System Optimal Dynamic Traffic Assignment Research Articles

Distributed Methodology for a Cell-Transmission-Based System Optimal Dynamic Traffic Assignment

This study introduces a distributed methodology for system optimal dynamic traffic assignment formulated using the cell transmission model (CTM). Using CTM increases the methodology’s accuracy in predicting link flows and its dynamics; however, it increases the computational complexity significantly. Our methodology is specifically designed to address this challenge and provide a balance between the quality of the solution and computational complexity while ensuring first-in-first-out (FIFO) queuing discipline. The methodology follows a receding horizon framework and distributes the network-level traffic assignment into several intersection-level sub-problems and solves them in parallel. Therefore, this heuristic significantly reduces the computational complexity and finds solutions in real-time. The distribution is achieved by relaxing coupling constraints among different sub-problems. The sub-problems coordinate their decisions with each other by sharing information and implementing it in the re-introduced constraints that were previously relaxed. This process was used to avoid infeasible solutions, reduce the likelihood of finding local solutions, and promote system-level optimality. The information that needs to be exchanged is estimated using CTM simulation runs. All optimal sub-problem solutions are implemented in network-level CTM simulations, and cell occupancies and flows are obtained. The FIFO discipline is also approximated in CTM. We have tested the methodology in networks of 20 and 40 intersections with 15 and 25 origin-destination pairs, respectively, under various demand levels, and compared the performance with a benchmark approach capable of finding the optimal solutions. The maximum observed optimality gap in case studies with 20 and 40 intersections was 3.1%, and the solutions were found in real-time in all scenarios.

Maximin headway control of automated vehicles for system optimal dynamic traffic assignment in general networks

This study develops the headway control framework in a fully automated road network, as we believe headway of Automated Vehicles (AVs) is another influencing factor to traffic dynamics in addition to conventional vehicle behaviors (e.g. route and departure time choices). Specifically, we aim to search for the optimal time headway between AVs on each link that achieves the network-wide system optimal dynamic traffic assignment (SO-DTA). To this end, the headway-dependent fundamental diagram (HFD) and headway-dependent double queue model (HDQ) are developed to model the effect of dynamic headway on roads, and a dynamic network model is built. It is rigorously proved that the minimum headway could always achieve SO-DTA, yet the optimal headway is non-unique. Motivated by these two findings, this study defines a novel concept of maximin headway, which is the largest headway that still achieves SO-DTA in the network. Mathematical properties regarding maximin headway are analyzed and an efficient solution algorithm is developed. Numerical experiments on both a small and large network verify the effectiveness of the maximin headway control framework as well as the properties of maximin headway. This study sheds light on deriving the desired solution among the non-unique solutions in SO-DTA and provides implications regarding the safety margin of AVs under SO-DTA.

A Distributed Gradient Approach for System Optimal Dynamic Traffic Assignment

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.

Resilience-oriented optimal post-disruption reconfiguration for coupled traffic-power systems

The increasing penetration of grid-enabled electric vehicles (EVs) renders road networks (RNs) and power networks (PNs) increasingly interdependent for normal operation. For this reason, recently few studies have started to investigate the vulnerability of a highly coupled traffic-power system in the presence of disruptive events. Actually, however, only very few of these studies have considered the impact of EVs on the interdependent traffic-power system during restoration from a disruptive event. In an attempt to fill this gap, in this study, we investigate the restoration planning of both independent RNs and PNs, and interdependent traffic-power systems. A mixed integer program model is formulated to provide optimal reconfiguration and operational solutions for post-disruption traffic-power systems recovery. The objective of the model is to minimize the total cost incurred by system performance loss, which is quantified by the cumulative unmet traffic demand for RNs and load shedding cost for PNs. Several reconfiguration strategies are considered, including links reversing in RNs and line switching in PNs, to optimize system resilience. In the proposed model, the integrated problem of system optimal dynamic traffic assignment and optimal power flow is solved to derive the optimal traffic-power flow. RNs and PNs are coupled through the coordinately allocated spatio-temporal charging demand of EVs. A partial highway network in North Carolina (NC), USA, and a modified IEEE-14 bus system are used to illustrate the application of the model. The numerical results obtained show the added value of coordinately planning restoration for traffic-power systems and the effects of different levels of EV penetration.

