A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach
{"title":"A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach","authors":"Raghavendran. R, V. Vidhya","doi":"10.1016/j.asej.2025.103293","DOIUrl":null,"url":null,"abstract":"<div><div>In this research work we study the correlation impact between the inter arrival time and service time of packets arriving to the system for transmission. By assuming the arrival in modulated form the service utilization provided by server acts with varying rate of service. The queuing quantities are obtained in closed form by using matrix geometric method. The expected waiting length of packets and other performance measures are calculated in the stationary state distribution of the process. We establish the analytic frame work of the Markov model between the inter arrival and service time to get correlation impact to study the behavioural effect in queue length, time and other performance measures.</div></div>","PeriodicalId":48648,"journal":{"name":"Ain Shams Engineering Journal","volume":"16 3","pages":"Article 103293"},"PeriodicalIF":5.9000,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Ain Shams Engineering Journal","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2090447925000346","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
In this research work we study the correlation impact between the inter arrival time and service time of packets arriving to the system for transmission. By assuming the arrival in modulated form the service utilization provided by server acts with varying rate of service. The queuing quantities are obtained in closed form by using matrix geometric method. The expected waiting length of packets and other performance measures are calculated in the stationary state distribution of the process. We establish the analytic frame work of the Markov model between the inter arrival and service time to get correlation impact to study the behavioural effect in queue length, time and other performance measures.
期刊介绍：
in Shams Engineering Journal is an international journal devoted to publication of peer reviewed original high-quality research papers and review papers in both traditional topics and those of emerging science and technology. Areas of both theoretical and fundamental interest as well as those concerning industrial applications, emerging instrumental techniques and those which have some practical application to an aspect of human endeavor, such as the preservation of the environment, health, waste disposal are welcome. The overall focus is on original and rigorous scientific research results which have generic significance.
Ain Shams Engineering Journal focuses upon aspects of mechanical engineering, electrical engineering, civil engineering, chemical engineering, petroleum engineering, environmental engineering, architectural and urban planning engineering. Papers in which knowledge from other disciplines is integrated with engineering are especially welcome like nanotechnology, material sciences, and computational methods as well as applied basic sciences: engineering mathematics, physics and chemistry.
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