Arterial Traffic Signal Optimization: A Person-based Approach

This paper presents a traffic responsive signal control system that optimizes signal settings based on minimization of person delay on arterials. The system’s underlying mixed integer linear program minimizes person delay by explicitly accounting for the passenger occupancy of autos and transit vehicles. This way it can provide signal priority to transit vehicles in an efficient way even when they travel in conflicting directions. Furthermore, it recognizes the importance of schedule adherence for reliable transit operations and accounts for it by assigning an additional weighting factor on transit delays. This introduces another criterion for resolving the issue of assigning priority to conflicting transit routes. At the same time, the system maintains auto vehicle progression by introducing the appropriate delays for when interruptions of platoons occur. In addition to the fact that it utilizes readily available technologies to obtain the input for the optimization, the system’s feasibility in real-world settings is enhanced by its low computation time. The proposed signal control system was tested on a segment of San Pablo Avenue arterial located in Berkeley, California. The findings have shown the system’s capability to outperform static optimal signal settings and have demonstrated its success in reducing person delay for bus and in some cases even auto users. TRB 2013 Annual Meeting Paper revised from original submittal. Christofa, Aboudolas, and Skabardonis 2 INTRODUCTION With the continuous growth of population and car ownership and the limited funds available, there is an imperative need to design and manage mutimodal transportation systems more efficiently while maximizing the use of existing infrastructure. With traffic signal control systems already widely deployed in urban street networks, one of the most cost-effective ways to improve efficiency and sustainability of urban transportation systems is to develop signal control strategies that enhance person mobility. This can be achieved with the development of signal control strategies that in addition to resolving conflicts between vehicles, give preferential treatment to high occupancy transit vehicles while accounting for the overall traffic conditions in the network. Several advanced signal control systems have incorporated transit signal priority strategies in their algorithms in order to manage multimodal systems more efficiently. However, none of the systems is explicitly optimizing signal settings by minimizing person delay in a network. On the contrary, they usually minimize vehicle delays (1, 2, 3) and provide priority based on rules that are not directly included in the optimization process (4) or pre-select a subset of transit vehicles to apply their priority strategies (5, 6). As a result, existing systems lack an efficient way of assigning priority to transit vehicles when they are traveling on conflicting routes. Furthermore, they often ignore the importance of transit schedule adherence in providing priority which in some cases can cause further disruptions to the transit system. Recently, an adaptive signal control system was developed that utilizes information from mobile sources to optimize signal settings on arterial networks (7). However, the requirement for high penetration of probe vehicles and the long computation times constraint its applicability in the real world. A person-based traffic responsive signal control system for isolated intersections was recently developed by the authors (8, 9). The system minimizes person delay by explicitly accounting for the passenger occupancy of autos and transit vehicles. This results to provision of signal priority to transit vehicles and introduces an efficient way for resolving the issue of priority assignment when transit vehicles travel in conflicting directions. The system uses information that can be obtained form currently deployable surveillance and communication technologies (i.e., detectors, Automated Vehicle Location (AVL) and Automated Passenger Counter (APC) systems). This paper presents an extension of the existing traffic responsive signal control system to arterials, that accounts for vehicle progression and transit schedule adherence. The paper is organized as follows: first, the optimization procedure and the underlying mathematical model that minimizes person delay are described. The next sections describe the test arterial and present the application of the signal control system. Finally, the paper discusses the findings of this work and outlines areas for future research. MATHEMATICAL MODEL The optimization of signal settings for an arterial is based on a pairwise optimization strategy introduced by Newell (10, 11). According to this strategy signal timings are optimized for a pair of consecutive intersections. Therefore, the mathematical program is formulated to minimize the total person delay at two consecutive intersections, r and r + 1, for all vehicles that are present during the design cycle, T . The optimization