A Study on Performance Analysis of Multi Server Markovian Queueing Models with Variant Vacation and Breakdown

Abstract

This thesis examines a variety of Markovian queueing models that incorporate vacations, newlinetaking into consideration both single and multiple servers. The primary model being newlineinvestigated is a queue in which service times are exponentially distributed and arrivals newlineare subject to a Poisson process. In addition, vacation follows exponential distribution. newlineThe arrival and the service patterns are single. The queueing discipline functions on a newlineFirst Come First Service basis and has an infinite waiting line capacity. Throughout newlinethe research, a variety of models are developed and analyzed, including concepts such newlineas heterogeneous servers, differentiated vacation, multiple vacation, working vacation, newlinebreakdown, differentiated breakdown, working breakdown and disaster. newlineThe primary aim of this thesis is to give steady state solution using matrix geometric newlinemethod and to give transient state solution using Laplace transform and Modified Bessels newlinefunction and subsequently analyze the numerical solutions. The performance measures newlinesuch as mean number of customers in the system, probabilities in various states are newlinederived. Our proposed models are intended to model real-world scenarios in which newlinedemand exceeds service capacity, rendering them applicable to a variety of sectors, such newlineas manufacturing, networking, contact centers, hospitals, and similar industries. newlineThe results of this investigation have the potential to be implemented in real-world newlinescenarios where queueing phenomena are prevalent. MATLAB software is employed to newlinedisplay numerical illustrations and cost evaluations for all proposed models newline