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Day-to-day evolution of the traffic network with Advanced Traveler Information System

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  • Han, Linghui
  • Sun, Huijun
  • Wu, Jianjun
  • Zhu, Chengjuan

Abstract

Since the notion of user equilibrium (UE) was proposed by Wardrop [13], it has become a cornerstone for traffic assignment analysis. But, it is not sufficient to only ask whether equilibrium exists or not; it is equally important to ask whether and how the system can achieve equilibrium. Meanwhile, stability is an important performance in the sense that if equilibrium is unsustainable, both the equilibrium and the trajectory are sensitive to disturbances, even a small perturbation will result in the system evolution away from the equilibrium point. These incentive a growing interest in day-to-day dynamics. In this paper, we develop a dynamical system with Advanced Traveler Information System (ATIS) and study the stability of the network with ATIS. A simple network is used to simulate the model, and the results show that there exist periodic attractors in the traffic network in some cases (for example, the market penetration level of ATIS is 0.25 and traffic demand is 2 unit). It is found that the logit parameter of the dynamical model and the traffic demand can also affect the stability of the traffic network. More periodic attractors appear in the system when the traffic demand is large and the low logit parameter can delay the appearance of periodic attractors. By simulation, it can be concluded that if the range of the periodic attractors’ domain of the simple network is known, the road pricing based on the range of the attraction domain is effective to alleviate the instability of the system.

Suggested Citation

  • Han, Linghui & Sun, Huijun & Wu, Jianjun & Zhu, Chengjuan, 2011. "Day-to-day evolution of the traffic network with Advanced Traveler Information System," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 914-919.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:10:p:914-919
    DOI: 10.1016/j.chaos.2011.07.007
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    References listed on IDEAS

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    Cited by:

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    2. Stefano de Luca & Roberta Di Pace & Silvio Memoli & Luigi Pariota, 2020. "Sustainable Traffic Management in an Urban Area: An Integrated Framework for Real-Time Traffic Control and Route Guidance Design," Sustainability, MDPI, vol. 12(2), pages 1-20, January.
    3. Han, Linghui & Zhu, Chengjuan & Wang, David Z.W. & Sun, Huijun & Tan, Zhijia & Meng, Meng, 2019. "Discrete-time dynamic road congestion pricing under stochastic user optimal principle," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 24-36.

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