System Optimal Traffic Assignment Research Articles

Global optimization methods for the discrete network design problem

This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper level aims to minimize the total travel time via adding new lanes to candidate links and the lower level is a traditional Wardrop user equilibrium (UE) problem. We propose two global optimization methods by taking advantage of the relationship between UE and system optimal (SO) traffic assignment principles. The first method, termed as SO-relaxation, exploits the property that an optimal network design solution under SO principle can be a good approximate solution under UE principle, and successively sorts the solutions in the order of increasing total travel time under SO principle. Optimality is guaranteed when the lower bound of the total travel time of the unexplored solutions under UE principle is not less than the total travel time of a known solution under UE principle. The second method, termed as UE-reduction, adds the objective function of the Beckmann-McGuire-Winsten transformation of UE traffic assignment to the constraints of the SO-relaxation formulation of the multi-capacity DNDP. This constraint is convex and strengthens the SO-relaxation formulation. We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation. Numerical experiments based on a two-link network and the Sioux-Falls network are conducted.

Optimize Evacuation Route Considering the Operational Cost as a Constraint

Evacuation planning involves modeling, operation, and management of evacuation routes before and during emergency evacuation. This paper presents the development and examination of a route optimization model which considers the operational cost as a constraint. The study is focused on the situation when the backbone evacuation route, usually the interstate highway system, is over congested and some traffic need to be directed to local street networks. As intersections are the key control components of a street network, traffic operations at intersections cannot be neglected in route selection. In order to consider the operational cost in the modeling process, a street network is first presented by an extended graph network which has cost information associated with each node. Then, a system optimal traffic assignment approach is used to select and optimize the evacuation routes. The property of the approach is examined by a numerical test which includes a network composed of a backbone interstate highway and a grid network with over 30 intersections.

An Efficient VBA Spreadsheet Algorithm and Model for the System Optimum Traffic Assignment

The traffic assignment involves assigning traffic to a transportation network consisting of highways, arterials, or transit routes. To obtain an optimal traffic assignment scheme, a mathematical program (MP) should be formulated and solved. The process of formulating an MP requires identifying all possible paths connecting each origin-to-destination pair through the network, since the number of those paths turns out to be the number of the decision variables. Consequently, formulating and solving such an MP is difficult due to the large number of the decision variables and constraints. For that reason, practitioners prefer heuristics for a large-scale transportation network. In this paper, the authors suggest a new and efficient way of formulating an MP and develop a Microsoft Excel model with Visual Basic for Applications (VBA) to find the optimal assignment scheme for the traffic assignment problem. The developed Excel model with VBA can be easily expanded to a large-scale transportation network.

A Dynamic Emergency Evacuation Network Optimization Problem with Crossing Elimination Strategy

This paper presents a dynamic evacuation network optimization problem that incorporates crossing elimination strategy. Bottleneck problem at intersections during evacuation process is analyzed for the effective evacuation planning. The developed model is formulated as a system-optimum traffic assignment based on cell transmission model (CTM), which can effectively investigate the characteristics of randomness and dynamics of evacuation flow’s spatial and temporal distribution. The numerical results show that the model can provide crucial theoretical support for evacuation decision-making for traffic managers.

A Mixed Integer Linear Program for the Single Destination System Optimum Dynamic Traffic Assignment Problem with Physical Queue

In order to solve the system optimum dynamic traffic assignment problem, the whole link model with physical queue is used to formulate the single destination system optimum dynamic traffic assignment problem as a mixed linear program. A relationship between the cumulative curves and the wave speed presented by Newell (1993) is used to present a dynamic network model in considering spillback queue. And nonlinear constrains are relaxed into mixed linear constrains; the linear program software is used to solve the system optimum dynamic traffic assignment problem. A numerical example illustrates the simplicity and applicability of the proposed approach. KEYWORDS: Dynamic System Optimum Traffic Assignment; physical queue; mixed integer linear programming

Dynamic system optimal traffic assignment – a state-dependent control theoretic approach

This study investigates analytical dynamic system optimal assignment with departure time choice in a rigorous and original way. Dynamic system optimal assignment is formulated here as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimised. Solution algorithms are presented and the effect of time discretisation on the quality of calculated assignments is discussed. Calculating dynamic system optimal assignment and the associated optimal toll is shown to be difficult for practical implementation. We therefore consider some practical tolling strategies for dynamic management of network traffic. The tolling strategies considered include uniform and congestion-based tolling strategies. This study contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area.

