Spatial Distribution of Traffic Flow in a Rectangular City with a Grid Network and a Rectangular Barrier

Abstract

This paper develops a continuous approximation model for analyzing the spatial distribution of traffic flow in the presence of a barrier to travel. The traffic flow density is derived for a rectangular city with a grid road network and a rectangular barrier. The traffic flow density describes traffic flow as a function of position and provides a fundamental understanding of the effect of the barrier. The analytical expression for the traffic flow density demonstrates how the location and shape of the barrier affect the spatial distribution of traffic flow. The effect of the shape of the city is also examined. The model is useful for transportation and logistics problems with barriers.