A collective neurodynamic approach for solving distributed system optimum dynamic traffic assignment problems

In this paper, the traditional system optimum dynamic traffic assignment (SO-DTA) problem is solved by distributed multi-agent dynamics. The goal of SO-DTA is to optimally control the route choice of each user to minimize the total travel time by all users over the assignment time period. It is beneficial for reducing the congestion of the traffic network with time-varying demand. Different from the traditional SO-DTA which is formulated and solved in a centralized scheme, we aim at solving it from a multi-agent perspective in a communication network. Based on the cell transmission model, two connector-based relaxed SO-DTA models are provided in a multi-agent system framework for the traffic network with a single destination and multiple destinations, respectively. In the provided models, each cell connector is treated as an agent, which could exchange information with its adjacent connectors to accomplish the system optimization objective. Then, a collective neurodynamic system equipped with the proposed distributed protocol is used to solve general network optimization problems including the above SO-DTA models as special cases. The convergence analysis is further given for the proposed algorithm. Numerical studies over various traffic networks are presented to show the effectiveness of the proposed method.

Freeway network design with exclusive lanes for automated vehicles under endogenous mobility demand

Automated vehicles (AV) have the potential to provide cost-effective mobility options along with overall system-level benefits in terms of congestion and vehicular emissions. Additional resource allocation at the network level, such as AV-exclusive lanes, can further foster the usage of AVs rendering this mode of travel more attractive than legacy vehicles (LV). However, it is necessary to find the crucial locations in the network where providing these dedicated lanes would reap the maximum benefits. In this study, we propose an integrated mixed-integer programming framework for optimal AV-exclusive lane design on freeway networks which accounts for commuters’ demand split among AVs and LVs via a logit model incorporating class-based utilities. We incorporate the link transmission model (LTM) as the underlying traffic flow model due to its computational efficiency for system optimum dynamic traffic assignment. The LTM is modified to integrate two vehicle classes namely, LVs and AVs with a lane-based approach. The presence of binary variables to represent lane design and the logit model for endogenous demand estimation results in a nonconvex mixed-integer nonlinear program formulation. We propose a Benders’ decomposition approach to tackle this challenging optimization problem. Our approach iteratively explores possible lane designs in the Benders’ master problem and, at each iteration, solves a sequence of system-optimum dynamic traffic assignment problems in an attempt to find fixed-points representative of logit-compatible demand splits. The proposed approach is implemented on three hypothetical freeway networks with single and multiple origins and destinations. Our numerical results reveal that the optimal lane design of freeway network is non-trivial while accounting for endogenous demand of each mode.

Lane-based multi-class vehicle collaborative evacuation management

Mixed traffic evacuation management is recognized as a critical and challenging task. This paper develops a bi-level model to address the multi-class vehicle collaborative evacuation problem. The upper-level program is a mixed-integer nonlinear programming (MINLP) model to determine the optimal lane allocation scheme according to the fleet size. The lower-level program is formulated as multiple independent system optimal dynamic traffic assignment (SO-DTA) problems to load mixed traffic flow. A two-layer solution method integrating branch-and-bound algorithm is developed to solve the model. Finally, the optimization model is applied in a small network and a real-world network. Results demonstrate that (1) the evacuation performance of multi-class vehicle collaboration is better than that of single-class vehicles under the medium demand levels; (2) the proposed model realizes the coupling among evacuation demand, fleet size, and road network capacity; (3) the shortest path should first be allocated to the bus during a mass evacuation.

