Victoria M. Orlando, Iván L. Degano, Pablo A. Lotito
{"title":"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","authors":"Victoria M. Orlando, Iván L. Degano, Pablo A. Lotito","doi":"10.1007/s10479-025-06604-w","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1785 - 1815"},"PeriodicalIF":4.5000,"publicationDate":"2025-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Social optimum in public transport networks when users choose strategies: analysis and comparison with Wardrop equilibrium\",\"authors\":\"Victoria M. Orlando, Iván L. Degano, Pablo A. Lotito\",\"doi\":\"10.1007/s10479-025-06604-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":8215,\"journal\":{\"name\":\"Annals of Operations Research\",\"volume\":\"349 3\",\"pages\":\"1785 - 1815\"},\"PeriodicalIF\":4.5000,\"publicationDate\":\"2025-04-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Operations Research\",\"FirstCategoryId\":\"91\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10479-025-06604-w\",\"RegionNum\":3,\"RegionCategory\":\"管理学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"OPERATIONS RESEARCH & MANAGEMENT SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06604-w","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
Social optimum in public transport networks when users choose strategies: analysis and comparison with Wardrop equilibrium
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.
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.