{"title":"The stability condition of BMAP/M/∞ queues","authors":"Moeko Yajima, Tuan Phung-Duc, H. Masuyama","doi":"10.1145/3016032.3016046","DOIUrl":null,"url":null,"abstract":"This paper considers a BMAP/M/∞ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/∞ queue is stable if and only if the expectation of the logarithm of the batch-size distribution is finite. Using this result, we also present the stability condition for an infinite-server queue with a multiclass batch Markovian arrival process and class-dependent exponential service times.","PeriodicalId":269685,"journal":{"name":"Proceedings of the 11th International Conference on Queueing Theory and Network Applications","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 11th International Conference on Queueing Theory and Network Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3016032.3016046","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
This paper considers a BMAP/M/∞ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/∞ queue is stable if and only if the expectation of the logarithm of the batch-size distribution is finite. Using this result, we also present the stability condition for an infinite-server queue with a multiclass batch Markovian arrival process and class-dependent exponential service times.
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