Instability of departure time choice problem: A case with replicator dynamics
Instability of departure time choice problem: A case with replicator dynamics
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DOI：
10.1016/j.trb.2018.08.005
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发表时间：
2019-08
期刊：
影响因子：
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通讯作者：
T. Iryo
中科院分区：
文献类型：
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作者：
T. Iryo
稳定性是真实的运输系统实现平衡解的重要条件。如果解是不稳定的，那么它很容易受到系统上的小扰动的影响，因此在真实的世界中不会观察到平衡。虽然人们已经知道，一个静态平衡分配问题的平衡解是稳定的各种类型的演化动力学与温和的条件，在动态用户平衡（DUE）分配的稳定性很少被调查。本文证明了当采用复制子动力学时，出发时间选择问题的平衡解不是李雅普诺夫稳定的。由于均衡解的唯一性得到了证明，因此，当复制者动力学为演化动力学时，出发时间选择问题不存在稳定的均衡解。
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.