. Given a precalculated signal coordination plan, the coordinated phase split, offset, and cycle length are defined. The total number of coordination requests is at most two because this is a two-cycle model. Every time the optimization problem is formulated, the earliest (l) and latest (u) arrival times of the coordination request for the next two cycles are calculated on

gmin p ≤ g kp ≤ gmax p

∀p, k; p ∉ CP; p ≠ p1 ; p ≠ p2

∀m, jm

(29)

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the basis of the given coordination plan and the current time in the cycle. Coordination request delay for coordinated phase p in the first cycle (c1p) and in the second cycle (c 2p) are calculated with constraints similar to Constraints 22 through 31, and djm is substituted with c1p and c 2p. Objective Function min t,g,θ,µ

α

(

∑

m ∈TM, j ∈Jm

) (∑c)

w m d jm + β

k p

(32)

k, p∈CP

Equation 32 is the objective function of the model. The two main terms form a weighted summation of weighted sum of priority request delay and coordination request delay. In the first term, requests for each mode have a predefined weight (w m) that reflect the importance of that mode. The second term is the summation of coordination requests delay over the next two cycles. The importance for priorityeligible vehicles compared with the coordination requests are shown by the weights α and β. The MILP has a polynomial solvable structure that makes it efficient in solution time and implementable in real-time applications. The maximum number of binary variables is |TM| × Σm∈TM|Jm| + 4, which is the number of priority-eligible vehicles plus the four binary variables for two coordinated phases in two cycles. For each binary variable, there is a corresponding intermediate variable. The maximum number of delay-related variables is the same as the maximum number of binary variables. Therefore, the total number of decision variables is 8 × 2 × 3 + 3 × (|TM| × Σm∈TM|Jm| + 4) for two cycles in an eight-phase signal controller. The formulation has been tested using the GLPK 4.4 solver on an embedded Linux machine with a 512 MHz processor and 256 megabytes of memory. The average solution time is less than 1 s. Flexible Implementation Algorithm Because the real-time traffic demand for each phase is unknown because of the stochastic nature of traffic flow, a flexible implementation algorithm was designed to consider vehicles not eligible for priority. This algorithm reduces the negative impacts on regular vehicles because it allows the signal to operate on the basis of actuated control while ensuring the priority requests are served with minimum delay. Integration of the MILP formulation and actuated control will result in the phases being allowed to gap out if no vehicles are detected; to extend if a priority request needs to be served; to force off the phase when the maximum green extension is reached; or to force off the phase when it is needed to serve the priority request in the next phase(s) or cycle. Given the assumption of a fixed-phase sequence, a phase–time diagram (13) was constructed with one horizontal axis representing time and two vertical axes representing the phases in each of the two rings (the left axis is Ring 1 and the right axis is Ring 2), as shown in Figure 2. The origin denotes the current time and current phase, which is shown as the start of Phases 1 and 5, but could be any feasible phase combination. The projection of every arc into the time axis determines the phase duration. Any piecewise line starting from the origin represents a signal plan in the phase–time diagram. However, the feasible region of the signal plan is bounded in a coneshaped area by the shortest path (shortest timing as determined by each phase’s minimal green times) and the longest path (longest time

