Analysis of Stability-To-Chaos in the Dynamic Evolution of Network Traffic Flows under a Dual Updating Mechanism

Shixu Liu, Hao Yan, Said M. Easa, Lidan Guo and Yingnuo Tang
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Shixu Liu: College of Civil Engineering, Fuzhou University, Fuzhou 350108, China
Hao Yan: College of Civil Engineering, Fuzhou University, Fuzhou 350108, China
Said M. Easa: Department of Civil Engineering, Ryerson University, Toronto, ON M5B 2K3, Canada
Lidan Guo: College of Civil Engineering, Fuzhou University, Fuzhou 350108, China
Yingnuo Tang: College of Civil Engineering, Fuzhou University, Fuzhou 350108, China

Sustainability, 2018, vol. 10, issue 11, 1-17

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.

Keywords: network traffic flow; dynamic evolution; stability; chaos (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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