{"title":"开放排队网络中极端队列长度的迭代对数律","authors":"S. Minkevičius, L. Sakalauskas","doi":"10.1080/23799927.2021.1969432","DOIUrl":null,"url":null,"abstract":"The purpose of this research in the field of the open queueing network is to prove the Law of the Iterated Logarithm (LIL) for the extreme value of the queue length of customers in an open queueing network. LIL is proved for the extreme values of the queue length of customers the important probability characteristic of the queueing system under conditions of heavy traffic. Also, we present for extreme queue length of jobs Probability Laws ((theorems on the LIL, Fluid Limits Theorem and Diffusion Limit Theorem) in various conditions of traffic and simulating an open queueing network in Appendices 1 and 2.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the law of iterated logarithm for extreme queue length in an open queueing network\",\"authors\":\"S. Minkevičius, L. Sakalauskas\",\"doi\":\"10.1080/23799927.2021.1969432\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this research in the field of the open queueing network is to prove the Law of the Iterated Logarithm (LIL) for the extreme value of the queue length of customers in an open queueing network. LIL is proved for the extreme values of the queue length of customers the important probability characteristic of the queueing system under conditions of heavy traffic. Also, we present for extreme queue length of jobs Probability Laws ((theorems on the LIL, Fluid Limits Theorem and Diffusion Limit Theorem) in various conditions of traffic and simulating an open queueing network in Appendices 1 and 2.\",\"PeriodicalId\":37216,\"journal\":{\"name\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/23799927.2021.1969432\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Computer Mathematics: Computer Systems Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/23799927.2021.1969432","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
On the law of iterated logarithm for extreme queue length in an open queueing network
The purpose of this research in the field of the open queueing network is to prove the Law of the Iterated Logarithm (LIL) for the extreme value of the queue length of customers in an open queueing network. LIL is proved for the extreme values of the queue length of customers the important probability characteristic of the queueing system under conditions of heavy traffic. Also, we present for extreme queue length of jobs Probability Laws ((theorems on the LIL, Fluid Limits Theorem and Diffusion Limit Theorem) in various conditions of traffic and simulating an open queueing network in Appendices 1 and 2.
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