{"title":"带工作假期的M/M/2排队模型优化","authors":"S. Gupta, P. Joshi, K. Rajeshwari","doi":"10.3329/jsr.v15i1.59348","DOIUrl":null,"url":null,"abstract":"The paper deals with an M/M/2 Queueing Model with working vacations and reneging of customers due to impatience. The matrix geometric method is used to find the distribution of the number of customers in the system. A cost function is constructed to obtain the optimal value of the service rate to optimize (minimize) the cost function using the Quadratic Fit Search Method (QFSM). Further, the effects on the system's performance measures using numerical analysis and graphical representation are studied.","PeriodicalId":16984,"journal":{"name":"JOURNAL OF SCIENTIFIC RESEARCH","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimization of M/M/2 Queueing Model with Working Vacations\",\"authors\":\"S. Gupta, P. Joshi, K. Rajeshwari\",\"doi\":\"10.3329/jsr.v15i1.59348\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper deals with an M/M/2 Queueing Model with working vacations and reneging of customers due to impatience. The matrix geometric method is used to find the distribution of the number of customers in the system. A cost function is constructed to obtain the optimal value of the service rate to optimize (minimize) the cost function using the Quadratic Fit Search Method (QFSM). Further, the effects on the system's performance measures using numerical analysis and graphical representation are studied.\",\"PeriodicalId\":16984,\"journal\":{\"name\":\"JOURNAL OF SCIENTIFIC RESEARCH\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"JOURNAL OF SCIENTIFIC RESEARCH\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3329/jsr.v15i1.59348\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"JOURNAL OF SCIENTIFIC RESEARCH","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/jsr.v15i1.59348","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了具有工作假期和顾客因不耐烦而违约的M/M/2排队模型。采用矩阵几何方法求出系统中顾客数量的分布。利用二次拟合搜索法(Quadratic Fit Search Method, QFSM)构造了一个成本函数，以获得服务率的最优值，从而优化(最小化)成本函数。进一步，利用数值分析和图形表示研究了对系统性能指标的影响。
Optimization of M/M/2 Queueing Model with Working Vacations
The paper deals with an M/M/2 Queueing Model with working vacations and reneging of customers due to impatience. The matrix geometric method is used to find the distribution of the number of customers in the system. A cost function is constructed to obtain the optimal value of the service rate to optimize (minimize) the cost function using the Quadratic Fit Search Method (QFSM). Further, the effects on the system's performance measures using numerical analysis and graphical representation are studied.
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