{"title":"单假期Geom/G/1队列的性能分析","authors":"Xiu-li Xu, Yance Li, N. Tian","doi":"10.1145/1837856.1837858","DOIUrl":null,"url":null,"abstract":"In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.","PeriodicalId":347695,"journal":{"name":"International Conference on Queueing Theory and Network Applications","volume":"97 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Performance analysis for the Geom/G/1 queue with single working vacation\",\"authors\":\"Xiu-li Xu, Yance Li, N. Tian\",\"doi\":\"10.1145/1837856.1837858\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.\",\"PeriodicalId\":347695,\"journal\":{\"name\":\"International Conference on Queueing Theory and Network Applications\",\"volume\":\"97 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-07-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Conference on Queueing Theory and Network Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1837856.1837858\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Conference on Queueing Theory and Network Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1837856.1837858","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Performance analysis for the Geom/G/1 queue with single working vacation
In this paper, we analyzed a Geom/G/1 queue with single working vacation. Firstly, we obtained the M/G/1-type structure matrix of the two-dimensional embedded Markov chain. Using the matrix analysis method, highly complicated PGF of the stationary queue size is firstly derived. Furthermore, we got the stochastic decomposition formulae for the PGF of the stationary queue size and the stationary waiting time. Finally, several numerical examples are presented to verify these results.
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