Dynamic system optimal traffic assignment with atomic users: Convergence and stability
Dynamic system optimal traffic assignment with atomic users: Convergence and stability
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DOI：
10.1016/j.trb.2021.11.001
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发表时间：
2021-01
期刊：
影响因子：
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通讯作者：
Koki Satsukawa;Kentaro Wada;D. Watling
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文献类型：
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作者：
Koki Satsukawa;Kentaro Wada;D. Watling
在这项研究中，我们分析了固定出发时间的动态系统最优（DSO）交通分配的收敛性和稳定性。我们首先制定的DSO交通分配问题作为一个战略游戏，其中原子用户选择的路线，最大限度地减少他们的边际社会成本，称为“DSO游戏”。利用DSO博弈是一个势博弈的事实，证明了在logit响应动力学下，全局最优状态是随机稳定的，而最优/最佳响应动力学收敛于局部最优状态.此外，作为DSO分配的一个应用，我们研究了边际成本定价的进化实施方案的特点。通过与固定定价方案的理论比较，我们发现了进化实施方案的以下性质：（i）总行程时间更平滑地减少到有效的交通状态，因为拥塞外部性完全内在化;（ii）交通状态将达到更有效的状态，因为全局最优状态是稳定的。数值实验还表明，这些属性使进化方案的鲁棒性，在这个意义上说，他们防止交通状态去更糟糕的交通状态与高的总行程时间。
In this study, we analyse the convergence and stability of dynamic system optimal (DSO) traffic assignment with fixed departure times. We first formulate the DSO traffic assignment problem as a strategic game wherein atomic users select routes that minimise their marginal social costs, called a ‘DSO game’. By utilising the fact that the DSO game is a potential game, we prove that a globally optimal state is a stochastically stable state under the logit response dynamics, and the better/best response dynamics converges to a locally optimal state. Furthermore, as an application of DSO assignment, we examine characteristics of the evolutionary implementation scheme of marginal cost pricing. Through theoretical comparison with a fixed pricing scheme, we found the following properties of the evolutionary implementation scheme: (i) the total travel time decreases smoother to an efficient traffic state as congestion externalities are perfectly internalised; (ii) a traffic state would reach a more efficient state as the globally optimal state is stabilised. Numerical experiments also suggest that these properties make the evolutionary scheme robust in the sense that they prevent a traffic state from going to worse traffic states with high total travel times.