Efficient particle-based estimation of marginal costs in a first-order macroscopic traffic flow model

Marginal costs in traffic networks are the extra costs incurred to the system as the result of extra traffic. Marginal costs are required frequently e.g. when considering system optimal traffic assignment or tolling problems. When explicitly considering spillback in a traffic flow model, one can use a numerical derivative or resort to heuristics to calculate the marginal costs. Numerical derivatives are computationally demanding, restricting its use to simple networks. Heuristic approaches in most cases approximate the marginal costs by only considering the extra costs on the links which are traveled by the extra traffic, excluding the possibly external costs incurred on other links due to spillback. This paper proposes a novel way to estimate the true marginal costs of traffic in a dynamic discrete LWR model which correctly deals with congestion onset, spillback and dissolution. The proposed methodology tracks virtual changes in density through the network by means of particles which travel along with the characteristics of traffic. By using density based cost functions, the virtual changes in density can be directly related to the marginal costs. The computational efficiency of the methodology stems from the fact that only local conditions are considered when propagating the virtual change in density. The paper discusses the methodology and necessary model extensions, provides a numerical validation experiment illustrating the exact detail of the solution by comparison to a numerical derivative and discusses some generalizations

Properties of system optimal traffic assignment with departure time choice and its solution method

This paper investigates dynamic system optimal traffic assignment with departure time choice and its solution method. Dynamic system optimal assignment is formulated as a state-dependent optimal control problem. A fixed volume of traffic is assigned to departure times and routes such that the total system travel cost is minimized. We derive and discuss the necessary conditions on the network inflow for operating the transportation system optimally. We further provide detailed mathematical analysis and discussion of dynamic system optimal assignment when the deterministic queuing model is adopted. Solution algorithm is developed and investigated for solving the traffic assignments. The effect of choosing the underlying traffic model and time discretization on the quality of the corresponding assignment results are also discussed. This paper contributes to the literature on dynamic traffic modelling and management, and to support further analysis and model development in this area.

Risk Averse Dynamic System Optimal Traffic Assignment

This paper presents a method for solving a dynamic system optimal (DSO) traffic assignment problem with uncertain travel time. Formulating the DSO assignment in a network with two parallel links as a stochastic control problem, we derive the optimality conditions of the assignment problem. We then show that the optimality conditions can be equivalently stated as a dynamical system of generalized complementarity problems (GCP). Based on this reformulation, we provide an efficient algorithm for solving the stochastic control problem.

Comparison of System- and User-Optimal Stochastic Dynamic Network Design Models Using Monte Carlo Bounding Techniques

This paper compares the continuous network design problem formulations using system-optimal (SO) and user-optimal (UO) dynamic traffic assignment when the following independent stochastic parameters with known discrete probability distributions are considered: time-dependent origin-destination demands, time-varying saturation flow rates and jam density, and network improvement unit costs. These models propagate traffic according to Daganzo's cell transmission model. Two Monte Carlo bounding techniques, common random numbers (CRN) and independent random numbers (IRN) strategies, are used to solve the stochastic models. The results show that the CRN strategy outperforms IRN on a simple test network resembling a freeway corridor. The network size is sacrificed to gain higher confidence probabilistic behavior and to understand intuitively the effects of different network improvement policies. Although the findings may not necessarily be generalized, they provide interesting and insightful information. First, ...

Dynamic Optimal Traffic Assignment and Signal Time Optimization Using Genetic Algorithms

Abstract: 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.

Dynamic congestion pricing models for general traffic networks

In this paper we develop two types of dynamic congestion pricing model, based on the theory of marginal cost pricing. The first model is appropriate for situations where commuters have the ability to learn the best route choices through day-to-day explorations on a network with arc capacities and travel demands that are stable from day to day. The second model is appropriate for situations where commuters optimize their routing decisions each day on a network with arc capacities and travel demands that fluctuate significantly from day to day. We show that two types of time-varying congestion tolls can be determined by solving a convex control formulation of the dynamic system optimal traffic assignment problem on a network with many origins and many destinations. We also show that the dynamic system optimal traffic assignment is an equilibrium for commuters under the tolls in both cases.

