Stability is an important condition for equilibrium solutions to be realised in a real transport system. If the solution is not stable, it is vulnerable to a small perturbation onto the system, and consequently equilibrium would not be observed in the real world. While it has been known that an equilibrium solution of a static equilibrium assignment problem is stable in a various types of evolution dynamics with mild conditions, the stability of solutions in dynamic user equilibrium (DUE) assignments has rarely been investigated. This study proves that an equilibrium solution of the departure time choice problem is not Lyapunov stable when the replicator dynamics is employed. As the uniqueness of the equilibrium solution has been proven, it can be concluded that there is no stable equilibrium solution in the departure time choice problem when the replicator dynamics is assumed as an evolution dynamics.
- Day-to-day dynamics
- Departure time choice problem
- Replicator dynamics
ASJC Scopus subject areas
- Civil and Structural Engineering