as determined by each phase’s maximal green times). The black dashed lines in Figure 2 show this feasible region. A priority request jm with requested phase p( jm) is associated with a desired service time interval, [ljm ujm], which represents the earliest arrival time and latest arrival time of the jth request of mode type m. In Figure 2c, the thin orange piecewise line represents the timing of Ring 1 and the thick blue piecewise line represents the timing of Ring 2. In Figure 2c, there are three requests. Two are mode m = 2, and one is mode m = 5. The first request of mode m = 2 has service time interval [l12 u12] = [2.0 6.0] and the requested phase p(12) = P2. This request has delay because the feasible starting time of the requested phase is larger than the earliest arrival time of the request (7.0 > 2.0). The second request of mode m = 2 has service time interval [l22 u22] = [36.0 41.0] and the request phase p(22) = P7. This request does not have any delay because the starting time of the requested phase is smaller than the earliest arrival time of the request (21.0 < 36.0). The first request of mode m = 5 has service time interval [l15 u15] = [26.0 30.0] and the requested phase p(15) = P4. This request does not have any delay. Assume there is just one priority request in the request list. If the optimal delay for that request is not zero, there is one optimal signal timing schedule. The optimal signal timing would allocate minimum green time to the phases so that the requested phase starts as soon as possible. However, if the optimal delay is zero, there are multiple optimal solutions for the problem. Figure 2, a and b, shows two time–phase diagrams for request jm with service time interval [ljm ujm] and the requested phase p( jm) = P8. The only mutual part of these two realizations is that phase P8 is green during the interval [ljm ujm]. To ensure that phase P8 is green during the service time interval, the predecessor phases should be held (phase hold) or forced off (phase force off) at a specific threshold. Figure 2d shows an illustration of the set of backward critical points for serving request jm without delay. These points are divided into two groups, backward left (BL) and backward right (BR). The backward left points are calculated on the basis of the backward right points. Equations 33 through 39 explain how backward right and backward left points are calculated. BR1 = u jm

(33)

BR2 = l jm − ( yP7 + rP7 )

(34)

BR3 = BR2 − gmin P7 − ( yP6 + rP6 )

(35)

BR4 = BR3 − gmin P6 − ( yP5 + rP5 )

(36)

BL1 = BR1 − gmax P8 − ( yP7 + rP7 )

(37)

BL2 = BR2 − gmax P7 − ( yP6 + rP6 )

(38)

BL3 = BR3 − gmax P6 − ( yP5 + rP5 )

(39)

where gmax and gmin are maximum and minimum times. As Figure 2d shows, some of the backward left and backward right points are infeasible points. For example, BR4, BL2, and BL3 are out of the feasible region that is created by minimum and maximum green time lines. Figure 2e shows the forward critical points (Equations 40 through 45). These points are also divided into two parts, forward right (FR) and forward left (FL). The forward right

Zamanipour, Head, Feng, and Khoshmagham

91

P5

P3

P7

P2

P6

P1

P5 0

10

20

30 Time (s)

40

50

Phases in Ring 1

P8

P5

P4 P3

P7

P2

P6

P1

P5 0

60

10

20

30 Time (s)

(a)

P7

22

P6

12

P1

Phases in Ring 1

Phases in Ring 1

P3

Phases in Ring 2

P8

15

P5 0 delay 10

20

30 Time (s)

40

50

P4

jm BL1

P3

60

BL3

0

BR4

10

20

30 ljm ujm 40 Time (s)

jm

FL1

Phases in Ring 1

Phases in Ring 1

P1

FL2

P2

FR3

FR2

FR1

P1 10

20

30 Time (s)

P4

40

50

60

50

60

jm

CLP3

CRP3

P3

CLP2 CRP2

P2

CLP1 CRP1

0

10

20

30 Time (s)

(e)

40

(f)

P2

P6

P1

P5

P4

P8

P3

P7

P2

P6

P1

P5

P4

P8

P3

P7

P2

P6

Phases in Ring 2

Phases in Ring 1

60

CRP4

P1 0

50

(d)

FL3

P3

BR1

BR3

BL2

P2 P1

FL4

P4

60

BR2

(c)

P1

50

P1

P5

P2

40

(b)

P1 P4

P8

jm

P5

P1 0

Split

Cycle 1

Split

Cycle 2

Split Cycle 3

(g) FIGURE 2   Time–phase diagram and critical points illustration (CLP 5 critical left point; CRP 5 critical right point).

Phases in Ring 2

jm

P4

P1 Phases in Ring 2

Phases in Ring 1

P1

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points are points at which each phase has been extended to its maximum time. The forward left points are points at which only minimum green time has been allocated to each phase. FR1 = max ( 0, gmax P5 − Elaps P5 + Init P5 )

(40)

FR2 = FR1 + gmax P6 − ( yP5 + rP5 )

(41)

FR3 = FR2 + gmax P7 − ( yP6 + rP6 )

(42)

FL1 = max ( 0, gmin P5 − Elaps P5 + Init P5 )

(43)

FL2 = FL1 + gmin P6 − ( yP5 + rP5 )

