{"title":"An Efficient Convolution Method to Compute the Stationary Transition Probabilities of the G/M/c Model and its Variants","authors":"M. El-Taha","doi":"10.23919/PEMWN53042.2021.9664677","DOIUrl":"https://doi.org/10.23919/PEMWN53042.2021.9664677","url":null,"abstract":"The multi-server G/M/c model is a fundamental building block in the analysis of many systems including computer, communication, and telecommunication networks. Consider this model with c servers, general arrivals and exponential service times. Inter-arrival times and service times are i.i.d. and independent of each other. The key contribution is developing a convolution method to compute transition probabilities exactly, thus avoiding numerical integration. We show how this can lead to a remarkably simple algorithm to derive an exact solution for the steady state system size probabilities.","PeriodicalId":196945,"journal":{"name":"2021 10th IFIP International Conference on Performance Evaluation and Modeling in Wireless and Wired Networks (PEMWN)","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127540292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}