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Delay transition of a recurrent bus on a circular route

Author

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  • Nagatani, Takashi

Abstract

We study the behavior of a recurrent bus on a circular route with many bus stops. We present the basic model determining the recurrent time (one period) on each bus stop. The recurrent times on M bus stops are given by M simultaneous nonlinear equations. It is found that the dynamical phase transition between the delay and schedule-time phases occurs with varying the initial period. The dynamical transition depends on number M of bus stops. When M is larger than the critical value, the recurrent time diverges with the number of rotation. The recurrent time is described, approximately, in terms of a nonlinear map. The schedule-time phase is determined by the basin of attraction.

Suggested Citation

  • Nagatani, Takashi, 2001. "Delay transition of a recurrent bus on a circular route," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 297(1), pages 260-268.
    • Handle: RePEc:eee:phsmap:v:297:y:2001:i:1:p:260-268
    DOI: 10.1016/S0378-4371(01)00193-5
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    Cited by:

    1. Hossain, Md. Anowar & Tanimoto, Jun, 2022. "A microscopic traffic flow model for sharing information from a vehicle to vehicle by considering system time delay effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).

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