Hysteresis Behind a Road Bottleneck with Location-Dependent Capacity

Abstract

Macroscopic fundamental diagrams (MFDs) and related network traffic dynamics models have received both theoretical support and empirical validation with the emergence of new data collection technologies. However, the existence of well-defined MFD curves can only be expected for traffic networks with specific topologies and is subject to various disturbances, most importantly hysteresis phenomena. This study aims to improve the understanding of hysteresis in Macroscopic Fundamental Diagrams and Network Exit Functions (NEFs) during rush hour conditions. We apply the LWR theory to a highway corridor featuring a location-dependent downstream bottleneck to identify a figure-eight hysteresis pattern, clockwise on the top and counter-clockwise on the bottom. We discuss why this general pattern is rare in practical scenarios, where a single clockwise loop is more typical. The paper discusses the impact of the road topology and demand patterns on the formation and intensity of hysteresis loops analytically. To substantiate these findings, we employ numerical simulations using the Cell Transmission Model (CTM). Our simulations show that even a slight reduction in the capacity of the homogeneous section can significantly decrease MFD hysteresis while maintaining outflow at the corridor's downstream end. These reductions can be achieved with minimal intervention through standard traffic control measures, such as dynamic speed limits or ramp metering.

Keywords: Traffic Flow Theory, Macroscopic Fundamental Diagram, Network Exit Function, LWR Theory, Continuous Bottleneck, Hysteresis