Hysteresis Behind A Freeway Bottleneck With Location-Dependent Capacity

TL;DR

This paper investigates hysteresis phenomena in Macroscopic Fundamental Diagrams (MFDs) at freeway bottlenecks, revealing how topology and demand asymmetries influence hysteresis patterns through empirical data and traffic modeling.

Contribution

It provides new insights into the formation of hysteresis loops in MFDs at bottlenecks, supported by empirical analysis and theoretical modeling, highlighting the effects of capacity variations and demand asymmetries.

Findings

Counter-clockwise hysteresis loops are confirmed in real traffic conditions.

Discontinuous bottlenecks exhibit more hysteresis than continuous ones.

Reducing capacity slightly can significantly decrease hysteresis with minimal control measures.

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. Our empirical observations confirm the occurrence of counter-clockwise loops in real conditions, an effect which we can attribute to demand asymmetries through theoretical analysis. 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 analyze empirical MFD data from two bottlenecks and present statistical evidence that, under otherwise identical conditions, a continuous bottleneck causes less hysteresis than a discontinuous one. We conduct numerical experiments using the Cell Transmission Model (CTM) to 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.