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System Optimal Signal Optimization Formulation
Abstract
A mixed-integer linear programming formulation is proposed to solve the combined system optimal dynamic traffic assignment and signal optimization problem. Traffic conditions are modeled with the cell transmission model, a convergent numerical approximation to the hydrodynamic model of traffic flow. The formulation is suited to respond to oversaturated traffic conditions. It also can be adapted to account for turning movements, protected and permissive phases (gap acceptance), and multiple signal controller types: dynamic (traffic adaptive) and pretimed. Trials with a test network validated the formulation and achieved promising results. Specifically, dynamic signal control proved to be substantially more effective than pretimed control for incident conditions. In addition, potential benefits of rerouting vehicles in both directions of a roadway were revealed even when only one direction is closed.
... DTA deployment has brought many benefits to a wide range of applications over the past decades. Network design [1]- [4], traffic operations [5], [6], congestion pricing [7], evacuation planning [8], and traffic management systems [9] are some of DTA applications. DTA with accurate network loading models has many decision variables and constraints to encompass its spatial/temporal scales and the number of origin-destination (OD) pairs. ...
... Centralized approaches solve the optimization model with no decomposition, distribution, or parallelism. Central optimization frameworks do not scale with the size of DTA, especially when complex network loading concepts, such as CTM are in use [5], [10]- [13]. Decomposition approaches convert the model into sub-problems and a master problem. ...
... He solved the program centrally using the Simplex method for a small network with 10 cells. Beard and Ziliaskopoulos [5] further improved this formulation to jointly optimize signal timing parameters and traffic assignment considering multiple OD pairs. This formulation was a mixed-integer linear program and was solved centrally for only two intersections. ...
This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of common decision variables. A sub-problem receives proposed values for common decision variables from all adjacent sub-problems and incorporates them into its own offered values by weighted averaging and enforcing a gradient step to minimize its objective function. Then, the updated values are projected onto the feasible region of the sub-problems. The algorithm finds high quality solutions in all tested scenarios with a finite number of iterations. The algorithm is tested on a case study network under different demand levels and finds solutions with at most a 5% optimality gap.
... Many studies have proposed rule-based heuristics [4]- [6] and optimization models [1], [2] to address the issues of transit priority requests from conflicting movements. However, not enough attention has been given to formulating an optimization program using the cell transmission model (CTM) [7], [8] in a multi-class environment, despite promising progress on signal timing optimization for a single class of vehicles using the CTM [9]- [14]. CTM can explicitly consider different vehicle classes and turning movements in an intersection. ...
... The position χ t b of bus b ∈ B n at time step t ∈ T is updated based on its position χ t −1 b and speed u t −1 b,i in the previous time step, see constraints (14). Note that when bus b ∈ B n is present in cell i ∈ P b n i at time step t, ϕ t b,i will be one and ensures that constraints (14) are active. ...
... The position χ t b of bus b ∈ B n at time step t ∈ T is updated based on its position χ t −1 b and speed u t −1 b,i in the previous time step, see constraints (14). Note that when bus b ∈ B n is present in cell i ∈ P b n i at time step t, ϕ t b,i will be one and ensures that constraints (14) are active. Constraints (15) are used to set the initial position χ t =0 b to all buses on the network. ...
Existing multi-class cell transmission model (CTM) based methodologies for signal timing or traffic assignment may transfer prioritized transit vehicles from one cell to the next one before processing their preceding passenger cars. In addition, existing CTM-based methodologies process a proportion of a slow-moving transit vehicle in each time step. As such a portion of each transit vehicle remains in each cell and it never clears them. This paper presents constraints to project the position of transit vehicles based on the speed and cell occupancy variations between different classes of vehicles and incorporates them into the CTM. The resulting optimization program is a mixed-integer nonlinear problem. We used a distributed receding horizon control framework to solve it in real-time. The proposed formulation is executed in a simulated arterial street with four signalized intersections in Springfield, IL with different traffic volume levels and transit vehicle frequencies. The results showed that the proposed algorithm addressed the mentioned issues of the existing multi-class CTM, and yielded more efficient network performance than the conventional transit signal priority-based (CTSP) systems. The proposed formulation reduced average bus delay by 1% to 70% and car delay by 52% to 76% compared to CTSP.
... These typically require the use of integer variables, particularly if time is treated as a discrete variable. Examples of such formulations include [25]- [28], which use large numbers of binary variables, and researchers often resort to metaheuristic solution methods given such difficulties; see for example [29]. ...
... Note that all of the associated connector flows y t iu , y t pu , y t uv , y t vj , and y t vq are binary variables in this modified representation. In this setup, separate cells for each of the turning movements proposed in previous work [27], [28] is not needed. Our setup can also accommodate many different types of phasing schemes when considering signal timing; any two movements may proceed through the intersection simultaneously as long as they do not conflict. ...
... Our setup can also accommodate many different types of phasing schemes when considering signal timing; any two movements may proceed through the intersection simultaneously as long as they do not conflict. This is in contrast to the two phase setups in [25], [27] and [28]. Also, the binary variables α t ij representing the conflicting signal phases are no longer required to enforce conflict free flows at the intersection and we, henceforth, shall treat them as exogenous variables that are inferred from the other flow variables. ...
This paper investigates the vulnerability of urban traffic networks to cyber attacks on traffic lights.We model traffic signal tampering as a bi-objective optimization problem that simultaneously seeks to reduce vehicular throughput in the network over time (maximize impact) while introducing minimal changes to network signal timings (minimize noticeability). We represent the Spatio-temporal traffic dynamics as a static network flow problem on a time-expanded graph. This allows us to reduce the (non-convex) attack problem to a tractable form, which can be solved using traditional techniques used to solve linear network programming problems. We show that minor but objective adjustments in the signal timings over time can severely impact traffic conditions at the network level. We investigate network vulnerability by examining the concavity of the Pareto-optimal frontier obtained by solving the bi-objective attack problem. Numerical experiments are carried to illustrate the types of insights that can be extracted from the Pareto-optimal frontier. For instance, our experiments suggest that the vulnerability of a traffic network to signal tampering is independent of the demand levels.
... Other work does not consider turning flows at all [68,[70][71][72][73][74] . In these papers [71,[75][76][77][78] , extra cells in the center area in the intersections are introduced to model vehicle turning and spillbacks. All the turnings were modeled explicitly in the research of Pohlmann et al. [76] to consider the travel time that drivers spend in the conflict area. ...
... Every proportion of the traffic flow assigned to a route when entering the network is assumed to follow through the route. In the intersection area, center cells L i , T i and R i (i = 1, 2, 3, 4) are used to model vehicle conflict and spillback behaviors [71,[75][76][77][78] . The merging and diverging behaviors at the intersection are complicated since different vehicle traveling routes are considered. ...
... Underlying constraints on signal cycle, offset and split are considered. A mixed-integer linear programming formulation was proposed by Beard et al. [77] to solve the combined system optimal dynamic traffic assignment and signal optimization problem with CTM. The formulation is suited for different signal types and oversaturated situations. ...
Transportation system is an important component in modern society. It is necessary to understand different traffic phenomena in order to achieve transportation efficiency, and potential economic and social benefits. With the ever-increasing traffic all over the world, effective control and optimization of transportation system has always been demanded. This thesis investigates comprehensive traffic system dynamics and proposes novel optimization algorithms for development of intelligent transportation system. Common traffic systems are studied in this thesis, including urban street, highway, intersection, urban network and intelligent vehicle.
Urban street consists of a wide variety of traffic participants including cars, bicycles, pedestrians and so forth. Significant influence of interactions between different entities on traffic system has been observed. In this thesis, we focus on the interaction between vehicles and pedestrians, and its effect on different traffic performance including transportation efficiency, traffic safety and energy consumption. Pedestrian noncompliance crossings are investigated, as well as vehicle lane-changing behaviors to avoid pedestrians.
While vehicle longitudinal behaviors have been studied extensively in the literature, lane-changing movements receive much less attention, especially in highway system with bottlenecks. Because of traffic accident, some lanes are closed along the highway, and the bottleneck due to lane reduction is formed. Vehicles have to change lane to cross the forbidden area, that leads to complex interactions among vehicles before the incident place. Due to malfunction, some vehicle travels much slower than the other ones, that results in a moving bottleneck. The models of traffic bottlenecks are formulated in this thesis, and the influence of the bottleneck on traffic performance is studied.