Resilience assessment of electrified road networks subject to charging station failures

AbstractThe number of electric vehicles (EVs) and charging facilities is expected to increase significantly in the near future, further coupling the existing transportation system with the power system. This may bring new stresses and risks to such a system of systems. This paper presents a mathematical framework to analyze the resilience of an electrified road network (ERN) subject to potential failures of its supporting fast‐charging stations (FCSs). Within this framework, a novel linear optimization model is proposed for the first time to solve the system optimal dynamic traffic assignment problem of ERN. The characteristics considered in the modeling framework include the location, capacity, and charging speed of FCSs, as well as the driving range, charging time, and state of charge (SoC) of EVs. The linear model is proposed based on the cell transmission model. It is used as the first‐stage model to assign the traffic under normal FCS operations. A second‐stage model is, then, extended to minimize the total travel time after the stochastic occurrence of FCS failures, that is, in the failure and recovery phases. Two metrics are considered to quantify the ERN performance and the impacts of FCS failures. A numerical example is studied to illustrate the usefulness of the proposed framework for analyzing ERN resilience. The results show that deploying FCSs near the highway entrances and maintaining their operation are relevant factors to enhance the system's resilience. The analysis can provide guidelines to the system operators for effective management of the ERN operation and identify resilience‐critical FCSs for system resilience improvement.

Allocating exclusive and intermittent transit lanes in dynamic traffic networks with connected and automated vehicles

Exclusive bus lanes (XBLs) have been widely discussed and implemented worldwide in recent years. An improved and more flexible transit lane management strategy—intermittent bus lanes (IBLs)—prove to be potentially more efficient and car-friendly than XBLs. The common benefit of XBLs and IBLs arises from the fact that they separate the bus and car traffic and hence eliminate the impacts of slowly moving buses on the car traffic. Compared to XBLs, the application of IBLs has not been broadly adopted in the real world so far except very few cases, because managing an urban IBL segment or area typically involves extra traffic signals and message signs and the switch between its regular and protected statuses could potentially cause unexpected traffic chaos and safety issues. The recent emergence of connected and automated vehicle (CAV) technologies, however, favors relieving these concerns and bring the dawn to a future application of this theoretically sound traffic control strategy. This paper is dedicated to evaluating the network performance of XBLs and IBLs and optimizing the networkwide configurations of these two strategies for future urban traffic networks where CAVs prevail. For this purpose, we formulate a system-optimal dynamic traffic assignment (SO-DTA) problem with car-exclusive lane segments, on the basis of a cell transmission model for separate car and bus traffic (CTM-SCB). By limiting its applicable context to morning commute networks and emergency evacuation networks, this model is set with only one real or virtual destination, which greatly eases its modeling and solution complexity. On the basis of the single-destination SO-DTA model, an XBL-based network design problem and an IBL-based network design problem are then both formulated into mixed integer programming models and solved by a discrete optimization solver, where the former problem statically configures bus lanes while the later one allows a dynamic allocation of bus lanes. Insightful findings obtained by applying the models and solver to a synthetic corridor network and a real commute network illustrate the great promise of these two lane-based strategies in mixed car and bus traffic management.

Multiclass dynamic system optimum solution for mixed traffic of human-driven and automated vehicles considering physical queues

Dynamic traffic assignment (DTA) is an important method in the long term transportation planning and management processes. However, in most existing system optimum dynamic traffic assignment (SO-DTA), no side constraints are used to describe the dynamic link capacities in a network which is shared by multiple vehicle types. Our motivation is based on the possibility for dynamic system optimum (DSO) to have multiple solutions, which differ in where queues are formed and dissipated in the network. To this end, this paper proposes a novel DSO formulation for the multi-class DTA problem containing both human driven and automated vehicles in single origin-destination networks. The proposed method uses the concept of link based approach to develop a multi-class DTA model that equally distributes the total physical queues over the links while considering explicitly the variations in capacity and backward wave speeds due to class proportions. In the model, the DSO is formulated as an optimization problem considering linear vehicle composition constraints representing the dynamics of the link capacities. Numerical examples are set up to provide some insights into the effects of automated vehicles on the queue distribution as well as the total system travel times.