process starts by determining the critical intersection of the subject arterial, which could be defined as the one with the highest intersection flow ratio (i.e., demand to saturation flow ratio for critical lane groups) or the one with the highest transit traffic. Starting with the critical intersection, progression is maintained for the heaviest direction of traffic on the arterial. Once the signal settings for the first two intersections, r and r+1, are optimized, the next pair, r+1 and r+2, will be optimized. For this optimization, the beginning of green for the coordinated phase (i.e., phase that serves the heaviest direction) at r+1 will be constrained by the optimization outcome of r and r+1. This constraint ensures that the beginning of the green for that phase will be held constant when optimizing the second pair of intersections. Assuming that TRB 2013 Annual Meeting Paper revised from original submittal. Christofa, Aboudolas, and Skabardonis 3 the yellow times are constant, this can be expressed as: cr+1−1 ∑ i=1 gr+1 i,T (2) = cr+1−1 ∑ i=1 gr+1 i,T (1) (1) where cr+1 is the phase that serves the heaviest direction at intersection r+1, gr+1 i,T (1) are the optimal green times for phase i during cycle T at intersection r + 1 obtained from the optimization of the first pair of intersections, and gr+1 i,T (2) are the corresponding green times obtained from the optimization of the second pair of intersections in which intersection r+ 1 belongs. The same pairwise optimization is repeated until all intersections in the subject arterial network are optimized. In case it is not clear which direction has the heaviest traffic, the same process can be repeated in the opposing traffic direction, and the signal settings that give the lowest total person delay can be chosen. The mathematical program that minimizes total person delay at two consecutive intersections is formulated under the assumption of perfect information on traffic demand and passenger occupancies. It is also based on the assumption of deterministic vehicle arrivals (for delay estimation purposes), fixed phase sequence, and constant lane capacities. Vehicles arrive at each intersection in platoons when traveling on the arterial and on the cross-street links, since the subject arterial is considered to be part of a larger arterial signalized network. It is also assumed that there is negligible platoon dispersion. The cycle length is kept constant for the analysis period and it is common for all intersections along the arterial to maintain signal coordination. Finally, the model is formulated assuming that transit vehicles travel on mixed-use traffic lanes along with autos. However, the formulation of the mathematical model holds even when dedicated lanes for transit vehicles exist. The generalized formulation of the mathematical program that minimizes person delay for two consecutive intersections and for a cycle T is as follows: min 2 ∑ r=1 [ AT ∑ a=1 oad a + BT ∑ b=1 ob,T (1+δ r b,T )d r b ] (2a) s.t. dr a,T = d r a ( gi,T ) (2b) dr b,T = d r b ( gi,T ) (2c) gimin ≤ gi,T ≤ gimax (2d) Ir ∑ i=1 gi,T +L r =C (2e) where: r: intersection index a: auto vehicle index b: transit vehicle index AT : total number of autos present at intersection r during cycle T BT : total number of transit vehicles present at intersection r during cycle T oa: passenger occupancy of auto a [ pax veh ] ob,T : passenger occupancy of transit vehicle b for cycle T at intersection r [ pax veh ] dr a,T : delay for auto a for cycle T at intersection r [sec] dr b,T : delay for transit vehicle b for cycle T at intersection r [sec] δb,T : factor determining the weight for schedule delay of transit vehicle b for cycle T at intersection r dr a ( gi,T ) : function relating the delay for auto a to green times dr b ( gi,T ) : function relating the delay for transit vehicle b to green times TRB 2013 Annual Meeting Paper revised from original submittal. Christofa, Aboudolas, and Skabardonis 4 gi,T : green time allocated to phase i in cycle T at intersection r [sec] gimin: minimum green time for phase i at intersection r [sec] gimax: maximum green time for phase i at intersection r [sec] Ir: total number of phases in a cycle for intersection r Lr: total lost time at intersection r [sec] C: cycle length [sec]. The mathematical program is run once for every cycle for each pair of intersections and its objective function consists of the sum of the delay for all auto and transit passengers that are present at the intersection during that cycle T . Delays for autos, dr a,T , and transit vehicles, d r b,T , depend on the green times, g r i,T , which are the decision variables of the mathematical program. In fact, dr a,T and d r b,T also depend on the green times of the previous and next cycles, the yellow times, and the traffic demand. These are either pre-specified by the user or collected with the use of surveillance technologies. To simplify the notation, the delays for each platoon, lane group, and transit vehicle are included in the objective function as a variable and this variable is constrained to