As crucial nodes in the city traffic network, intersections have significant impact on the traffic performance. Effective regulation of vehicle flow at intersections has always been an important issue in traffic systems. The intersection system is extensively studied in this thesis. The influence of vehicle flow, pedestrian flow, speed limit, driver rational rate and so forth on the intersection performance is investigated. A multi-objective optimization algorithm is proposed to achieve better traffic performance including reducing traffic delays, enhancing safety and achieving energy economy. Signal setting and lane assignment are optimized simultaneously. We find the performance improvement by the combined optimization method can not be achieved by the signal optimization alone.
Furthermore, multiple turning lanes are often used at large intersections to discharge strong turning traffic flows. While transportation efficiency can be usually improved by multiple turning lanes, traffic safety tends to be compromised. The effects of multiple turning lanes on large intersection systems are investigated. A multi-objective optimization algorithm is proposed to design optimal lane assignment at large intersections. It is observed that turning lane number has significant influence on large intersection performance, and improvements in the optimization results can be obtained if turning lane assignment is incorporated in the design space.
Traffic network congestion in urban area has been a serious problem all over the world. Transportation system suffers from long delays derived from intersections in network. This thesis proposes two coordinated signal optimization methods to improve network performance. Since popular network models in the literature are often over simplified, we develop a traffic network model considering many realistic issues such as route choices and vehicle turning behaviors. A static signal optimization method is proposed. Signal timing, left-turn signal type and lane assignment at each intersection in the network are optimized based on the prior information of the network such as traffic demands. It is an offline algorithm, that can handle large networks with many intersections. The other optimization method is dynamic predictive network signal control. It is an online algorithm that considers instant traffic environment information. The optimal Pareto solution set can be obtained at each control step by predicting the system behavior in the prediction horizon with different designs. The dynamic optimization method is robust to uncertainty, disturbances and model mismatch. The online computational load can be significantly reduced to be acceptable with the help of CPU parallel computing.
Autonomous vehicle intelligence has great potential to improve mobility, enhance traffic safety and achieve energy economy in intelligent transportation system. However, the state-of-the-art autonomous driving technologies such as sensing, decision making and motion planning have not achieved the same performance as those of good human drivers. In this thesis, we present a study on the autonomous ground vehicle planning and control. A dynamic high-level motion and trajectory planning method is proposed. Following the idea of defensive driving, the autonomous vehicle is supposed to avoid careless-driving and aggressive neighbors. The trajectory is optimized based on the desired motion plan considering stability, safety, travel efficiency, driving comfort and so forth. Moreover, an optimization on the low-level adaptive cruise control is carried out. We propose a PID form control in the car-following mode. A wide variety of scenarios are created to test the effectiveness of the proposed method.
... System optimal dynamic traffic assignment (SODTA) has been studied in a wide range of applications, either as an independent problem or embedded in other problems. Applications include eco-friendly routing problems (Aziz & Ukkusuri, 2012;Long, Chen, Szeto, & Shi, 2016;Lu et al., 2016), network policy evaluation (Karoonsoontawong & Waller, 2010), supply chain management (Hajibabai, Bai, & Ouyang, 2014), congestion management (Beard & Ziliaskopoulos, 2006;Doan, Ukkusuri, & Han, 2011;Hajbabaie from the beginning of a link to its end. Moreover, the anisotropic property of traffic and queue spillbacks is not captured. ...
... The formulation is solved centrally using Simplex algorithm for a very simplified network of 10 cells without any signalized intersections. Beard and Ziliaskopoulos (2006) have proposed a cell-based mixed integer linear formulation to include signal timing optimization and multiple OD pairs in the previous problem. This formulation is tested centrally on a small network of two intersections. ...
... 1. Limited scalability (Beard & Ziliaskopoulos, 2006;Chiu & Zheng, 2007;Li et al., 2003;Zheng & Chiu, 2011). Our proposed methodology addresses this issue by decomposing the CTM-based SODTA into several single OD subproblems. ...
This paper presents a decomposition scheme to find near-optimal solutions to a cell transmission model-based system optimal dynamic traffic assignment problem with multiple origin-destination pairs. A linear and convex formulation is used to define the problem characteristics. The decomposition is designed based on the Dantzig-Wolfe technique that splits the set of decision variables into subsets through the construction of a master problem and subproblems. Each subproblem includes only a single origin-destination pair with significantly less computational burden compared to the original problem. The master problem represents the coordination between subprob-lems through the design of interactive flows between the pairs. The proposed methodology is implemented in two case study networks of 20 and 40 intersections with up to 25 origin-destination pairs. The numerical results show that the decomposition scheme converges to the optimal solution, within 2.0% gap, in substantially less time compared to a benchmark solution, which confirms the computational efficiency of the proposed algorithm. Various network performance measures have been assessed based on different traffic state scenarios to draw managerial insights.
... Concerning the study of traffic lights (and the control thereof) there exists a broad literature, see for example [1, 6,8,10,12,22,23,28,33,35,39,44,48,46,49,50,53,54,61,59]. The discussion depends on the used model to predict traffic flow. ...
... For notational convenience we set A i (t) = 1 for roads and junctions without traffic lights. Summarizing, the set of coupling at junctions is given by the maximization of flow subject to (9), (10) and the conservation of mass (6). ...
... Several approaches on optimal traffic light switching are found in literature, see for example [6,9,10,22,23,28,33,39,44,46,49,53,54,62]. Usually models based on cell transmission [8,50], fluid equations [13,25], mixed-integer formulations [48] and heuristics [35] are considered. ...
We discuss continuous traffic flow network models including traffic lights. A mathematical model for traffic light settings within a macroscopic continuous traffic flow network is presented, and theoretical properties are investigated. The switching of the traffic light states is modeled as a discrete decision and is subject to optimization. A numerical approach for the optimization of switching points as a function of time based upon the macroscopic traffic flow model is proposed. The numerical discussion relies on an equivalent reformulation of the original problem as well as a mixed-integer discretization of the flow dynamics. The large-scale optimization problem is solved using derived heuristics within the optimization process. Numerical experiments are presented for a single intersection as well as for a road network.
... A recently developed strategy of this type is the signal control strategy TUC [13] that will be outlined later. More recently, a number of strategies have been proposed employing various computationally expensive numerical solution algorithms, including genetic algorithms [14], [15], multi-extended linear complementary programming [16], and mixed-integer linear programming [17], [18]. In [17], [15], and [18] the traffic flow conditions are modeled using the cell transmission model [19] , a convergent numerical approximation to the first-order hydrodynamic model of traffic flow. ...
... More recently, a number of strategies have been proposed employing various computationally expensive numerical solution algorithms, including genetic algorithms [14], [15], multi-extended linear complementary programming [16], and mixed-integer linear programming [17], [18]. In [17], [15], and [18] the traffic flow conditions are modeled using the cell transmission model [19] , a convergent numerical approximation to the first-order hydrodynamic model of traffic flow. However, these approaches are in a relatively premature stage and their implementation and feasibility in real-life and real-time conditions are still questionable. ...
... Finally, offset and cycle time have no impact within the SFM and must be either fixed or updated in real time independently [20]. These consequences of simplification (5) is the price to pay for avoiding the explicit modeling of red-green switchings which would render the resulting optimization problem discrete (combinatorial) and lead to exponential increase of computational complexity as in910111415161718. For the application of the open-loop QPC and NOC methodologies in real time, the corresponding algorithms may be embedded in a rolling horizon (model-predictive) scheme. ...
The problem of designing real-time traffic signal control strategies for large-scale congested urban road networks via suitable application of control and optimization methods is considered. Three alternative methodologies are proposed, all based on the store-and-forward modeling (SFM) paradigm. The first methodology results in a linear multivariable feedback regulator derived through the formulation of the problem as a linear-quadratic (LQ) optimal control problem. The second methodology leads to an open-loop constrained quadratic optimal control problem whose numerical solution is achieved via quadratic-programming (QP). Finally, the third methodology leads to an open-loop constrained nonlinear optimal control problem whose numerical solution is effectuated by use of a feasible-direction algorithm. A simulation-based investigation of the signal control problem for a large-scale urban network using these methodologies is presented. Results demonstrate the efficiency and real-time feasibility of the developed generic control methods.
... However, the linearization caused flow holding-back problem. Beard and Ziliaskopoulos (2006) integrated Lo's (1999) formulation with the system optimal traffic assignment and stated that the optimization program resulted in a set of flows and densities that do not fall "on" the fundamental diagram (flow holding-back problem), and thus the flow of vehicles is not realistic. Similarly, Guilliard et al. (2016) developed an MILP for optimal traffic signal timing. ...
... Note that and are the variables in this constraint. (7) and (8) specify a maximum and minimum green time for through and left-turning movement in cell ∈ ( ) at intersection ∈ , respectively (Beard and Ziliaskopoulos, 2006). The variables in these constraints are (or ). ...
