Optimum and equilibrium in a transport problem with queue penalization effect
Optimum and equilibrium in a transport problem with queue penalization effect
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DOI：
10.1515/acv.2009.009
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发表时间：
2009-07-01
影响因子：
1.7
通讯作者：
Pratelli, Aldo
中科院分区：
文献类型：
--
作者：
Crippa, Gianluca;Jimenez, Chloe;Pratelli, Aldo
考虑在城市地区的公民分布，其中一些服务（超市，邮局.）都在场每个公民，为了使用服务，花费一定量的时间，这是由于旅行时间的服务和排队等待的服务。每个公民选择使用何种服务是为了更快地获得服务。可以考虑两种类型的问题：整个城市公民花费的总时间的全局优化（我们定义了全局最优值，并使用最优公共交通技术来研究它）和个人优化，其中每个公民选择服务试图最大限度地减少他自己的时间费用（我们定义了均衡的概念，并使用博弈论的技术来研究它）。在这个框架中，我们也能够展示两个时间依赖的策略（分别基于谨慎和记忆的概念）收敛到均衡。
Consider a distribution of citizens in an urban area in which some services (supermarkets, post offices...) are present. Each citizen, in order to use a service, spends an amount of time which is due both to the travel time to the service and to the queue time waiting in the service. The choice of the service to be used is made by every citizen in order to be served more quickly. Two types of problems can be considered: a global optimization of the total time spent by the citizens of the whole city (we define a global optimum and we study it with techniques from optimal mass transportation) and an individual optimization, in which each citizen chooses the service trying to minimize just his own time expense (we define the concept of equilibrium and we study it with techniques from game theory). In this framework we are also able to exhibit two time-dependent strategies (based on the notions of prudence and memory respectively) which converge to the equilibrium.