Path-based system optimal dynamic traffic assignment: A subgradient approach

The system-optimal dynamic traffic assignment (SO-DTA) problem aims at solving for the time-dependent link and path flow of a network that yields the minimal total system cost, provided with the Origin-Destination (O-D) demand. The key to solving the path-based formulation of SO-DTA is to efficiently compute the path marginal cost (PMC). Existing studies implicitly assume that the total system cost (TC) is always differentiable with respect to the path flow when computing PMC. We show that the TC could be non-differentiable with respect to the link/path flow in some cases, especially when the flow is close or under the SO conditions. Overlooking this fact can lead to convergence failure or incorrect solutions while numerically solving the SO-DTA problem. In this paper we demonstrate when the TC would be indifferentiable and how to compute the subgradients, namely the lower and upper limit of path marginal costs. We examine the relations between the discontinuity of PMC and the SO conditions, develop PMC-based necessary conditions for SO solutions, and finally design heuristic solution algorithms for solving SO in general networks with multi-origin-multi-destination OD demands. Those algorithms are tested and compared to existing algorithms in four numerical experiments, two toy networks where we compare analytical solutions with numerical solutions, one small network and one sizable real-world network. We show that the proposed heuristic algorithms outperform existing ones, in terms of both the total TC, convergence, and the resultant path/link flow.

Robust dynamic traffic assignment for single destination networks under demand and capacity uncertainty

In this article, we discuss the system-optimum dynamic traffic assignment (SO-DTA) problem in the presence of time-dependent uncertainties on both traffic demands and road link capacities. Building on an earlier formulation of the problem based on the cell transmission model, the SO-DTA problem is robustly solved, in a probabilistic sense, within the framework of random convex programs (RCPs). Different from traditional robust optimization schemes, which find a solution that is valid for all the values of the uncertain parameters, in the RCP approach we use a fixed number of random realizations of the uncertainty, and we are able to guarantee a priori a desired upper bound on the probability that a new, unseen realization of the uncertainty would make the computed solution unfeasible. The particular problem structure and the introduction of an effective domination criterion for discarding a large number of generated samples enables the computation of a robust solution for medium- to large-scale networks, with low desired violation probability, with a moderate computational effort. The proposed approach is quite general and applicable to any problem that can be formulated through a linear programing model, where the stochastic parameters appear in the constraint constant terms only. Simulation results corroborate the effectiveness of our approach.

System optimum dynamic traffic assignment with departure time choice on two-terminal networks

ABSTRACTThis paper addresses the system optimum dynamic traffic assignment (SO-DTA) problem with departure time choice on a two-terminal network, where the travel cost consists of travel time and an early schedule delay cost. Under a certain condition, we show that SO-DTA reduces to the latest departure earliest arrival flow (LDEAF), and hence methodologies of LDEAF can be used to study SO-DTA. A successive shortest path (SSP) algorithm is used to solve the LDEAF problem. The benefit is that the SSP algorithm involves only the shortest path computations on a static network. System marginal costs, externalities and dynamic user equilibrium tolls are analyzed in the LDEAF context, and used to provide a better understanding of the SO-DTA problem characteristics. Further, the study findings can be used for the morning commute problem as it is a special case of the SO-DTA problem on a two-terminal network.

A decomposition scheme for parallelization of system optimal dynamic traffic assignment on urban networks with multiple origins and destinations

AbstractThis 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 subproblems 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.

Bi-level route guidance method for large-scale urban road networks

This paper proposes a bi-level route guidance method based on macroscopic fundamental diagram (MFD) for urban road network, which is a combination of central route guidance and distributed route guidance and it considers the intentions of both traffic management and traveler. It is a compromise of system optimum and user optimum. In upper-level route guidance, traffic dynamic evolution model of route guidance sub-region based on MFD is constructed and system optimal dynamic traffic assignment method on traffic guidance sub-region level is proposed. In lower-level route guidance, the traffic guidance paths are generated by solving the optimal path problem of the reactive users. Through analysis of the data gathering from Changchun City, China, it is verified that the proposed method not only meets the real-time requirements of dynamic traffic guidance but also provides benefits for the whole traffic system and individual traveler.