This paper formulates the network-level traffic signal timing optimization problem as a Mixed-Integer Non-Linear Program (MINLP) and presents a customized methodology to solve it with a tight optimality gap. The MINLP is based on the Cell Transmission Model (CTM) network loading concept and captures the fundamental flow-density diagram of the CTM explicitly by considering closed-form constraints in the model and thus, eliminates the flow holding-back problem. The proposed solution algorithm is based on the Benders decomposition technique and decomposes the original MINLP to an equivalent Integer Program (IP) (Master problem), and a new MINLP (Primal problem). We will show that the new MINLP has only one optimal non-holding-back solution that can be found by a CTM simulation run. We will prove that the proposed solution technique guarantees convergence to optimal solutions with a finite number of iterations. Furthermore, we propose a dual estimation algorithm for the new MINLP (the Primal problem), which utilizes a simulation-based approach to generate Benders cuts instead of solving a complex optimization program. We applied the proposed solution technique to a simulated network of 20 intersections under various demand patterns and observed an optimality gap of at most 2% under all tested conditions. We compared the solutions of the proposed algorithm with two benchmark algorithms and found reductions in total travel time ranging from 7.0% to 35.7%.
... Except for the early developed adaptive signal control systems, such as SCOOT (Hunt et al. (1982)), SCATS (Lowrie (1982)), the existing signal control problem generally contains two aspects: (1) a mathematical model for the complex traffic system, and (2) an appropriate control law such that the behavior of the system meets certain performance indices. Aboudolas et al. (2009), Lin et al. (2011, Zhou et al. (2014), Lo (2001), Beard and Ziliaskopoulos (2006) and Aziz and Ukkusuri (2012) described the signal control as a mathematical programming problem with embedded deterministic traffic flow models. However, for large-scale road networks, most of above strategies are with heavy computational burden. ...
... Except for the early developed adaptive signal control systems, such as SCOOT (Hunt et al. (1982)), SCATS (Lowrie (1982)), the existing signal control problem generally contains two aspects: (1) a mathematical model for the complex traffic system, and (2) an appropriate control law such that the behavior of the system meets certain performance indices. Aboudolas et al. (2009), Lin et al. (2011), Zhou et al. (2014, Lo (2001), Beard and Ziliaskopoulos (2006) and Aziz and Ukkusuri (2012) described the signal control as a mathematical programming problem with embedded deterministic traffic flow models. However, for large-scale road networks, most of above strategies are with heavy computational burden. ...
This paper proposes a Morkov state transition model for an isolated intersection in urban traffic and formulates the traffic signal control problem as a Markov Decision Process(MDP). In order to reduce computational burden, a sensitivity-based policy iteration(PI) algorithm is introduced to solve the MDP. The proposed model is stage-varying according to traffic flow variation around the intersection, and the state transition matrices and cost matrices are updated so that a new optimal policy can be searched by the PI algorithm. The proposed model also can be easily extended from an isolated intersection to a traffic network based on the space-time distribution characteristics of traffic flow, so as the PI algorithm. The numerical experiments of a small traffic network show that this approach is capable of reducing the number of vehicles substantially compared with the fixed-time control particularly for high traffic demand, while being computationally efficient.
... Most of the research approaches mentioned above employ computationally expensive numerical solution algorithms, including genetic algorithms [12,13], multi-extended linear complementary programming [14], mixed-integer linear programming [15,16], and ant colony optimization [17]. In view of the high-computational requirements, the networkwide implementation of these optimization-based approaches might face difficulties in terms of real-time feasibility [18]. ...
... The analysis of Table 3 and Fig. 5 shows that the average maximum queue lengths on the link of interest across different cycles decreased by 7.01 and 11.14 %, respectively, after the new and classic gating control plans were implemented. In another hand, the average vehicular delay and stops are reduced by 16.66 and 14.20 % after the new gating method was implemented; meanwhile, the two indexes are changed by 17.63 and 22.30 % with the classic gating logic. The results implied that both of the new and classic gating methods can improve the operation efficiency of the sub-area, and the effect of the classic one is better to a certain degree. ...
The purpose of this paper is to improve the intelligence and universality of the classical method for gating control in the SCOOT system. First, we introduce a method to identify spillovers, and use the occupancy threshold for spillover recognition to trigger this special control logic. Second, the interrelationship of the traffic flows among adjacent traffic links is analyzed. Accordingly, we present an influence rate model for upstream links of the bottleneck link and a share ratio model for the downstream links. With known threshold values for the influence rate and share ratio, we propose a rule and process for selecting the intersections that should be included in the sub-area of the gating control. Third, we determine total capacity adjustments for the incoming and outgoing streams of bottleneck links. Under the measures, the queue can be dissipated to a permissible length within a given period of time. After that, the apportion models for the total adjustments among different paths and links are presented. Therefore, the correlation coefficients of the traffic flows are between the bottleneck link and the other links. Next, we ascertain the capacity decrements and increments for the gated and benefiting streams. The optimization schemes are defined so as to calculate splits for the gated and benefiting intersections. Finally, we evaluate the advanced method using a VISSIM simulation. The results show that a new control method brings significant and positive effects to the bottleneck link itself and to the entire test area.
... TRANSYT-13 uses both the platoon dispersion model and the cell transmission model (CTM)) to capture traffic dynamics and different optimization techniques to optimize signal programs. CTM-based optimization approaches usually rely on the development of MILP formulations [11], [12] which are usually NP-hard; hence, meta-heuristic techniques such as genetic algorithms [13] and greedy heuristics [14] are often employed to achieve close to optimal and timely solutions. Pre-timed signal control strategies can perform fairly well during peak traffic periods, but their performance deteriorates during off-peak periods or when unexpected events create different traffic conditions than anticipated (e.g. ...
... Traffic dynamics are incorporated into the optimization problem through the CTM described in section II-A. Our formulation builds on existing centralized approaches such as [11] and [12], by relaxing the assumption of an initially zero-state system; this allows the temporal decomposition of the original problem into smaller subproblems. This implication is particularly important when one wants to solve problems over a large time period, as such problems are prohibitively large. ...
Traffic signal control is a key ingredient in intelligent transportation systems to increase the capacity of existing urban transportation infrastructure. However, to achieve optimal system-wide operation, it is essential to coordinate traffic signals at various intersections. In this paper, we model the multiple-intersection traffic signal control problem using the cell transmission model as a mixed-integer linear program. The solution of the problem is facilitated by its special structure, which allows both temporal and spatial decomposition. Temporal decomposition is employed to reduce the problem size by solving subproblems of a smaller time window compared to the original problem. Temporal subproblems can be further spatially decomposed into subproblems associated with different intersections, which are jointly solved by exchanging messages between neighboring intersections. The proposed distributed solution strategy is comprised of two phases. First, the relaxed linear problem is reformulated and distributedly solved via the alternating direction method of multipliers. Second, two distributed rounding schemes are developed to solve the original problem. Simulation results indicate that the proposed solution strategy is scalable to large transportation topologies, which is suitable for online execution, and provides close-to-optimal results.
... CTM divides each link of the network into cells. The advantage of CTM is that it represents queue spillover and shockwave propagation in traffic networks (Szeto and Sumalee, 2011;Sun et al., 2006;Ziliaskopoulos, 2000;Beard and Ziliaskopoulos, 2006;Ukkusuri et al., 2010 andLin, 2011). The flow propagation conditions in original CTM (Daganzo, 1994) constitute a feasible region of non-convex set. ...
... Ziliaskopoulos (2000) relaxed the formulation and proposed a linear programming formulation of system optimal objective with embedded CTM for single destination. However, CTM represented as a linear program contains the vehicle holding back problem and FIFO 1 violation (as a derivative of the holding back) for multiple origin-destination network (see Beard andZiliaskopoulos (2006), Ukkusuri andWaller (2008), and Zheng and Chiu (2010) for details). This paper adapts the basic framework of Ziliaskopoulos (2000), but extends the formulation to integrate the emission-based objective for multiple origin-destination networks. ...
Maintaining air‐quality standards is a major concern for transportation planners and policy makers in the United States. This necessitates considering nontraditional emission objectives in transportation systems modeling. In this research, we integrate emission‐based objective into the traditional travel time based dynamic assignment framework. Carbon monoxide (CO) emissions from vehicles are computed as functions of space mean speed (determined from an embedded mesoscopic traffic flow model). Different performance metrics (CO emission, system wide travel time, and speed profiles) from the integrated model are compared with traditional dynamic assignment model (with travel time minimization objective). In addition, results indicate changes in route choice behavior of the road users when emission objective is integrated to dynamic assignment framework.
