A Fluid Model of Spillback and Bottleneck Phenomena for Determining Dynamic Travel Times

Abstract

In this paper we introduce travel time models that incorporate spillback and bottleneck phenomena. In particular, we study a model for determining the link travel times for drivers entering a link as well as drivers already in the link but whose travel times are affected by a significant change in traffic conditions (e.g. spillback or bottleneck phenomena). To achieve this goal, we extend the fluid dynamics travel time models proposed by Perakis [11] and subsequently by Kachani and Perakis [6], [7], to also incorporate such phenomena. These models utilize 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 propose variants of these models that explicitly account for spillback and bottleneck phenomena. Our investigation considers both separable and non-separable velocity functions.