M. Ghahramani, A. Badamchi Zadeh, M. R. Salehi Rad
{"title":"Two M/M/1 Queues with Incongruent Arrivals and Services with Random Feedback","authors":"M. Ghahramani, A. Badamchi Zadeh, M. R. Salehi Rad","doi":"10.1080/01966324.2019.1597794","DOIUrl":null,"url":null,"abstract":"SYNOPTIC ABSTRACT The current study examines a queuing system with two incongruent arrivals and two services. In this regard, two types of customers enter the system by a Poisson process and the service times are assumed to have exponential distributions. After the first service is completed, the system may provide feedback to repeat the first service, leave the system, or continue to give the second service. The same policy is utilized for the other kind of customers. The whole stochastic processes involved in the system are considered as independent random variables. A probability generating function is derived for each type and for the system that yield the performance measures. We examine the validity of the results through numerical approaches.","PeriodicalId":35850,"journal":{"name":"American Journal of Mathematical and Management Sciences","volume":"38 1","pages":"386 - 394"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/01966324.2019.1597794","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Mathematical and Management Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/01966324.2019.1597794","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Business, Management and Accounting","Score":null,"Total":0}
引用次数: 1
Abstract
SYNOPTIC ABSTRACT The current study examines a queuing system with two incongruent arrivals and two services. In this regard, two types of customers enter the system by a Poisson process and the service times are assumed to have exponential distributions. After the first service is completed, the system may provide feedback to repeat the first service, leave the system, or continue to give the second service. The same policy is utilized for the other kind of customers. The whole stochastic processes involved in the system are considered as independent random variables. A probability generating function is derived for each type and for the system that yield the performance measures. We examine the validity of the results through numerical approaches.