... The literature on the combined signal optimization and static user equilibrium problem is such as (3)- (7). The literature on the combined signal optimization and system-optimal dynamic traffic assignment (SODTA) problem is such as (8)- (9). The literature on the combined signal optimization and dynamic user equilibrium problem is such as (10). ...
... The best solution found on Network 2 by RTS-MT2 is the following. The cycle lengths for signalized intersection nodes 10,8,16,6,9,17 and 18 are 235, 96, 137, 65, 59, 144 and 166 seconds, respectively; the time offsets 223, 27, 102, 6, 13, 49 and 94 seconds, respectively; the phase sequence numbers 9, 13, 9, 0, 1, 0 and 0, respectively. The green times in seconds for the 5-leg intersection, the two 4-leg intersections and the four 3-leg intersections are (46, 26, 12, 49, 72), (10,10,31,21), (10,15,10,78), (17,12,18), (10,20,11), (28, 44, 54), (14,31,103), respectively. ...
A new mixed-zero-one continuous linear bilevel formulation is presented. It simultaneously solves the traffic signal optimization problem and the dynamic user equilibrium problem and yields a mutually consistent solution. The upper-level problem finds optimal traffic signal settings (cycle lengths, green times, time offsets, and phase sequences) for prespecified signalized intersections such that the total system travel time is minimized. The lower-level problem is the existing user-optimal dynamic traffic assignment (UODTA) linear program that embeds Daganzo's cell transmission model (CTM). The reactive tabu search (RTS), based on the analogy between the direct search and the dynamical systems theory, is modified to solve the problem. There are three major modifications. First, the binary-string solution representation is chosen, and the associated encoding and decoding procedures are developed for three-, four-, and five-leg intersections. Second, three neighborhood definitions for RTS are proposed; they yield three variations of the algorithm: RTS-MT0, RTS-MT1, and RTS-MT2. RTS-MT0 uses the deterministic neighborhood definition, and the others are based on probabilistic neighborhood definitions. Third, the functional evaluation uses the existing simulation-based UODTA that uses the CTM. Comparisons of algorithm performance are conducted on a hypothetical grid network and a modified Sioux Falls, Iowa, network. The performances are compared by using three criteria: solution quality, convergence speed, and CPU time. The CPU times for RTS-MT0, RTS-MT1, and RTS-MT2 on the two test networks are approximately equal. On the other two criteria, RTS-MT2 appeared to be the best, and RTS-MT1 and RTS-MT0 were the second and the third best, respectively.
... Delay and queuing processis the critical problem of any convergence, and through these problems, we can analyze and design the intersection for a greater extent of services. The primary research area of improving the traffic light and traffic flow at the intersection are such as fuzzy logic [7][8][9], mathematical model [10][11][12][13][14], rolling horizon approach [16], neural network-based control [17], Petri Net based control [18][19][20], Markovian based control [21], queue theory [22] and some agent-based learning methods [23][24][25][26]. Some authors [27] proposed V2X communication where some vehicles negotiate with the intersection controller for the green light. ...
In today's transportation system, intersection management is one of the most difficult challenges to solve. Traffic lights are unable to cope with the system's increased mobility due to its growth. Cooperative junction management is new intersection management that has emerged as technology and communication mediums have advanced. All elements, such as road users, infrastructure, and traffic signal controllers, may efficiently communicate and coordinate traffic flow in collaborative junction management. We'll talk about how to improve road crossings using new adaptive communication approaches, as well as the obstacles that come with it.
... Delay and queuing process is the critical problem of any convergence, and through these problems, we can analyze and design the intersection for a greater extent of services. The primary research area of improving the traffic light and traffic flow at the intersection are such as fuzzy logic [7][8][9], mathematical model [10][11][12][13][14], rolling horizon approach [16], neural network-based control [17], Petri Net based control [18][19][20], Markovian based control [21], queue theory [22] and some agent-based learning methods [23][24][25][26]. Some authors [27] proposed V2X communication where some vehicles negotiate with the intersection controller for the green light. ...
Intersection management is one of the biggest challenging problems in the current scenario of the transportation system. Due to the expansion in the mobility of the system, traffic lights cannot deal with it. Nowadays, advancement in the technology and communication medium has developed one different type of intersection management: cooperative intersection management. In collaborative intersection management, all the entities like road users, infrastructure, and traffic light controllers can efficiently communicate and coordinate traffic flow. We will discuss practical techniques for improving the road's intersections through new adaptive communication techniques and the challenges of doing such things.
... Constraints (3)-(5) guarantee finding a set of dynamic signal timing parameters with protected left turn phases and do not impose a fixed cycle length to ensure as much flexibility as possible (Islam and Hajbabaie, 2017). Constraints (6) and (7) allocate minimum and maximum values to green times of through and left-turning movement ∈ ( ) in intersection ∈ (Beard and Ziliaskopoulos, 2006). Constraint (8) accounts for the effects of signal indication on the saturation flow rate of intersection cell ∈ over time by setting the variable saturation flow rate equal to zero, when the signal is red, or equal to the maximum saturation flow rate when the signal is green. ...
This paper presents an integrated formulation and a distributed solution technique for cooperative signal control and perimeter traffic metering in urban street networks with various market penetration rates of connected vehicles. The problem is formulated as a mixed integer nonlinear program thus, does not scale well with the size of the network in a centralized optimization framework due to the presence of many mixed integer decision variables and constraints. To address this limitation, we will develop a distributed model predictive control that distributes the network-level cooperative problem into several intersection-level sub-problems and coordinates their decisions. Our numerical analyses show that the proposed distributed methodology finds solutions to the problem in real-time with the optimality gap of at most 3.6% in our case studies. We have implemented the distributed methodology in Vissim and observed that cooperative signal timing and perimeter control yielded significant improvements in traffic operations. Our case study results show that the cooperative approach increases the number of completed trips by 6.0%-12.8% and 10.9%-11.0% and reduces the total travel times by 8.1%-9.0% and 23.6%-24.2% compared to independent signal control and independent perimeter control, respectively.
... In the intersection area, center cells L i , T i , and R i (i ¼ 1; 2; 3; 4) are used to model vehicle conflict and spillback behaviors (Lertworawanich, Kuwahara, & Miska, 2011;Aziz & Ukkusuri, 2011, 2012Pohlmann and Friedrich, 2010;Beard & Ziliaskopoulos, 2006;Li & Sun, 2016b). The merging and diverging behaviors at the intersection are complicated since different vehicle traveling routes are considered. ...
Traffic congestion in urban network has been a serious problem for decades. In this paper, a novel dynamic multi-objective optimization method for designing predictive controls of network signals is proposed. The popular cell transmission model (CTM) is used for traffic prediction. Two network models are considered, i.e., simple network which captures basic macroscopic traffic characteristics and advanced network that further considers vehicle turning and different traveling routes between origins and destinations. A network signal predictive control algorithm is developed for online multi-objective optimization. A variety of objectives are considered such as system throughput, vehicle delay, intersection crossing volume, and spillbacks. The genetic algorithm (GA) is applied to solve the optimization problem. Three example networks with different complexities are studied. It is observed that the optimal traffic performance can be achieved by the dynamic control in different situations. The influence of the objective selection on short-term and long-term network benefits is studied. With the help of parallel computing, the proposed method can be implemented in real time and is promising to improve the performance of real traffic network.
... The mixed-integer problem arises as each of the discrete time intervals is assigned to a certain phase and traffic belong to all other phases have to wait till the respective phase gets the green time. Beard and Ziliaskopoulos (2006) proposed an approach that combines dynamic route guidance and dynamic signal timing. In the proposed technique, the nonlinear CTM contributed by Daganzo was modified to represent signal control at the intersections. ...
Abstract Dynamic Traffic Assignment formulations are mathematical frameworks for optimal
transport system planning, assessing, and strategic traffic management. In this thesis several
novel Dynamic Traffic Assignment frameworks are proposed. These models can offer
following benefits to the society: 1. The proposed models can help us to reduce traffic
congestion. 2. They can enable us to manage traffic strategically which would reduce
emission and fuel consumption. 3. The proposed Bus Rapid Transit with Transit Signal
Priority can help us to design and analyse public transport system which would eventually
reduce passenger travel-time.
... Several SODTA-SC formulations have been proposed in the literature. Lo (1999Lo ( , 2001, Lo et al. (2001), Lin and Wang (2004), Beard and Ziliaskopoulos (2006), Zhang et al. (2010), Li (2011), Lertworawanich et al. (2011, Wang et al. (2013), Hajbabaie and Benekohal (2015), and Gao et al. (2017) present mixed-integer or non-linear SODTA-SC frameworks which have very high computational complexity. Similarly, Aziz and Ukkusuri (2012a), Hoang et al. (2016), and Mehrabipour and Hajbabaie (2017) present unified optimization frameworks for simultaneous traffic assignment and signal optimization. ...