(44)

FL3 = FL2 + gmin P7 − ( yP6 + rP6 )

(45)

Critical points for serving priority request jm are points that create a feasible region for signal control that ensures that the request is served without delay. Critical points are also divided into two major groups, critical left points and critical right points. Figure 2f shows these points and the feasible region that they create for serving priority request jm. The critical right points of this region are the minimum of the backward right points and forward right point for each phase, and the critical left points of the region are the maximum of the backward left points and forward left points for each phase. In the case of multiple requests, the optimal request cycle assignment can be sorted on the basis of the earliest time of service. The critical point can be obtained by following a similar procedure for every request. Figure 2g shows the critical point for two coordination requests for Phases 2 and 6. The bold blue line shows one possible timing realization of the phases in Ring 2.

Priority Control Framework The priority control framework has been designed, developed, and tested as part of the MMITSS project (23). Figure 3 shows the framework. The roadside unit and the onboard unit have software components that can receive, process, and broadcast messages. The onboard unit is a hardware device deployed on the vehicle that communicates with the roadside unit through DSRC on Channel 172 (safety) or Channel 182 (selected for the MMITSS priority control). The roadside unit radio broadcasts the intersection geometry (the authors label this as MAP) and signal phase and timing (SPAT) messages (message broadcaster component) to the nearby connected vehicles that are equipped with onboard units. Each nearby onboard unit receives the SPAT and MAP (the message receiver) and broadcast signal request messages through the priority request generator. The roadside unit receives signal request messages from the onboard unit and processes them in the priority request server. Whenever a new priority request is added to the request table, the optimization model is solved and the new schedule is implemented. This process happens whenever a priority vehicle leaves the intersection or whenever the vehicle speed changes beyond a specific threshold. The traffic configuration manager hosts section-level or system-level software components, such as a user interface, a section-level priority server, and a signal coordination and priority configuration manager. The roadside unit is connected to traffic controller through ethernet with National Transportation Communications for ITS Protocol (NTCIP) commands to set control commands and get signal timing parameters and real-time signal status (NTCIP 1202 v01.0724). The proposed priority control model resides in the signal priority algorithm component that acquires the signal status message from the priority request server and priority configuration from traffic configuration manager. From these inputs, the signal priority algorithm

SPAT Data Roadside Unit

Onboard Unit

SPAT, MAP, SSM

Web Server (GUI)

DSRC Channel 172 SPAT, MAP, BSM

Message Transceiver

Message Receiver

Real Network– Vissim

Traffic Controller

MAP, SPAT, PSM MAP, PSM

Incomplete SRM

SPAT, MAP, SSM

Message Transceiver

Priority Request Server

DSRC Channel 182 SRM, SSM

SRM

PSM

PrioConf

Signal Priority Algorithm

Vehicle Config

Priority Request Generator

SRM

MAP

Message Broadcaster

Optimal Signal Control Events Traffic Controller Interface

SRM

Traffic Manager

Signal Status NTCIP Commands

FIGURE 3   Priority control framework (SPAT 5 signal phase and timing; GUI 5 graphical user interface; SSM 5 signal status message; SRM 5 signal request message; BSM 5 basic safety message; MAP 5 intersection map).

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formulates the mathematical model and solves it in real time to obtain the optimal signal timing schedule. Then, the flexible implementation algorithm is applied to the optimal solution and the critical points are obtained. A list of optimal signal control events is generated from the critical points. The event list is sent to the traffic controller interface to be implemented on the controller. The traffic controller interface implements the optimal plan on the traffic controller by sending NTCIP hold and force-off commands.

Numerical Experiments The priority control framework was implemented on two sample network models based on networks in San Mateo, California, and Anthem, Arizona. Vissim models were created and calibrated to match the field sites so that GPS data could be created for connected vehicle operations. In the first scenario in both networks, transit vehicles were considered priority vehicles. In the second scenario in the Arizona network, transit vehicles and trucks were considered priority vehicles.

