TY - JOUR
T1 - Instability of departure time choice problem
T2 - A case with replicator dynamics
AU - Iryo, Takamasa
N1 - Funding Information:
This study was supported by JSPS Grant-in-aid (KAKENHI) # 16H02368 .
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2019/8
Y1 - 2019/8
N2 - 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.
AB - 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.
KW - Day-to-day dynamics
KW - Departure time choice problem
KW - Instability
KW - Replicator dynamics
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U2 - 10.1016/j.trb.2018.08.005
DO - 10.1016/j.trb.2018.08.005
M3 - Article
AN - SCOPUS:85052758403
VL - 126
SP - 353
EP - 364
JO - Transportation Research, Series B: Methodological
JF - Transportation Research, Series B: Methodological
SN - 0191-2615
ER -