Social optimum in public transport networks when users choose strategies: analysis and comparison with Wardrop equilibrium

IF 4.5 3区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Victoria M. Orlando, Iván L. Degano, Pablo A. Lotito
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Abstract

The effective design and management of public transport systems are essential to ensuring the best service for users. The performance of a transport system will depend heavily on users behavior and decisions. Generally, users have individual objectives, such as seeking to minimize their own travel time. These decisions can affect the performance of the entire system, making it inefficient. A measure that allows to quantify the inefficiency of the system in the face of non-cooperative behavior is the price of anarchy. Our objective is to investigate the price of anarchy in the common-lines problem. In this approach, users choose which lines to use based on the best strategy for them. While Wardrop equilibrium has been studied for the common-lines problem, no contributions have been made toward the social optimum. In this work, we propose two optimization problems to obtain this optimum on simple networks, using strategy flow and line flow formulations. In addition, we prove that both optimization problems are equivalent, and we obtain a characterization of the social optimum flows. These contributions allow us to obtain results about the behavior of the price of anarchy in simple networks as demand increases.

Abstract Image

用户选择策略时公共交通网络的社会最优:与Wardrop均衡的分析与比较
有效地设计和管理公共交通系统,对确保为使用者提供最佳服务至关重要。运输系统的性能在很大程度上取决于用户的行为和决策。一般来说,用户都有自己的目标,比如尽量减少自己的旅行时间。这些决策会影响整个系统的性能,使其效率低下。在面对非合作行为时,一种可以量化系统效率低下的方法就是无政府状态的代价。我们的目标是调查公共线路问题中无政府状态的代价。在这种方法中,用户根据最适合他们的策略来选择使用哪些行。虽然对共线问题的Wardrop均衡进行了研究,但尚未对社会最优做出贡献。在这项工作中,我们提出了两个优化问题,以获得简单网络上的最优,使用策略流和线流公式。此外,我们还证明了这两个优化问题是等价的,并得到了社会最优流的一个表征。这些贡献使我们能够获得简单网络中无政府状态的价格随需求增加的行为的结果。
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来源期刊
Annals of Operations Research
Annals of Operations Research 管理科学-运筹学与管理科学
CiteScore
7.90
自引率
16.70%
发文量
596
审稿时长
8.4 months
期刊介绍: The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications. In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.
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