Jocelyn Begeot, Irène Marcovici, P. Moyal, Youssef Rahme
{"title":"多图上的一般随机匹配模型","authors":"Jocelyn Begeot, Irène Marcovici, P. Moyal, Youssef Rahme","doi":"10.30757/alea.v18-49","DOIUrl":null,"url":null,"abstract":"We extend the general stochastic matching model on graphs introduced in (Mairesse and Moyal, 2016), to matching models on multigraphs, that is, graphs with self-loops. \nThe evolution of the model can be described by a discrete time Markov chain whose positive recurrence is investigated. \nNecessary and sufficient stability conditions are provided, together with the explicit form of the stationary probability in the case where the matching policy is `First Come, First Matched'.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"A general stochastic matching model on multigraphs\",\"authors\":\"Jocelyn Begeot, Irène Marcovici, P. Moyal, Youssef Rahme\",\"doi\":\"10.30757/alea.v18-49\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We extend the general stochastic matching model on graphs introduced in (Mairesse and Moyal, 2016), to matching models on multigraphs, that is, graphs with self-loops. \\nThe evolution of the model can be described by a discrete time Markov chain whose positive recurrence is investigated. \\nNecessary and sufficient stability conditions are provided, together with the explicit form of the stationary probability in the case where the matching policy is `First Come, First Matched'.\",\"PeriodicalId\":8470,\"journal\":{\"name\":\"arXiv: Probability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30757/alea.v18-49\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30757/alea.v18-49","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A general stochastic matching model on multigraphs
We extend the general stochastic matching model on graphs introduced in (Mairesse and Moyal, 2016), to matching models on multigraphs, that is, graphs with self-loops.
The evolution of the model can be described by a discrete time Markov chain whose positive recurrence is investigated.
Necessary and sufficient stability conditions are provided, together with the explicit form of the stationary probability in the case where the matching policy is `First Come, First Matched'.
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