Date of Award

31-8-2024

Document Type

Thesis

School

School of Arts, Sciences, Humanities & Education

Programme

Ph.D.-Doctoral of Philosophy

First Advisor

Dr.D.Narasimhan

Keywords

Retrial Queues, Working Vacations, Working Breakdowns, Supplementary Variable Technique, Optimization

Abstract

The Chapter One titled “Introduction and Preliminaries” deals with the basic definition of queues; characteristics of the queueing theory. It also presents the motivation for this thesis. The literature survey in the area of retrial queue with different phases of service, priority arrivals, feedback, breakdowns, repairs, working vacations and working breakdown service models together with their applications are analyzed.

In Chapter Two “Analysis of an M/G/1 Retrial Queueing System with Priority Customers Under J number of Working Vacations” elaborates on a single server retrial queueing system with priority arrivals under J number of working vacations. If an arriving priority customer finds the server free, the customer begins his service immediately. While the server is working with an ordinary customer, the arriving priority customer will interrupt the service time of the ordinary customer and the server begins its service immediately. If an arriving ordinary customer finds the server busy or on working vacation, the arrivals join a pool of blocked customers called an orbit in accordance with FCFS discipline.

As soon as the orbit becomes empty at regular service completion instant, the server takes at most J number of working vacations until at least one customer is received in the orbit when the server returns from a working vacation. During the working vacation period, the server serves at a lower speed service rate (μv< μb). The steady state probability generating function of the orbit size and system size is obtained using supplementary variable technique and also obtained some analytic expressions for various performance measures such as system state probabilities, mean orbit size, and mean system size of this model. Numerical illustrations are analyzed to identify the effect of system parameters.

In Chapter Three “Performance Analysis of an M/G/1 retrial G-queue with Feedback under Working Breakdown Services” discusses a new type of retrial queueing model with feedback and working breakdown services has been discussed. The regular busy server may become defective due to disasters (negative customers) at any point of time. The negative customers arrive only at the service time of positive customer and will remove positive customer from the service. At a failure instant, the main server will be sent to repair and the repair period immediately begins. During the repair period, the server provides service at a low speed (working breakdown period). The steady state probability generating function for system size and orbit size are obtained using supplementary variable technique. Some analytical expressions for various performance measures such as system state probabilities, mean orbit size, mean system size of this model and some important special cases are derived. Finally, some numerical examples are presented to study the impact of system parameters.

In Chapter Four titled “Analysis of Retrial queue with Different Classes of Customers under Working Vacation Schedule” describes a working vacation queueing model with three different classes of customers: regular, priority, and disaster. The regular server serves all arriving customers, whereas the optional reservice is only provided to those who request it. The Bernoulli Working Vacation (BWV) schedule is considered. In WV time, the server serves at a slower rate. The Generating Functions (GF) technique is used to determine the system capacity of various server states. Different system performances, reliability indices, and cost optimization values are numerically shown. For the current Covid19 pandemic situation, the motivation for this approach is presented in telephonic communication system.

Chapter Five examines a new class of working vacation queueing models that contain regular (original) and retrial waiting queues. Upon arrival, a customer either starts their service instantly if the server is available, or they join the regular queue if the server is occupied. When it is empty, the server departs the system to take a Working Vacation (WV). The server provides services more slowly during the WV period. If the server is on vacation, new customers join the retrial queue (orbit). The Supplementary Variable Technique (SVT) examines the steady state Probability Generating Functions (PGF) of queue size for different server states. Several system performances are numerically displayed by including system state probabilities, mean busy cycles, mean queue lengths, sensitivity analysis, and cost optimization values. The motivation for this model in a pandemic situation is to analyze new healthcare service systems and reflect the characteristics of patient services.

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