A convex control model of dynamic system-optimal traffic assignment

In this paper, a dynamic system-optimal traffic assignment model is formulated as a convex control problem for a congested general network with many origins and many destinations. Analytical and computational difficulties caused by the nonconvexity of the previous models are eliminated. The modeling of arc traffic dynamics is improved to prohibit instantaneous flow propagation on each arc even though the concave exit functions are still employed to represent the physical process of traffic congestion. An economic interpretation of the optimality conditions is given as a dynamic assignment principle which requires equilibration of actual marginal costs on all the paths that are used. A numerical example is also presented.

A Convex Control Model of Dynamic System Optimal Traffic Assignment

In this paper, the dynamic system optimal traffic assignment model is formulated as a convex control problem for general networks with many origins and many destinations. Analytical and computational difficulties caused by the nonconvexity of previous models are eliminated. The modeling of arc traffic dynamics is also improved to prohibit instantaneous flow propagation on each arc even though the concave exit functions are still employed to represent the physical process of traffic congestion. Lastly, an economic interpretation of the optimality conditions is given as a dynamic assignment principle which requires equilibration of actual marginal costs on all the paths that are used.

A model for the dynamic system optimum traffic assignment problem

We describe a deterministic queueing assignment model which seeks to reduce total travel delays in a road traffic network by routeing drivers according to the total delay caused on each link (the local marginal delay). The model is approximate and is applicable to networks with many origin-destination pairs and many bottlenecks. Optimality of the solution determined by the model is discussed. It is particularly shown that, unlike in the steady state (Dafermos and Sparrow, 1969), reducing total travel times by using the local marginal delay will not generally result in an optimal solution. Results are provided for two networks.

The Augmented Lagrangian Method for Solving Dynamic Network Traffic Assignment Models in Discrete Time

We develop and test an augmented Lagrangian method for solving dynamic traffic assignment models formulated as optimal control problems. Our presentation is in terms of the discrete time, system optimal traffic assignment problem. However, the basic ideas presented here are readily applied to continuous time models and to other behavioral assumptions regarding traffic assignment which may be expressed as optimal control problems. The proposed algorithm obviates the need for path enumeration and exploits the natural decomposition of the traffic assignment problem by time period which is possible when an optimal control formulation is employed.

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.

Dynamic System Optimum Traffic Assignment Models and the Solution Methods

This paper studies the basic constraints of dynamic traffic assignment problem and dynamic system optimum model. First, Merchant and Nemhauser's dynamic system optimum model is analyzed in detail. Second, link exit function and other constraints in dynamic traffic assignment problem are qualified strictly. Third, a continuous dynamic system optimum model and a discrete dynamic system optimum model are developed. The models can be applied to the network with multiple origin and multiple destination. Finally, an algorithm for the discrete model is developed. Test example showed that the algorithm can solve the dynamic optimum efficiently.

A comparison of user-optimum versus system-optimum traffic assignment in transportation network design

In this report, we compare the computational efficiency and results of solving two alternative models for the problem of determining improvements to an urban road network. Using a 1462 link, 584 node test network of the north Dallas area, we compare a model which assumes user-optimum behavior of travelers with a model which assumes system-optimum flows. Both of these models allow improvements to the road network to take on any nonnegative value, rather than requiring discrete improvement values. Investment costs are modeled by functions with decreasing marginal costs. Unfortunately, the user-optimum model, which is much more realistic than the system-optimum one, normally cannot be solved optimally. However, the simpler system-optimum model can be optimally solved, provided that investment costs are approximated by linear functions. Thus, for this network design problem we compare an accurate representation which can be solved only approximately with an approximate representation which can be solved optimally. Our computational testing showed that the system-optimum model produces solutions as good as those from the user-optimum model, and thus seems justified when favored by other considerations, such as ease of coding, availability of “canned” programs, etc.

Bi-Criteria System Optimum Traffic Assignment in Networks With Continuous Value of Time

For an elastic demand transportation network with continuously distributed value of time, the system disutility can be measured either in time units or in cost units. The user equilibrium model and the system optimization model are each formulated in two different criteria. The conditions required for making the system optimum link flow pattern equivalent to the user equilibrium link flow pattern are derived. Furthermore, a bi-objective model has been developed which minimizes simultaneously the system travel time and the system travel cost. The existence of a pricing scheme with anonymous link tolls which can decentralize a Pareto system optimum into the user equilibrium has been investigated.