San Mateo Network

(a)

The simulation network is a segment along El Camino Real that consists of eight intersections from 20th Avenue to 42nd Avenue (Figure 4a). The main street (El Camino Real) has two to three lanes in each direction and the side streets have one to two lanes. Some intersections are closely spaced, with the distance between the intersections is approximately 100 m. The total simulation period is 5 h with 30 min of warmup time (0 s to 1,800 s) and 4 h and 30 min of data collection (1,800 s to 18,000 s). There are five traffic demand levels over the time period. Each level lasts 1 h, except the last demand level, which is half an hour. The demand levels and corresponding time are defined as follows: Level 1. 1,800 s to 5,400 s (low), Level 2. 5,400 s to 9,000 s (medium), Level 3. 9,000 s to 12,600 s (high), Level 4. 12,600 s to 16,200 s (medium), and Level 5. 16,200 s to 18,000 s (low). The low, medium, and high demands are 1,000 vehicles per hour (vph), 1,200 vph, and 1,500 vph on the main street, respectively. The demand on the side streets was increased by the same ratio as the main street. The traffic signal control simulation used the Econolite ASC/3 SIL, which supports the NTCIP interface. The vehicle composition was 98% passenger vehicles and 2% trucks. There are 14 bus stops in this arterial, seven in the northbound direction and seven in the southbound direction. The headway is 10 min in both directions. The dwell time distribution of transit vehicles at each bus stop is N(20, 2) s. The results presented in this section are from the base case test scenario, in which each intersection was operated independently without coordination. Priority was provided for transit vehicles only. Fully actuated control was implemented with TSP. Average bus travel time and average bus delay in the southbound and northbound directions for five different simulation replications are presented in Table 2. The performance of the priority control model with respect to these measurements is compared with fully actuated control. Table 3 summarizes the benefits of transit priority compared with the baseline case. The average transit travel time was decreased by

(b) FIGURE 4   Overview of studied networks: (a) California and (b) Arizona. (Source: Google Maps.)

TABLE 2   Delay and Travel Time for Transit Vehicles in California Network: Fully Actuated Control: Baseline Performance Measure Average transit vehicle delay (s) Average transit vehicle travel time (s) Transit vehicle travel time SD Average weighted delay of regular vehicles

Southbound

Northbound

200.92 586.49  42.90

224.33 607.42   45.71  18.23

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TABLE 3   Delay and Travel Time for Transit Vehicles in California Network: Transit Priority Performance Measure Average transit vehicle delay (s) Average transit vehicle travel time (s) Transit vehicle travel time SD Average weighted delay of regular vehicles

9.85% in the northbound direction and by 8.02% in the southbound direction. The delay was decreased by 24.04% in the northbound direction and 23.20% in the southbound direction. Comparison of the average travel time standard deviation shows that the model increased the reliability of travel time by 42.8% in the southbound direction and 41.91% in the northbound direction. Figure 5, a and b, illustrates bus-by-bus comparison of each bus under fully actuated control and transit priority control for the northbound direction considering bus delay and bus travel time, respectively. Figure 5, c and d, shows the southbound comparison. These figures show that transit priority is beneficial for almost every individual transit vehicle.

Arizona Network The Arizona simulation network is a segment along Daisy Mountain Drive that consists of six intersections from Gavilan Peak Parkway to Anthem Way (Figure 4b). The main street (Daisy Mountain Drive) has three lanes in each direction and the side streets have one to two lanes. The total simulation period is 3 h with 30 min of warm-up time and 2 h and 30 min of data collection. During the data collection

Southbound 154.27 539.45  24.05

% −23.20 −8.02 −42.8

Northbound 170.42 547.55  26.54  18.94

% −24.04   −9.85 −41.91 3.9

period, there were five different traffic demand levels. Each level lasted for half an hour. The demand levels, corresponding time, and vehicle composition are defined similar to the California network. The performance of transit priority control was compared with fully actuated control. There are five bus stops on this arterial, three in the westbound direction and two in the eastbound direction. All of the bus stops are far side. The dwell time distribution of transit vehicles at each bus stop is N(20, 2) s. Average bus travel time and average bus delay in the corridor for the baseline for five simulation runs are presented in Table 4. Tables 4 and 5 summarize the benefits of transit priority compared with the baseline case. The average travel time decreased by 15.24% in the eastbound direction and by 11.54% in the westbound direction. The delay decreased by 43.8% in the eastbound direction and 32.07% in the westbound direction. Comparison of the standard deviation for average travel time shows that transit priority decreased the reliability of travel time by 3.02% in the eastbound direction and increased it by 24.83% in the westbound direction. In addition, the average weighted delay of regular vehicles decreased by 0.06%. Average weighted delay of the regular vehicles in the network was defined as the number of served vehicles in each section times the average delay of the vehicles in that section divided by the total number of vehicles in all sections.

