An analysis of instability in a departure time choice problem

Takamasa Iryo

29 citations0/0 files storedJournal of Advanced Transportation

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Transportation Planning and Optimization Traffic control and management Railway Systems and Energy Efficiency

Abstract

Abstract This study performs a theoretical analysis of instability in a departure time choice problem. Stability of equilibrium is an important factor for reliability of travel time. If equilibrium is not stable, travel time changes over a period of days even if demand and network performance are stable. This study examines the stability of a dynamic user equilibrium problem by using the departure time choice problem. The mechanism of day‐to‐day changes in a traveller's behaviour is determined first, and then a function that indicates dissimilarity to equilibrium is defined. The day‐to‐day changes in the dissimilarity function are mathematically examined using approximations. A numerical test is also carried out to verify the result. Results of these analyses show that there can be a case where the system does not converge to equilibrium. It is also indicated that this instability should be caused by the non‐monotonicity of the schedule cost.

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References

1969CONGESTION THEORY AND TRANSPORT INVESTMENT 1984The Stability of a Dynamic Model of Traffic Assignment—An Application of a Method of Lyapunov 1985The Uniqueness of a Time-dependent Equilibrium Distribution of Arrivals at a Single Bottleneck 2004Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes 2006DYNAMIC TRAFFIC ASSIGNMENT: PROPERTIES AND EXTENSIONS 1999Stability of the stochastic equilibrium assignment problem: a dynamical systems approach 2006Convergence in a continuous dynamic queueing model for traffic networks

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2017Day-to-day departure time choice under bounded rationality in the bottleneck model 2016Day-to-day dynamical model incorporating an explicit description of individuals’ information collection behaviour 2020Stable Day-to-Day Dynamics for Departure Time Choice 2023The Day-to-Day Departure Time Choice of Heterogeneous Commuters Under an Anonymous Toll Charge for System Optimum 2019Responsive bus dispatching strategy in a multi-modal and multi-directional transportation system: a doubly dynamical approach

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