equal a function as shown in equations (2b) and (2c). The optimal green times also determine the beginning time of the coordinated phase (i.e., offset). As a result, offsets are effectively optimized through this process in those cases that the coordinated phase is not the first one in the cycle. Otherwise, offsets cannot be changed, because the cycle length remains constant. In those cases, in order to maintain progression in a selected direction, the offset between successive intersections is set equal to the average free flow travel time. The delays of both autos and transit vehicles are weighted by their respective passenger occupancies in the objective function. The delays for transit vehicles are also weighted by a factor (1+δb,T ) in order to account for the schedule delay that a transit vehicle b has when arriving at intersection r during cycle T . This factor, δb,T , which is user-specified, can be a linear function of the schedule delay of the transit vehicle or a binary variable indicating whether a transit vehicle is ahead or behind schedule based on a predetermined threshold. In either case, the delay for a transit vehicle that is behind schedule is weighted more than a transit vehicle that is arriving early or on time at the intersection. Three constraints are introduced for the decision variables. The green times of each phase i and intersection r are constrained by their minimum and maximum green times (constraint (2d)). Minimum green times, gimin, are necessary to ensure safe vehicle and pedestrian crossings and guarantee that no phase is skipped. Maximum green times, gimax, are used to restrict the domain of solutions for the green times of the phases and reduce computation times. The phase green times are also constrained such that the sum of the green times for all phases at each intersection plus the total lost time adds up to the cycle length (constraint (2e)). The total lost time is assumed to be the summation of the yellow times per phase. After the first pair is optimized the additional constraint described in equation (1) is added for each subsequent pair of intersections to ensure that the optimal decision from the optimization of the previous pair is accounted for in the optimization of the next one. Auto Delay For each pair of intersections, the auto delays that contribute to the objective function of the optimization consist of three terms: 1) the delay experienced by vehicles that travel in platoons on incoming links during cycle T , 2) the delay experienced by vehicles that travel on shared links during cycle T , and 3) the delay experienced by vehicles that did not get served during the previous cycle, which constitute the residual queues at the approaches of the two intersections during cycle T . This means that during cycle T a platoon could be experiencing delay while traveling on the incoming link (approaching the first intersection of the arterial it arrives at) and a portion of that platoon that continues in the subject network could be experiencing delay while traveling on the shared link (approaching the second intersection of the arterial it arrives at). These TRB 2013 Annual Meeting Paper revised from original submittal. Christofa, Aboudolas, and Skabardonis 5 two delay components ensure that the effect of disrupting progression is accounted for in both directions. Since the optimization is conducted using a pairwise approach, the delays are calculated for each pair of intersections r and r+ 1 in order to optimize the signal settings for that pair. There is symmetry in the formulas for the delays of vehicles traveling in the direction of progression and those traveling in the opposing direction. Suppose that r is the first intersection of the pair being optimized, and the optimization sequence is r and then r+1, which is the second intersection of the pair. For any platoon, the first intersection at which it arrives is denoted by u, and the second intersection at which a portion of it arrives is denoted by v. This means that for a platoon traveling in the direction of progression u = r and v = r+ 1, while for a platoon traveling in the opposing direction u = r+ 1 and v = r. The same holds for transit vehicles. This notation is used for the remainder of the paper for both auto and transit delays. The auto delays are estimated based on the assumption that vehicles arrive and are served at both intersections at capacity since they travel in platoons with no dispersion. Consequently, assuming that kinematic wave theory (12, 13) holds, all vehicle trajectories are parallel at all times, as shown in Figure 1. This means that the first and last vehicle that get stopped in a platoon will experience the same delay. So, the collective delay for all vehicles can be easily estimated knowing only the arrival time of the first vehicle in a platoon at the back of its lane group’s queue at intersection r, tj,T , the size of that platoon, P r j,T , and the traffic conditions at the approach as expressed by the size of the residual queue of lane group j at the end of the previous cycle T −1, Nj,T−1.