March 15, 2005
User equilibrium is a central concept for studying transportation networks, and one can view it as the result of a dynamical process of drivers' route choice behavior. In this paper, based on a definition of O-D First-In-First-Out violation, we propose a new dynamical system model of the route choice behavior at the aggregate, route level for both static and dynamic transportation networks. An equilibrium of such a dynamical system can be a user equilibrium or a partial user equilibrium. We prove that, for static, symmetric traffic assignment problem with fixed or variable demand, only user equilibria are stable for the dynamical system, and the objective function in the mathematical programming formulation (Beckmann, McGuire, and Winsten, 1956) can be considered as the potential energy of the dynamical system. We then present an Euler-based perturbation method for finding user equilibrium and solve two examples for both static and dynamic traffic assignment problems. This new model is simple in form and could be applied to analyze other properties of transportation networks.
Similar papers 1
August 30, 2024
In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the preferred time at the destination. Each driver aims to minimize the time spent during the trip, making the time spent a measure of cost. The chosen routes and departure times impact the network loading. The goal is to find an equilibrium distributi...
March 15, 2005
The paper has been merged into math/0503283
April 30, 2018
We describe a software framework for solving user equilibrium traffic assignment problems. The design is based on the formulation of the problem as a variational inequality. The software implements these as well as several numerical methods for find equilirbria. We compare the solutions obtained under several models: static, Merchant-Nemhauser, `CTM with instantaneous travel time', and `CTM with actual travel time'. Some important differences are demonstrated.
October 1, 2018
Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment, in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the time-varying traffic flows on a network consistent with traffic flow theory and travel behavior. This paper documents theoretical and numerical advances in synthesizing traffic flow theory and DUE modeling, by presenting a holistic computationa...
August 6, 2020
In this paper we consider the application of several gradient methods to the traffic assignment problem: we search equilibria in the stable dynamics model (Nesterov and De Palma, 2003) and the Beckmann model. Unlike the celebrated Frank--Wolfe algorithm widely used for the Beckmann model, these gradients methods solve the dual problem and then reconstruct a solution to the primal one. We deal with the universal gradient method, the universal method of similar triangles, and t...
February 3, 2021
This study investigates dynamic system-optimal (DSO) and dynamic user equilibrium (DUE) traffic assignment of departure/arrival-time choices in a corridor network. The morning commute problems with a many-to-one pattern of origin-destination demand and the evening commute problems with a one-to-many pattern are considered. Specifically, a novel approach to derive closed-form solutions for both DSO and DUE problems is developed. We first derive a closed-form solution to the DS...
March 15, 2005
The paper has been merged into math/0503283
January 1, 2021
In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a 'DSO game'. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is a stochastically stable state under the logit response dynamics, and ...
October 14, 2008
Given a network with a continuum of users at some origins, suppose that the users wish to reach specific destinations, but that they are not indifferent to the time needed to reach their destination. They may have several possibilities (of routes or deparure time), but their choices modify the travel times on the network. Hence, each user faces the following problem: given a pattern of travel times for the different possible routes that reach the destination, find a shortest ...
January 15, 2024
The lack of a unique user equilibrium (UE) route flow in traffic assignment has posed a significant challenge to many transportation applications. The maximum-entropy principle, which advocates for the consistent selection of the most likely solution as a representative, is often used to address the challenge. Built on a recently proposed day-to-day (DTD) discrete-time dynamical model called cumulative logit (CULO), this study provides a new behavioral underpinning for the ma...