In this paper, we propose a novel mathematical framework to formulate a unified Bus Rapid Transit (BRT) with Transit Signal Priority (TSP) system for single destination networks, namely, Bus Priority System Optimal Dynamic Traffic Assignment with Signal Control (BP SODTA-SC). This framework considers dedicated bus lanes, bus routes, and priority for public bus transport in mixed bus-car scenarios. Furthermore, this approach assures fairness to all road users. It is linear and can be applied to analyze city-size BRT-TSP systems. Our numerical results show that bus priority significantly reduces Total System-wide Passenger Travel Time (TSPT).
... etc. An important property of the CTM is the possibility to reformulate it as a relaxed set of linear constraints so that a linear programming model for the SO-DTA problem for a network can be solved efficiently (Beard et al., 2006;Li et al., 2003;Ukkusuri et al., 2008;Ziliaskopoulos, 2000). ...
This thesis develops a series of novel analytical traffic assignment frameworks to study the adaptive routing in the transportation network for a given real-time information. The analytical study shows the relation between two typical principles of route choice, i.e., user equilibria and system optimality, and the role of First-In-First-Out conditions in these principles. This relation enables the development of incremental loading method to obtain the solutions efficiently by solving a sequence of linear programs. The proposed frameworks have a wide range of applications in reality, including the congestion management and the forecast of road traffic in the network.
... To formulate a DTA framework with control, several signal control models have been proposed in the literature. Aziz and Ukkusuri (2012b), Beard and Ziliaskopoulos (2006), Lo (1999), Wang et al. (2013), Li (2011, Zhang, Yin, and Lou (2010), Lin and Wang (2004), and Lo, Chang, and Chan (2001) have presented network-wide system optimal traffic assignment and traffic signal control based on a mixed-integer optimization formulation. Non-linear (continuous) signal control formulations have been developed by Pohlmann and Friedrich (2010), and Ren et al. (2013. ...
Dynamic Traffic Assignment (DTA) is a mathematical framework that with a System Optimal (SO) objective is often used for long-term transport planning, design, and traffic management. However, the conventional SO-DTA formulation gives optimal solutions having an unrealistic vehicle Holding-Back (HB) property. Existing approaches in the literature aiming to resolve the HB problem are either computationally intractable or suffer from recursive parameter selection problem. In addition, most of the existing Signal Control (SC) models considered in the DTA formulation are mixed-integer or non-linear in nature that are not scalable for large networks. With an exception, there exists a linear signal control model that can only set signal control cycle-length equal to DTA time-slot duration, and thus trades the accuracy of the SO-DTA solution for a more realistic cycle-length. In this paper, we address the above issues by proposing a linear Non-Holding-Back SO-DTA with SC (NHB DTA-SC) formulation for single destination networks. The embedded signal control in the proposed framework enables us to set realistic cycle-length using any DTA time-slot (i.e., flexible time-scale). We find that the time-scale has a significant impact on traffic density which affects vehicle-discharged emissions. To this end, we develop a novel linear Emission-Based DTA with SC (EB DTA-SC) formulation that obtains NHB flows as well as lowest possible emission. Our results show that there is a 32% difference between NOX emission estimated by 60-second and 5-second time-scales.
... Several network-wide system optimal traffic assignment and mixed integer signal optimization formulations are presented in the literature (Aziz and Ukkusuri, 2012;Beard and Ziliaskopoulos, 2006;Lo, 1999;Zhang, Yin and Lou, 2010). The mixed-integer problem arises as each of the time units is assigned to a certain phase and traffic belonging to all other phases has to wait till the respective phase gets the green time. ...
Dynamic Traffic Assignment (DTA) provides an approach to determine the optimal path and/or departure time based on the transportation network characteristics and user behavior (e.g., selfish or social). In the literature, most of the contributions study DTA problems without including traffic signal control in the framework. The few contributions that report signal control models are either mixed-integer or nonlinear formulations and computationally intractable. The only continuous linear signal control method presented in the literature is the Cycle-length Same as Discrete Time-interval (CSDT) control scheme. This model entails a trade-off between cycle-length and cell-length. Furthermore, this approach compromises accuracy and usability of the solutions. In this study, we propose a novel signal control model namely, Signal Control with Realistic Cycle length (SCRC) which overcomes the trade-off between cycle-length and cell-length and strikes a balance between complexity and accuracy. The underlying idea of this model is to use a different time scale for the cycle-length. This time scale can be set to any multiple of the time slot of the Dynamic Network Loading (DNL) model (e.g. CTM, TTM, and LTM) and enables us to set realistic lengths for the signal control cycles. Results show, the SCRC model not only attains accuracy comparable to the CSDT model but also more resilient against extreme traffic conditions. Furthermore, the presented approach substantially reduces computational complexity and can attain solution faster.
... Several network-wide system optimal traffic assignment and mixed integer signal optimization formulations are presented in the literature (Aziz and Ukkusuri, 2012;Beard and Ziliaskopoulos, 2006;Lo, 1999;Zhang, Yin and Lou, 2010). The mixed-integer problem arises as each of the time units is assigned to a certain phase and traffic belonging to all other phases has to wait till the respective phase gets the green time. ...
Dynamic Traffic Assignment (DTA) provides an approach to determine the optimal path and/or departure time based on the transportation network characteristics and user behavior (e.g., selfish or social). In the literature, most of the contributions study DTA problems without including traffic signal control in the framework. The few contributions that report signal control models are either mixed-integer or non-linear formulations and computationally intractable. The only continuous linear signal control method presented in the literature is the Cycle-length Same as Discrete Time-interval (CSDT) control scheme. This model entails trade-off between cycle-length and cell-length. Furthermore, this approach compromises accuracy and usability of the solutions. In this study, we propose a novel signal control model namely, Signal Control with Realistic Cycle-length (SCRC) which overcomes the trade-off between cycle-length and cell-length and strikes a balance between complexity and accuracy. The underlying idea of this model is to use a different time scale for the cycle-length. This time scale can be set to any multiple of the time slot of the Dynamic Network Loading (DNL) model (e.g. CTM, TTM, and LTM) and enables us to set realistic lengths for the signal control cycles. Results show, the SCRC model not only attains accuracy comparable to the CSDT model but also more resilient against extreme traffic conditions. Furthermore, the presented approach substantially reduces computational complexity and can attain solution faster.
... proposed by Daganzo (1994 and1995) and a Mixed-Integer Linear Program (MILP) for system optimal 20 signal timing optimization proposed by Beard & Ziliaskopoulos (2006). 21 ...
This article develops an efficient methodology to optimize the timing of signalized intersections in urbanstreetnetworks.Ourapproachdistributesanetworklevel mixed-integer linear program (MILP) to intersection level. This distribution significantly reduces the complexity of the MILP and makes it real-time and scalable. We create coordination between MILPs to reduce the probability of finding locally optimal solutions. The formulationaccountsforoversaturatedconditionsbyusing an appropriate objective function and explicit constraints on queue length. We develop a rolling-horizon solution algorithm and apply it to several case-study networks under various demand patterns. The objective function of the optimization program is to maximize intersection throughput. The comparison of the obtained solutions to an optimal solution found by a central optimization approach (whenever possible) shows a maximum of 1% gap on a number of performance measures over different conditions.
... Cette approximation est connue sous le nom de "The cell transmission model ".[Lo et al. 2001] ont proposé le système DISCO qui se base sur le même modèle que[Lo, H.K , 1999] mais qui permet de traiter des réseaux plus larges. La programmation mixte en nombre entier a été remplacée par les algorithmes génétiques pour pouvoir appliquer la stratégie en temps réel.Toujours utilisant "The cell transmission model '',Beard et Ziliaskopoulos [Beard Ziliaskopoulos, 2006] ont introduit une stratégie combinant l'optimisation des plans de feu et la résolution d'un problème d'affectation dynamique. L'objectif de la stratégie est de minimiser les temps de parcours dans le réseau.[Teodorović, ...
Au cours de ces dernières années, l’Algérie a connu une explosion énorme dans le parc
national d’automobiles, de plus l’incapacité de la plupart des villes à supporter tous ces
véhicules a provoqué plusieurs problèmes de circulations (bouchons, files de circulation,
congestions, ...etc.). Pour faire face à ces situations contraignantes, on fait appel soit à une
étude globale de l’infrastructure pour l’aménagement urbain, soit à la recherche des solutions
innovantes dans le domaine de la surveillance et de la régulation améliorant à cet égard
la mobilité en agglomération. Les travaux présentés dans cette thèse se situent dans la cadre
des Systèmes de transport Intelligents (STI) et s’intéressent aux problèmes de commande du
trafic urbain via le développement d’un modèle adéquat. Nos travaux visent principalement
le contrôle la circulation au niveau des intersections adjacentes de l’aire Guelmoise.
