Quasi-stationary Approach in Mathematical Modeling of Traffic Flows Dynamics in a City Road Network

Abstract

The paper proposes a new approach for traffic flows modeling in a city road network for typical conditions of heavy traffic. The model is created according to the assumption of flow uniformity in space (but not in time) for each road segment between junctions. In format, it resembles quasi-stationary flow models for technological network that proved their usefulness for control problems. Some evidence for the model adequacy is obtained from computational experiments based on simulation of car motion ruled by the safe distance law. With a certain hypothesis of path choice by informed drivers the model gives the possibility to predict traffic dynamics. The paper expresses Bellman’s type relationships for conditionally optimum route choice that may be combined with general balance equations expressing the quasi-stationary approach, which yields a closed predictive model.