Approximate Analysis of an Unreliable M/M/2 Retrial Queue

<p>This thesis considers the performance evaluation of an M/M/2 retrial queue for which both servers are subject to active and idle breakdowns. Customers may abandon service requests if they are blocked from service upon arrival or if their service is interrupted by a server failure. Customers choosing to remain in the system enter a retrial orbit for a random amount of time before attempting to re-access an available server. We assume that each server has its own dedicated repair person and repairs begin immediately following a failure. Interfailure times repair times and times between retrials are exponentially distributed and all processes are assumed to be mutually independent. Modeling the number of customers in the orbit and status of the servers as a continuous-time Markov chain we employ a phase- merging algorithm to approximately analyze the limiting behavior. Subsequently we derive approximate expressions for several congestion and delay measures. Using a benchmark simulation model we assess the accuracy of the approximations and show that when the algorithm assumptions are met the approximation procedure yields favorable results. However as the rate of abandonment for blocked arrivals decreases the performance declines while the results are insensitive to the rate of abandonment of customers preempted by a server failure.</p><p>This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact and remains as true to the original work as possible. Therefore you will see the original copyright references library stamps (as most of these works have been housed in our most important libraries around the world) and other notations in the work.</p><p>This work is in the public domain in the United States of America and possibly other nations. Within the United States you may freely copy and distribute this work as no entity (individual or corporate) has a copyright on the body of the work.</p><p>As a reproduction of a historical artifact this work may contain missing or blurred pages poor pictures errant marks etc. Scholars believe and we concur that this work is important enough to be preserved reproduced and made generally available to the public. We appreciate your support of the preservation process and thank you for being an important part of keeping this knowledge alive and relevant.</p>