L’idée consiste à rapprocher le comportement du trafic à un modèle hybride puis à rechercher
un plan de coordination optimal des feux de signalisation pour le contrôle du flux.
La démarche utilise conjointement deux représentations hybrides : les réseaux de Pétri hybrides
et les automates hybrides. L’intérêt de ce couplage est de bénéficier des avantages des
deux modèles permettant ainsi d’aboutir à un modèle d’Automate Hybride Rectangulaire
(AHR) imitant tous les aspects importants de la dynamique des flux de trafic où les phénomènes
de sursaturation sont illustrés par des sommets interdits.
Après avoir effectué une analyse d’atteignabilité pour vérifier ce modèle, une stratégie
de contrôle est élaboré pour générer un plan optimal des feux de trafic où de nouvelles
contraintes sont imposées pour éliminer ces sommets interdits. La synthèse consiste à limiter
l’espace de variations des variables continues (flux). Le contrôle est alors obtenu par
modification des dates d’occurrence associées aux transitions correspondant aux temps des
feux. Les résultats de comparaison montrent que l’approche de contrôle proposée surpasse
ceux obtenus par le logiciel d’optimisation de synchronisation de signaux SYNCHRO en
termes de débit total et de rapport moyen volume/capacité.
Dans cette optique, nos contributions peuvent se décliner en ces points :
² Proposition d’un modèle hybride à base d’un réseau de Pétri hybride D-élémentaire
pour la description de deux intersections adjacentes du trafic urbain;
² Construction du modèle automate hybride rectangulaire par la traduction du modèle
Réseau de Petri hybride D-élémentaire développé;
Conception d’une nouvelle approche de commande de feux de trafic basée sur le modèle
hybride combiné;
² Validation des résultats via un ensemble de simulations avec des données réelles de la
ville de Guelma.
... For a CTM-based simultaneous signal timing optimization and system optimized assignment model, we refer to Lo (2001) and to Lo et al. (2001) for the solution strategy. Other models were proposed by Lin and Wang (2004) and Beard and Ziliaskopoulos (2006) and a new approach that extends the approach proposed here will be presented in a sequel. ...
... It is because knowing the timespace dynamics of traffic flow within the link will facilitate a better understanding of the resulting SO solution, for example the level of congestion and spillback location in the network, etc. An important property of the CTM is the possibility to reformulate it as a relaxed set of linear constraints so that a linear programming model for the DSO-DTA problem for a network can be solved efficiently (Beard and Ziliaskopoulos, 2006, Li et al., 2003, Ukkusuri and Waller, 2008, Ziliaskopoulos, 2000. However, the choice to adopt CTM is not without its computational overheads. ...
... Significant works have been done to improve the traffic light control algorithms. Major research areas including mathematical model [28], [29], [30], [31], [32], [33], fuzzy logic [34], [35], [36], rolling horizon approach [37], Markovian-based control [38], neural networks-based control [39], Petri Net-based control [40], [41], [42], queue theory [43], as well as agent-based learning methods [44], [45], [46], [47]. More recently, studies on a network of signalized intersections based on max pressure and back pressure were presented in e.g., [48], [49], [50]. ...
Intersection management is one of the most challenging problems within the transport system. Traffic light-based methods have been efficient but are not able to deal with the growing mobility and social challenges. On the other hand, the advancements of automation and communications have enabled cooperative intersection management, where road users, infrastructure, and traffic control centers are able to communicate and coordinate the traffic safely and efficiently. Major techniques and solutions for cooperative intersections are surveyed in this paper for both signalized and nonsignalized intersections, whereas focuses are put on the latter. Cooperative methods, including time slots and space reservation, trajectory planning, and virtual traffic lights, are discussed in detail. Vehicle collision warning and avoidance methods are discussed to deal with uncertainties. Concerning vulnerable road users, pedestrian collision avoidance methods are discussed. In addition, an introduction to major projects related to cooperative intersection management is presented. A further discussion of the presented works is given with highlights of future research topics. This paper serves as a comprehensive survey of the field, aiming at stimulating new methods and accelerating the advancement of automated and cooperative intersections.
... More recently, a number of approaches have been proposed employing various computationally expensive numerical solution algorithms, including genetic algorithms ( [63]; [64]). In [65] and [66] the traffic flow conditions are modeled using the cell transmission model ( [43]), even if in view of the high computational requirements, the real-life implementation of these optimisation-based approaches might face some difficulties in terms of real-time feasibility. ...
In this paper a brief state of art on signal setting design is reported. Preliminarily single junction optimisation methods are described both in under-saturation and in over-saturation condition. Then the main approaches adopted for signal setting design in urban networks are illustrated. Several open issues have been addressed as it concerns the decision variables, the optimisation algorithms, the optimisation criteria (mono and multi), the traffic flow modeling. Finally after some theoretical remarks, research perspectives are outlined.
... But only two-phase signal was considered in their work. (Beard & Ziliaskopoulos 2006) proposed a CTMbased system optimal signal optimization formulation combined with system optimal traffic assignment which provides several improvements over existing mixed-integer ...
... Among the first order traffic models, a switched Mode model (SMM) has been proposed more recently [10]. This latter is a piecewise linearization of the cell transmission model (CTM), which has been currently used in intelligent transportation systems, like as in traffic dynamic assignment [11], optimization [12], traffic network design applications [13], estimation [14], and ramp metering control [15]. ...
This paper deals with macroscopic traffic modelling. It investigates real magnetic sensor data, provided by the Performance Measurements System (PeMS), in order to identify some traffic parameters related to a portion of the SR60-E highway in Califorina. Then, these parameters are used to validate a switched linear traffic model.
... and solution methods for solving the DUE problems could be found in Friesz et al. (1993); Lo and Szeto (2002); Szeto and Lo (2004); Ramadurai et al. (2010); Nie and Zhang (2010); Han et al. (2011); Ukkusuri et al. (2012), etc. On the other hand, the signal control optimization problems were studied in Lo (1999Lo ( , 2001); Ceylan and Bell (2004); Beard and Ziliaskopoulos. (2006); Ukkusuri et al. (2010); Aziz and Ukkusuri (2012), etc. These studies did an excellent job in modeling either DUE or DSO separately. However, there are very few studies that consider the integrated DUESC model. ...
This paper formulates the combined dynamic user equilibrium and signal control problem (DUESC) as a bi-level optimization problem. The signal control operator in the upper level optimizes the signal setting to minimize the system travel time whereas the road users in the lower level minimize their own costs (by changing departure times, paths or both) leading to dynamic user equilibrium behavior. Three components of the bi-level formulation are discussed including network loading model, the dynamic user equilibrium model and the signal control model. Then the combined problems are formulated as a Nash-Cournot game and a Stackelberg game. A solution technique based on the iterative optimization and assignment (IOA) method is proposed to solve the DUESC problem. We use the projection algorithm to solve the lower level and the mixed integer programming solver to solve the upper level. Extensive numerical results demonstrate the benefits of using this model.
... OPAC and RHODES use dynamic optimization to obtain the signal settings. Further, existing literature include (not limited to) rolling horizon type of control (Newell, 1998), model predictive control (Hegyi et al., 2005), store-and-forward models for traffic control (Aboudolas et al., 2009), mathematical programs with embedded traffic flow models (Lo, 2001;Lin and Wang, 2004;Beard et al., 2006;Pavlis and Recker, 2009;Aziz and Ukkusuri, 2012) and so on. Most optimization models are computationally expensive and large scale implementation is often challenging. ...
... Ziliaskopoulos (2000) reformulated a relaxed form of the CTM as a set of linear constraints and hence developed a linear programming model for the single-destination system optimum DTA problem for a network. The model was further analysed and applied by Waller (2000), Li et al. (2003), Alecsandru (2006), Beard and Ziliaskopoulos (2006), Ukkusuri and Waller (2008), Zeng (2009) and Lin and Liu (2010). The present paper introduces a similar system optimising formulation, though it instead assumes that the flow-density function for each link may have a general nonlinear form rather than the triangular or trapezoidal form usually assumed in the CTM. ...
... For a CTM-based simultaneous 316 signal timing optimization and system optimized assignment model, we refer to Lo 317 (2001) and to Lo et al. (2001) for the solution strategy. Other models were proposed 318 by Lin and Wang (2004) and Beard and Ziliaskopoulos (2006) and a new approach 319 that extends the approach proposed here will be presented in a sequel. 320 ...
