Modeling Travel Times in Dynamic Transportation Networks; A Fluid Dynamics Approach

Abstract

In this paper, we take a fluid dynamics approach to determine the travel time in traversing a network's link. We propose a general model for travel time functions that utilizes fluid dynamics laws for compressible flow to capture a variety of flow patterns such as the formation and dissipation of queues, drivers' response to upstream congestion or decongestion and drivers' reaction time. We examine two variants of the model, in the case of separable velocity functions, which gives rise to two families of travel time functions for the problem; a polynomial and an exponential family. We analyze these travel time functions and examine several special cases. Our investigation also extends to the case of non-separable velocity functions starting with an analysis of the interaction between two links, and then extending it to the general case of acyclic networks.