Energy and Mobility Impacts of System Optimal Dynamic Traffic Assignment for a Mixed Traffic of Legacy and Automated Vehicles

This research develops a system optimal dynamic traffic assignment (DTA) model for mixed traffic of human drivers and automated vehicles (AVs) and investigates network level mobility and energy impacts for different market shares of AVs. A methodology based on vehicle-specific-energy is proposed to estimate the energy consumption from the embedded spatial-queuing traffic flow model within the DTA formulation. Results with a test network indicate that potential travel time and energy consumption reductions are possible with increased AV market share in transportation networks. Results also report a decrease in travel time as high as 49% and energy consumption as high as 28% at the system level. The developed DTA model will be able to assist in transportation planning and the investment decision process by estimating the mobility and energy impacts in future transportation networks with mixed traffic of human drivers and AVs.

Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks

Most current system optimum dynamic traffic assignment (SO-DTA) models do not contain first-in-first-out (FIFO) constraints and are limited to single-destination network applications. In “Link-based System Optimum Dynamic Traffic Assignment Problems in General Networks,” J. Long and W. Y. Szeto develop SO-DTA models either with or without FIFO constraints for general network applications using the concept of the link transmission model (LTM). The proposed SO-DTA problems without FIFO constraints are formulated as linear programs, and can address the vehicle holding problem by adding a penalty term to the objective function. The SO-DTA problems with FIFO constraints are formulated as nonconvex mixed-integer programs, and are solved by branch-and-bound algorithms. Two methods are developed to identify FIFO violations in feasible flow patterns and design a branching scheme for the proposed branch and bound algorithms. The authors show that the proposed LTM-based SO-DTA models are more computationally efficient than the CTM-based counterparts and maintain the same level of accuracy in terms of guaranteeing the same total system travel time in general networks.

System optimal dynamic traffic assignment: solution structures of the signal control in non-holding-back formulations

ABSTRACTThis paper devises locally optimal traffic Signal Control (SC) settings in a Non-Holding-Back Dynamic Traffic Assignment with SC (NHB DTA-SC) formulation for single destination (i.e. one source to one destination and many sources to one destination) networks. To this end, we apply temporal–spatial dual decomposition method and decompose the NHB DTA-SC problem into intersection cells and non-intersection cells. Then we further decompose the intersection cells into different subproblems, i.e. Occupancy Minimization (OM), Flow Maximization (FM), and SC. To study the optimal SC structures, we examine the Karush–Kuhn–Tucker (KKT) optimality conditions of the decomposed SC subproblem. Finally, we obtain the locally optimal SC structures under different network conditions that include over-saturated, under-saturated, and queue spillback traffic scenarios. We also present several numerical results to verify the optimality structures found by our theoretical derivations.

Graphical solution for system optimum dynamic traffic assignment with day-based incentive routing strategies

This paper analyzes the dynamic traffic assignment problem on a three-alternative network with day-based incentive routing strategies by using graphical solution method. It is assumed that the cumulative count curve of vehicles is known and that the arrival rate is unimodal. The dynamic system optimum (DSO) allocation lines are first drawn based on calculus of variations. Three possible optimal allocation lines are analyzed. A day-based incentive routing strategy is designed and conditions that when and how to implement the incentive scheme to realize DSO are then derived. Extension to general parallel networks is also given. Examples are presented to demonstrate the effectiveness of the scheme.

Link Transmission Model-Based Linear Programming Formulation for Network Design

This article presents a linear programming formulation to solve the network design problem using the link transmission model (LTM) as the underlying traffic flow model. The original LTM was adapted by incorporating link-sending and receiving flows using linear inequalities. Furthermore, route choice was relaxed, and transfer flow variables were used to model vehicles’ routing decisions within the network. The objective function of the linear program aimed to minimize the total difference between the cumulative vehicle numbers (CVN) at the upstream and at the downstream boundaries of each link subject to flow-conservation and budget constraints. CVN were represented using transfer flows from connected links. The resulting formulation is a linear program that represents a dynamic system optimum traffic flow pattern, embedding the LTM’s network loading procedure. In contrast to the single-destination system optimum dynamic traffic assignment, based on the cell transmission model, the proposed formulation requires considerably fewer decision variables, thus potentially providing a more scalable approach. The proposed formulation was implemented on an example network to illustrate the behavior of the model, and was compared with the cell-based formulation. We show that the model describes free-flow and congested traffic flow states accurately in terms of shock-wave propagation, queuing of vehicles, and optimal total system travel time.