When responding to unanticipated emergency events, time is of the essence. This paper proposes a heuristic algorithm for staged
traffic evacuation, referred to as HASTE, which is shown to approximate a solution to the cell transmission-based many-to-one
dynamic system optimum (DSO) traffic assignment problem. The proposed algorithm does not contain traffic holding, is fast
enough for online applications, and produces evacuee routing schedules as its output. As an application of HASTE, a mixed
0-1 integer programming extension to the DSO is proposed to identify critical signalized intersection locations in the network
for deployment of a limited number of police officers aimed at improving network throughput and further minimizing evacuee
exposure time to the hazard. For the combined problem, a genetic algorithms-based solution procedure is proposed that uses
HASTE for solution fitness. Efficiency and quality of the heuristic strategies are demonstrated via numerical experiments
for moderately sized problems.
This paper formulates a cooperative traffic control methodology that integrates traffic signal timing and ramp metering decisions into an optimization model to improve traffic operations in a corridor network. A mixed integer linear model is formulated and is solved in real time within a model predictive controller framework, where the cell transmission model is used as the system state predictor. The methodology is benchmarked in a case study corridor in San Mateo, CA, in VISSIM with two optimization scenarios, namely, optimal metering and optimal signal control, and two simulation scenarios with a preset metering plan and no metering. The numerical results show that integrated traffic signal and ramp metering control reduces delays, stops, and travel times of the corridor by up to 33.1%, 36%, and 16.4%, respectively, compared to existing benchmark conditions. With appropriate weights prioritizing freeway or arterial street operations, the integrated control balances traffic congestion between the arterial street and the freeway.
We develop and assess centralized and decentralized signal control systems with short-term origin-destination (OD) demands as inputs. Considering each intersection turning movement as a virtual link, we assign traffic demand to paths based on minimal instantaneous travel time. Then, the optimal control is formulated using a G/G/n/FIFO open queueing network model (QNM). We also solve the issue of optimal control using a three-step naïve method for the centralized system with the new inputs. Because the optimization of large-scale network traffic signals can involve sizeable numbers of decision variables and nonlinear constraints, making it a nondeterministic polynomial time (NP) complete problem, we further decompose the centralized system into a decentralized system where the network is divided into subnetworks. Each subnetwork has a dedicated agent that optimizes signals within it. Furthermore, traffic demand for the entire network is decomposed into demands for subnetworks via path decomposition index (PDI). The proposed control systems are applied to test scenarios constructed using different demand profiles in grid networks. We also investigate the impact of network decomposition strategy on signal control system performance. Results show that network decomposition with smaller subnetworks results in less computational time (CT) but increased average travel time (ATT) and total travel delay (TTD).
This paper proposes a multiobjective optimization method for signal control design at intersections in urban traffic network. The cell transmission model is employed for macroscopic simulation of the traffic. Additional rules are introduced to model different route choices from origins to destinations. Vehicle turning, merging, and diverging behaviors at intersections are considered. A multiobjective optimization problem (MOP) is formulated considering four measures in network traffic performance, i.e., maximizing system throughputs, minimizing traveling delays, enhancing traffic safety, and avoiding spillovers. The design parameters for an intersection include turning signal type, cycle time, signal offset, and green time in each phase. The resulting high-dimensional MOP is solved with the genetic algorithm (GA). An algorithm is proposed to assist the user to select and implement the optimal designs from the Pareto optimal solution set. A case study in a grid network of nine intersections is carried out to test the optimization algorithm. It is observed that the proposed method is able to achieve the optimal network performance with different traffic demands. The convergence and coefficient selection of GA are discussed. The guidelines for network signal design and operation from the current studies are presented.
With expanded development of subway systems, regenerative braking energy utilization has been intensively studied from a timetable synchronize point of view. Yet, even successful modeling approaches such as those based on regenerative braking technique still do not fully take into account the fact that at lower than threshold speed, no energy can be utilized. To achieve a better performance on energy-efficient operation with the actual problem, this paper formulated a timetable rescheduling model (TR model) to optimize the timetable by maximizing the overlapping time between accelerating and regenerative braking actions of trains in the same substation with the consideration of regenerative braking process. We design a genetic algorithm (GA) to solve the model and present some numerical experiments based on the actual operation data of Beijing Yizhuang subway line in China. It is shown that the model can reduce the energy consumption by 25.3% compared with the current timetable. In addition, numerical experiments show that the dwell-time and lower limits of headway have a strong effort on regenerative energy utilization.
This paper presents a Distributed-Coordinated methodology for signal timing optimization in connected urban street networks. The underlying assumption is that all vehicles and intersections are connected and intersections can share information with each other. The novelty of the work arises from reformulating the signal timing optimization problem from a central architecture, where all signal timing parameters are optimized in one mathematical program, to a decentralized approach, where a mathematical program controls the timing of only a single intersection. As a result of this distribution, the complexity of the problem is significantly reduced thus, the proposed approach is real-time and scalable. Furthermore, distributed mathematical programs continuously coordinate with each other to avoid finding locally optimal solutions and to move towards global optimality. We proposed a real-time and scalable solution technique to solve the problem and applied it to several case study networks under various demand patterns. The algorithm controlled
queue length and maximized intersection throughput (between 1% and 5% increase compared to the actuated coordinated signals optimized in VISTRO) and reduced travel time (between 17% and 48% decrease compared to actuated coordinated signals) in all cases.
This paper considers the distributed solution of the online network traffic signal control problem. Toward systemwide optimality, the problem is modeled as a large-scale mixed-integer linear program with the traffic dynamics captured by the cell transmission model. The alternating direction method of multipliers (ADMM) is used to achieve spatial problem decomposition and to design an iterative approach that achieves networkwide solution under a fully distributed architecture, where computation, communication, and control are performed locally at individual intersections. Two ADMM-based algorithms were developed on the basis of appropriate problem reformulations; these algorithms resulted in the solution of convex-nonconvex subproblems with distinct properties. The performance of the algorithms was demonstrated to be close to global optimality and comparative to that of genetic algorithms. Each algorithm offers a different trade-off between communication and computation complexity.
This paper provides an approach to solve the system optimal dynamic traffic assignment problem for networks with multiple O-D pairs. The path-based cell transmission model is embedded as the underlying dynamic network loading procedure to propagate traffic. We propose a novel method to fully capture the effect of flow perturbation on total system cost and accurately compute path marginal cost for each path. This path marginal cost pattern is used in the projection algorithm to equilibrate the departure rate pattern and solve the system optimal dynamic traffic assignment. We observe that the results from projection algorithm are more reliable than those from method of successive average algorithm (MSA). Several numerical experiments are tested to illustrate the benefits of the proposed model.
This research presents a unified framework for dynamic traffic assignment and signal control optimization. An objective function based on the system-optimal approach with an embedded traffic flow model (the cell transmission model) for dynamic traffic assignment was considered. The optimization model (a mixed-integer program) explicitly considered intersection delay and lost time from phase switches in addition to a traditional travel time objective. Two test networks were used to demonstrate the applicability of the proposed model. Results showed better performance of the models when they were compared with fixed-signal timing plans. The formulation of signal control design also accounted for the variation of cycle length, and results showed the variation of cycle lengths with different objective functions under different levels of congestion.
Traffic signal control is a key ingredient in intelligent transportation systems (ITS) to increase the capacity of existing urban transportation infrastructure. However, to achieve optimal system-wide operation it is essential to coordinate traffic signals at various intersections. In this paper we model the multiple-intersections traffic signal control problem using the cell transmission model. For its solution, we propose two online distributed strategies, which are based on spatially and temporally decomposing the problem into subproblems associated with different intersections and iteratively solving them by exchanging information between neighboring intersections. Simulation results for a four intersection topology indicate that the proposed strategies achieve distributed, online and close to optimal signal timing plans.
This paper presents a generalized signal optimization model for arterials experiencing multiclass traffic flows. Instead of using conversion factors for nonpassenger cars, the proposed model applies a macroscopic simulation concept to capture the complex interactions between different types of vehicles from link entry and propagation, to intersection queue formation and discharging. Since both vehicle size and link length are considered in modeling traffic evolution, the resulting signal timings can best prevent the queue spillback due to insufficient bay length and the presence of a high volume of transit or other types of large vehicles. The efficiency of the proposed model has been compared with the benchmark program TRANSYT-7F under both passenger flows only and multiclass traffic scenarios from modest to saturated traffic conditions. Using the measures of effectiveness of the average-delay-per-intersection approach and the total arterial throughput during the control period, our extensive numerical results have demonstrated the superior performance of the proposed model during congested and/or multiclass traffic conditions. The success of the proposed model offers a new signal design method for arterials in congested downtowns or megacities where transit vehicles constitute a major portion of traffic flows.
