{"title":"Analytical Investigation of a Single-Server Queueing System with an Incoming MAP Event Flow","authors":"A. M. Gortsev, L. A. Nezhelskaya","doi":"10.1134/S000511792307007X","DOIUrl":null,"url":null,"abstract":"<p>This paper considers a single-server queueing system with an incoming Markovian Arrival Process (MAP) request flow with two states. Explicit expressions are derived for the stationary probability distribution of the states and several numerical characteristics of the system (the probability of idle time of the server, the expected number of requests in the system, and the mean queue length). The resulting numerical characteristics are presented in tables and plotted in graphical form as well. The recurrent MAP flow with two states as a special case of correlated MAP request flows is studied.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automation and Remote Control","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1134/S000511792307007X","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper considers a single-server queueing system with an incoming Markovian Arrival Process (MAP) request flow with two states. Explicit expressions are derived for the stationary probability distribution of the states and several numerical characteristics of the system (the probability of idle time of the server, the expected number of requests in the system, and the mean queue length). The resulting numerical characteristics are presented in tables and plotted in graphical form as well. The recurrent MAP flow with two states as a special case of correlated MAP request flows is studied.
期刊介绍:
Automation and Remote Control is one of the first journals on control theory. The scope of the journal is control theory problems and applications. The journal publishes reviews, original articles, and short communications (deterministic, stochastic, adaptive, and robust formulations) and its applications (computer control, components and instruments, process control, social and economy control, etc.).