An Equilibrium Dynamic Traffic Assignment Model with Linear Programming Formulation

TL;DR

This paper presents a linear programming approach to find equilibrium traffic distributions in a dynamic transportation model, considering drivers' preferences and route choices, with potential for efficient algorithmic solutions.

Contribution

It introduces a linear programming formulation for equilibrium dynamic traffic assignment, extending previous models that only addressed social optima.

Findings

Equilibrium traffic distribution can be obtained via linear programming.

The model incorporates driver preferences for arrival times.

Algorithmic approaches using time-expanded networks are discussed.

Abstract

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 distribution across departure times and routes. For a relatively simplified transportation model we show that an equilibrium traffic distribution can be found as a solution to a linear program. In earlier works linear programming formulations were only obtained for social optimum dynamic traffic assignment problems. We also discuss algorithmic approaches for solving the equilibrium problem using time-expanded networks.