This work presents two analytical models for the traffic signal control problem within dynamic traffic assignment framework. The bi-level formulation is based on a Stackelberg Duopoly game where the upper level objective is to determine optimal signal timing plans with the lower level representing a dynamic user equilibrium conditions. In addition, a single level system optimal model is proposed. Cell transmission model is adapted as the embedded traffic flow model in the form of a mathematical program. The single level program is solved and tested on a network containing multiple signalized intersections. It is found that the proposed model performs better than pre-timed signal timing plans.
This paper proposes a trimodal model of urban traffic for controlling the traffic policy. A model predictive control is then designed. The model focuses on the general traffic (private vehicle and bus) mode and BRT (Bus Rapid Transit) mode. An innovative model is presented for both the BRT mode, the private vehicles mode (VP) and for the Buses mode. The model is essentially based on the TUC (Traffic-responsive Urban Control) strategy. Based on this model, a predictive control is presented by minimising a cost function in order to control the urban traffic. The effectiveness strategy is illustrated by simulation results.
SUMMARY This paper presents an integrated model to design routing and signal plans for massive mixed pedestrian-vehicle flows within the evacuation zone. The proposed model, with its embedded formulations for pedestrians and vehicles in the same evacuation network, can effectively take their potential conflicts into account and generate the optimal routing strategies to guide evacuees toward either the pickup locations or their parking areas during an evacuation. The proposed model, enhancing the cell transmission model with the notion of sub-cells, mainly captures the complex movements in the vehicle-pedestrian flows and can concurrently optimizes both the signals for pedestrian-vehicle flows and the movement paths for evacuees. An illustrating example concerning the evacuation around the M&T Bank Stadium area has been used to demonstrate the application potential of the proposed model. Copyright © 2013 John Wiley & Sons, Ltd.
Traffic holding-back is considered an undesirable issue in dynamic traffic assignment since the vehicles are artificially held back on links in spite of the availability of downstream capacity. Holding-back occurs naturally in some system optimal dynamic traffic assignment models. In this paper, we focus on the holding back issue in the cell transmission based models and review the current methods of solving holding-back to understand their advantages and drawbacks. Then, we propose improvements to overcome the drawbacks of the current models. Finally, we propose a novel model which completely eliminates holding-back in a system optimal dynamic traffic assignment for traffic networks with multiple O–D pairs. Rigorous numerical results illustrate the benefits of using the proposed models.
In this paper, three heuristic solution algorithms, (the Dive-and-Fix method, the Ratio-cluster method, and the Cumulative-departure method) are specially designed to solve the traffic signal control problem formulated as a 0-1 mixed-integer linear programming problem with cell transmission model. These three solution algorithms are based on two fundamental approaches. First, the 0-1 mixed-integer linear program is solved via linear relaxation (LR). Second, the non-integer solutions obtained from the LR are converted into the integer solutions by taking advantage of the underlying physical mechanism embedded in the LR solutions that lead to the optimal signal control. In particular, proportional capacities for different approaches and the cumulative exit flow at each intersection obtained from the LR solutions are utilized to determine green time allocation for each approach. It is demonstrated that the near-optimal solutions obtained with these algorithms are very close to the optimal solutions under both uncongested and congested traffic conditions.
Optimization of system performance in congested traffic networks is one of the main goals of intelligent transportation systems. A formulation and solution algorithm for the combined signal control and dynamic traffic assignment problem is presented. The solution algorithm is implemented and tested on an actual network, illustrating the benefits that could be attained through joint optimization of signal control and route guidance decisions.
In this article a dynamic system-optimal traffic assignment model is formulated for a congested urban road network with a number of signalized intersections. A simulation-based approach is employed for the case of multiple-origin-multiple-destination traffic flows. The artificial intelligence technique of genetic algorithms (GAs) is used to minimize the overall travel cost in the network with fixed signal timings and optimization of signal timings. The proposed method is applied to the example network and results are discussed. It is concluded that GAs allow the relaxation of many of the assumptions that may be needed to solve the problem analytically by traditional methods.
The existing network traffic signal optimization formulations usually do not include traffic flow models, except for control schemes such as SCOOT that use simulation for heuristic optimization. Other conventional models normally use isolated intersection optimization with traffic arrival prediction using detector information, or optimization schemes based on green bandwidth. A complete formulation of the problem is presented, including explicit constraints to model the movement of traffic along the streets between the intersections in a time-expanded network, as well as constraints to capture the permitted movements from modern signal controllers. The platoon dispersion model used is the well-known Robertson's model, which forms linear constraints. Thus, it is a rare example of a traffic simulation being analytically embedded in an optimization formulation. The formulation is an integer-linear program and does not assume fixed cycle lengths or phase sequences. It assumes full information on external inputs but can be incorporated in a sensor-based environment as well as in a feedback control framework. The formulation is an integer-linear program that may not be efficiently solved with standard simplex and branch and bound techniques. Network programming formulations to handle the linear platoon dispersion equations and the integer constraints at the intersections are discussed. A special-purpose network simplex algorithm for fast solutions is also mentioned.
An algorithm to design signal coordination for networks with oversaturated intersections is presented. The basic concept of signal coordination applied to oversaturated single arterials is extended for a grid network of arterials, which involves greater analytical and computing complexity. In this algorithm, signal coordination is formulated as a dynamic optimization problem. The problem is developed to coordinate oversaturated signals along an arterial that crosses multiple, parallel coordinated arterials. Signals along crossing arterials are also oversaturated. During an oversaturated period, the algorithm manages local queues by spatially distributing them over a number of signalized intersections and by temporarily spreading them over signal cycles. Depending on the traffic demand's variation and the position of critical signals, the algorithm intelligently generates optimal signal timing (green times and offsets) along individual arterials. If critical signals are located at the exit points, the algorithm sets the optimal signal timing that protects them from becoming excessively loaded. If critical signals are located at the entry points, the algorithm ensures that queues are reduced or cleared before released platoons arrive at a downstream signal system. In addition, the algorithm eventually finds a set of common cycles propagated from upstream signals, thus promoting traffic progression. The micro-genetic algorithm was used to solve the signal optimization problem. The algorithm was tested on a one-way arterial system with 20 signals. The results indicate that the algorithm successfully managed queues along coordinated arterials, made the signals share the burden of traffic, and created the opportunity for traffic progression in specified directions.
This paper reviews a class of models that combine equilibrium traffic assignment and intersection control into a single analysis framework under the assumption of flow-responsive signal settings. The most significant feature of these models is their capacity to take into account explicitly the mutual interactions between signal control policies and user route choices; such interactions are usually disregarded both in ordinary traffic assignment models and in traditional traffic engineering practice. After defining the combined traffic assignment and control problem, and reviewing alternative formulations and solution algorithms, this paper discusses possible approaches to modeling the various types of link interactions that arise from the joint use of intersections by competing traffic movements. Important conceptual issues and implementation aspects are considered, and their potential policy implications are emphasized. The main conclusion of the survey is that, while the theoretical properties of combined traffic assignment and control models have been studied over the last two decades and are now well understood, there seems to be a significant lack of empirical results and real-world applications, that are needed in order to promote the transfer of this modeling approach from research to professional practice.
The paper considers the traffic assignment problem when there are junctions controlled by traffic signals, and the traffic capacity of each junction is limited. We give certain properties of a control policy. If a particular policy possesses these properties then (under natural conditions) any feasible assignment problem has a solution consistent with that policy. In the mathematical model, traffic flows at one junction do not affect costs at others; this is the most important restriction on the work presented here.
We consider a network with interactions and capacity constraints at each junction. We give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution. Two illustrative examples are provided; the first arises naturally and does not satisfy our conditions, while the second does satisfy our conditions but is somewhat unnatural.
An enhanced 0-1 mixed-integer linear programming formulation based on the cell-transmission model is proposed for the traffic signal optimization problem. This formulation has several features that are currently unavailable in other existing models developed with a similar approach, including the components for handling the number of stops, fixed or dynamic cycle length and splits, and lost time. The problem of unintended vehicle holding, which is common in analytical models, is explicitly treated. The formulation can be utilized in developing strategies for adaptive traffic-control systems. It can also be used as a benchmark for examining the convergence behavior of heuristic algorithms based on the genetic algorithm, fuzzy logic, neural networks, or other approaches that are commonly used in this field. The discussion of extending the proposed model to capture traffic signal preemption in the presence of emergency vehicles is given. In terms of computational efficiency, the proposed formulation has the least number of binary integers as compared with other existing formulations that were developed with the same approach.