300 Delay (s)

250 200 150

TSP

100

Actuation

50 0

Travel Time (s)

1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627 Bus Number (a) 700 600 500 400 300 200 100 0

TSP Actuation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Bus Number (b) FIGURE 5   Comparison for California network: (a) southbound delay and (b) southbound travel time. (continued)

Delay (s)

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400 350 300 250 200 150 100 50 0

TSP Actuation

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Bus Number (c) 800 Travel Time (s)

700 600 500 400

TSP

300

Actuation

200 100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Bus Number (d)

FIGURE 5 (continued)   Comparison for California network: (c) northbound delay and (d) northbound travel time.

Figure 6, a and b, shows a bus-by-bus comparison under fully actuated control and transit priority control for eastbound travel considering bus delay and bus travel time, respectively. Figure 6, c and d, shows the westbound comparison. These figures show that on average, transit priority was beneficial for each bus in the five simulation replications. Both the Arizona and California simulation networks consisted of regular vehicles and transit vehicles. To investigate the performance of the proposed framework when there are multiple conflicting priority requests, another scenario was designed to consider priority for trucks and transit vehicles. Trucks accounted for 2% of the vehicles in the Arizona network and did not have specific origins or destinations. Therefore, they could have a priority conflict with each other or with transit vehicles. Transit routes and departure times of transit vehicles remained the same as the previous case study. The results of five simulation runs showed 9.7% and 6.7% improvement in the travel time of buses in the eastbound and westbound directions, respectively (Table 6). Average bus delay was reduced by 29.4% and

TABLE 4   Delay and Travel Time for Transit Vehicles in Arizona Network: Fully Actuated Control: Baseline Performance Measure Average transit vehicle delay (s) Average transit vehicle travel time (s) Transit vehicle travel time SD Average weighted delay of regular vehicles (s)

Eastbound

Westbound

143.38 409.95  26.25

144.43 430.25  24.18  21.17

24.1% in each direction. Average travel time and delay of trucks was reduced by 5.1% and 9.1%, respectively, when they received freight signal priority. Meanwhile, average weighted delay of all regular vehicles increased by 9.8%.

Field Testing Results The priority framework was implemented in the field network in Anthem. It was tested as part of the MMITSS impact assessment that was conducted on Tuesday, March 3, 2015, and Wednesday, March 4, 2015, in Anthem. From the detailed test plans, on Tuesday two trucks were enabled with signal priority and traveled for 10 round-trips northbound and southbound at Gavilan Peak and Daisy Mountain

TABLE 5   Delay and Travel Time for Transit Vehicles in Arizona Network: Transit Priority Performance Measure

Eastbound

Average transit vehicle delay (s) Average transit vehicle travel time (s) Transit vehicle travel time SD Average weighted delay of regular vehicles (s)

 80.56

−43.8

 98.01

−32.07

347.44

−15.24

364.02

−11.54

3.02

22.98

−24.83

21.04

  −0.06

 27.8

%

Westbound

%

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250 Delay (s)

200 150 TSP

100

Actuation

50 0 1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 Bus Number (a)

Travel Time (s)

500 400 300 TSP

200

Actuation

100 0 1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 Bus Number (b)

Delay (s)

200 150 100

TSP Actuation

50 0 1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 Bus Number (c)

Travel Time (s)

500 400 300 TSP

200

Actuation

100 0 1

2

3

4

5

6

7 8 9 10 11 12 13 14 15 Bus Number (d)

FIGURE 6   Comparison for Arizona network: (a) eastbound delay, (b) eastbound travel time, (c) westbound delay, and (d) westbound travel time. (continued)

