{"title":"带保护通道和保护缓冲区的 M/M/C/K 重审队列的渐近上限","authors":"Nesrine Zidani, Natalia Djellab","doi":"10.1007/s00186-024-00865-0","DOIUrl":null,"url":null,"abstract":"<p>The paper deals with Markovian multiserver retrial queuing system with exponential abandonments, two types of arrivals: Fresh calls and Handover calls and waiting places in the service area. This model can be used for analysing a cellular mobile network, where the service area is divided into cells. In this paper, the number of customers in the system and in the orbit form a level-dependent quasi-birth-and-death process, whose stationary distribution is expressed in terms of a sequence of rate matrices. First, we derive the Taylor series expansion for nonzero elements of the rate matrices. Then, by the expansion results, we obtain an asymptotic upper bound for the stationary distribution of both the number of busy channels and the number of customers in the orbit. Furthermore, we present some numerical results to examine the performance of the system.</p>","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"168 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer\",\"authors\":\"Nesrine Zidani, Natalia Djellab\",\"doi\":\"10.1007/s00186-024-00865-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The paper deals with Markovian multiserver retrial queuing system with exponential abandonments, two types of arrivals: Fresh calls and Handover calls and waiting places in the service area. This model can be used for analysing a cellular mobile network, where the service area is divided into cells. In this paper, the number of customers in the system and in the orbit form a level-dependent quasi-birth-and-death process, whose stationary distribution is expressed in terms of a sequence of rate matrices. First, we derive the Taylor series expansion for nonzero elements of the rate matrices. Then, by the expansion results, we obtain an asymptotic upper bound for the stationary distribution of both the number of busy channels and the number of customers in the orbit. Furthermore, we present some numerical results to examine the performance of the system.</p>\",\"PeriodicalId\":49862,\"journal\":{\"name\":\"Mathematical Methods of Operations Research\",\"volume\":\"168 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods of Operations Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00186-024-00865-0\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods of Operations Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00186-024-00865-0","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer
The paper deals with Markovian multiserver retrial queuing system with exponential abandonments, two types of arrivals: Fresh calls and Handover calls and waiting places in the service area. This model can be used for analysing a cellular mobile network, where the service area is divided into cells. In this paper, the number of customers in the system and in the orbit form a level-dependent quasi-birth-and-death process, whose stationary distribution is expressed in terms of a sequence of rate matrices. First, we derive the Taylor series expansion for nonzero elements of the rate matrices. Then, by the expansion results, we obtain an asymptotic upper bound for the stationary distribution of both the number of busy channels and the number of customers in the orbit. Furthermore, we present some numerical results to examine the performance of the system.
期刊介绍:
This peer reviewed journal publishes original and high-quality articles on important mathematical and computational aspects of operations research, in particular in the areas of continuous and discrete mathematical optimization, stochastics, and game theory. Theoretically oriented papers are supposed to include explicit motivations of assumptions and results, while application oriented papers need to contain substantial mathematical contributions. Suggestions for algorithms should be accompanied with numerical evidence for their superiority over state-of-the-art methods. Articles must be of interest for a large audience in operations research, written in clear and correct English, and typeset in LaTeX. A special section contains invited tutorial papers on advanced mathematical or computational aspects of operations research, aiming at making such methodologies accessible for a wider audience.
All papers are refereed. The emphasis is on originality, quality, and importance.