Analysis of Single and Multiple Server Retrial Queueing Systems with Various Modes of Breakdown and Vacation

Abstract

This research explores the complex domain of queueing theory by investigating various newlinecombinations of queueing aspects to create distinct queueing models. These models were newlineanalytically structured to analyse the impact of diverse service parameters, customer dynamics newlineand system behaviours on efficiency metrics. This work encompasses both single and multi newlineserver queueing environments, incorporating homogeneous and heterogeneous service rates, newlineregular and retrial queues. newlineIn each model, combinations of different aspects of queueing system were investigated newlineincorporating breakdown and repair processes, vacation, feedback, balking, reneging, optional newlineservice, admission control policies and a novel introduction of customer rejection policy. The newlineresearch also explored synchronised vacation schemes, two-way communication services and newlinediverse outgoing service outlets. Furthermore, the models also included scenarios with working newlinebreakdown and working vacation, adding a tinge of complexity to the investigation. newlineThe study adopted a detailed analytical structure, employing mathematical modelling and newlinesolving techniques like recursive approach and matrix geometric method to extract meaningful newlineinsights into each practical situation newline