Abstract

This paper proposes a traffic-flow evolutionary model under a dual updating mechanism that describes the day-to-day (DTD) dynamics of traffic flow and travel cost. To illustrate the concept, a simple two-route network is considered. Based on the nonlinear dynamic theory, the equilibrium stability condition of the system is derived and the condition for the division between the bifurcation and chaotic states of the system is determined. The characteristics of the DTD dynamic evolution of network traffic flow are investigated using numerical experiments. The results show that the system is absolutely stable when the sensitivity of travelers toward the route cost parameter (θ) is equal to or less than 0.923. The bifurcation appears in the system when θ is larger than 0.923. For values of θ equal to or larger than 4.402, the chaos appears in the evolution of the system. The results also show that with the appearance of chaos, the boundary and interior crises begin to appear in the system when θ is larger than 6.773 and 10.403, respectively. The evolution of network traffic flow is always stable when the proportion of travelers who do not change the route is 84% or greater.

Highlights

  • With the rapid development of the social economy and the acceleration of urbanization, traffic congestion becomes widespread during peak hours in urban areas

  • The results showed that the traffic flow distribution could converge to user equilibrium (UE)

  • The results showed that the assumption of perfect information is the most influencing on traffic assignment results

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Summary

Introduction

With the rapid development of the social economy and the acceleration of urbanization, traffic congestion becomes widespread during peak hours in urban areas. The preceding authors derived the stability condition of network traffic flow evolution and focused on the bifurcation and chaos phenomena when the system was unstable. They considered only the DTD updating of travel cost and did not consider the travelers’ habituation. The DTD dynamic assignment model by Cantarella [26], and Zhao and Orosz [27] considered updating both the travel cost and traffic flow, but analyzed only the stability and bifurcation behavior (the chaos phenomena was not analyzed). To answer these questions, taking the two-route network as the research object, this paper formulates a traffic flow evolutionary model under a dual updating mechanism considering travelers’ habits.

Mathematical Model
Evolution State and Critical Condition
Network Description
Findings
Evolution Characteristics
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