An analysis of traffic-flow stability in a microscopic heterogeneous network

Abstract

Microscopic traffic-flow networks are typicallydesigned to simulate vehicle acceleration behaviourusing a single mathematical model. The concept ofstability is a major objective of microscopic drivermodels for traffic simulations. Stable flow is trafficflow that does not fluctuate unaccountably, andchanges in flow do not unreasonably magnifydownstream, thereby reflecting real-world driverbehaviour. However, the stability of driver modelsis typically evaluated in isolation, with the singlemodel applied to all vehicles and road sections inthe traffic network. Yet as different models will bemore effective in different situations, it would bedesirable to mix multiple models within the onetraffic network. Heterogeneous approaches thatmix microscopic and macroscopic models exist, butmixing different types of microscopic driver modelshas been largely overlooked and no analysis of theconsequences on stability has been made. Thus thispaper investigates the stability characteristics ofsuch microscopic heterogeneous networks, mixingthe well-known Intelligent Driver Model (IDM),a continuous-space car-following model, with adiscrete-space cellular automata model. To thisend, a flaw in the stability of the IDM at the speedlimit is identified and corrected. Subsequentlyit is shown that model switch-over points willexperience instabilities despite the stability of theindividual driver models and, although carefulchoice of parameters can reduce the problem,it cannot be completely eliminated in practicalroad networks. However, the instability producesa signature ‘fingerprint’ effect on traffic density,and this fingerprint is readily identifiable usingsimple measures of traffic flow even in realisticroad networks.