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Travel Time (s)

1,200

With priority

1,000

Without priority

800 600 400 200 0

1

2

3

4

5 6 Round

7

8

9

10

(e)

Travel Time (s)

1,200

With priority

1,000

Without priority

800 600 400 200 0

1

2

3

4

5 6 Round

7

8

9

10

(f) 300

With priority

TT (s)

250

Without priority

200 150 100 50 0 1

2

3

4

5 6 Round

7

8

9

10

(g) 250

With priority

TT (s)

200

Without priority

150 100 50 0

1

2

3

4

5 6 Round

7

8

9

10

(h) FIGURE 6 (continued)   Comparison for Arizona network: (e) Transit 1, (f ) Transit 2, (g) Truck 1, and (h) Truck 2.

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TABLE 6   Delay and Travel Time for Transit Vehicles in Arizona Network: Transit and Truck Priority Performance Measure Eastbound average transit vehicle delay (s) Eastbound average transit vehicle travel time (s) Westbound average transit vehicle delay (s) Westbound average transit vehicle travel time (s) Average truck delay (s) Average truck travel time (s) Average weighted delay of regular vehicles (s)

Fully Actuated

FSP + TSP

139.3

98.3

−29.4

421.1

380.1

−9.7

116.7

88.6

−24.1

417.2

389.1

−6.7

19.8 57.1 21.21

18.0 54.1 23.28

%

−9.1 −5.1 9.8

Note: FSP = freight signal priority.

Drive. Meanwhile, two transit vehicles were enabled with signal priority and traveled eastbound and westbound through the network of six intersections for 10 round-trips. The headway for the transit vehicles was 20 min. There are five far-side bus stops in the network. The average dwell time at each bus stops was 20 s. Travel time sections were designed to capture travel time in each round for each vehicle. Wednesday was designated for the base-case data collection using GPS units in the vehicles. No priority was provided on Wednesday. Two trucks and two transit vehicles traveled 10 roundtrips, and their departure times were exactly the same as on Tuesday. Figure 6, e and f, shows a one-by-one comparison of travel time for the two transit vehicles in each of the 10 round-trips on Tuesday (with priority) and on Wednesday (without priority). There was a 10.3% improvement in the average travel time of the two transit vehicles. Travel time standard deviation of the buses decreased by 41.3%. Figure 6, g and h, shows the results for the two trucks. GPS unit data of Truck 1 in the first round was unavailable. On Wednesday, Truck 1 stopped in Round 5 and 7 for pedestrians (pedestrian clearance interval was 45 s). A similar situation occurred for Truck 2 in the fourth round. There was a 3.84% improvement in the average travel time of the two trucks. Travel time standard deviation of the trucks decreased by 21.78%. The results show the effectiveness of the priority control framework in real-world conditions. Conclusion In this paper, a priority control model for multimodal traffic signal control is presented. The approach is based on an MILP and a flexible implementation algorithm that considers real-time vehicle actuation. The model is designed to be used in a connected vehicle environment. The model has been used in the Arizona connected vehicle test bed in Anthem. Several successful demonstrations show the potential for efficient multimodal traffic signal operations (19). The model has been tested in a simulation framework on two different networks: San Mateo, California, and Anthem, Arizona. Although the numerical examples in this paper consider only trucks and transit vehicles, other traffic modes such as emergency vehicles and passenger vehicles can be considered in a similar manner. The simulation experiments show that the proposed control model is able to reduce

average transit and truck delay without having a significant negative influence on passenger cars. For future research, the authors plan to elaborate the effects of mode weights in the formulation. Extensive experimental analyses, including time–space diagram-based deterministic analysis and simulation-based scenario analysis, will be performed, and results will be compared with conventional TSP strategies. The integration of the priority control model and adaptive control models is another interesting and open area that is being investigated.

Acknowledgments This work has been supported by the Arizona Connected Vehicle Initiative, a collaboration between the Maricopa County Department of Transportation SMARTDrive Program, the Arizona Department of Transportation, and the Connected Vehicle Pooled Fund Multimodal Intelligent Traffic Signal System Project.

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