基于改进批量服务规则和动态服务速率的马尔可夫批量服务队列平稳系统长度分布

IF 0.9 Q3 COMPUTER SCIENCE, THEORY & METHODS
Gagandeep Singh, A. Kumari, U. C. Gupta
{"title":"基于改进批量服务规则和动态服务速率的马尔可夫批量服务队列平稳系统长度分布","authors":"Gagandeep Singh, A. Kumari, U. C. Gupta","doi":"10.1080/23799927.2021.2000503","DOIUrl":null,"url":null,"abstract":"In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.","PeriodicalId":37216,"journal":{"name":"International Journal of Computer Mathematics: Computer Systems Theory","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2021-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Stationary system-length distribution of Markovian bulk service queue with modified bulk service rule and dynamic service rates\",\"authors\":\"Gagandeep Singh, A. Kumari, U. C. Gupta\",\"doi\":\"10.1080/23799927.2021.2000503\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.\",\"PeriodicalId\":37216,\"journal\":{\"name\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Computer Mathematics: Computer Systems Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/23799927.2021.2000503\",\"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/10.1080/23799927.2021.2000503","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 4

摘要

在本文中,我们考虑一个单服务器批量服务队列,该队列具有修改后的批量服务规则,即规则,其中客户以最大批大小K和最小阈值l为批,并且如果服务器已经开始服务并且客户少于K,我们允许客户进入服务。此外,批次的服务率被认为依赖于批次的大小。导出了队列中顾客数量和有服务器时的联合概率分布的解析表达式,以及队列中顾客数量、系统中顾客数量和有服务器时的边际概率分布。数值研究了各种参数对上述分布的影响,并以表格和图表的形式给出了数值结果。我们还获得各种性能度量(包括封闭形式和数字形式),例如排队、系统和服务器中的平均客户数量等。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stationary system-length distribution of Markovian bulk service queue with modified bulk service rule and dynamic service rates
In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
International Journal of Computer Mathematics: Computer Systems Theory
International Journal of Computer Mathematics: Computer Systems Theory Computer Science-Computational Theory and Mathematics
CiteScore
1.80
自引率
0.00%
发文量
11
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信