Age Replacement and Service Rate Control of Stochastically Degrading Queues

<p>This thesis considers the problem ofoptimally selecting a periodic replacement time for a multiserver queueing system in whicheach server is subject to degradation as a function of the mean service rate and a stochastic and dynamic environment. Also considered is the problem of optimal service rate selection for such a system. In both cases the performance metric is the long-run average cost rate. Analytical expressions are obtained in terms of Laplace transforms for the nonlinear objective functions necessitating the use of numerical Laplace transform inversion to evaluate candidate solutions in conjunction with standard numerical algorithms. Due to the convexity of the objective function the optimal replacement time is computed using a hybrid bisection-secant method which yields globally optimal solutions. The optimal service rates are obtained via gradient search methods but are only guaranteed to provide locally optimal solutions. The analytical results are implemented on three notional examples that demonstrate the benefits of dynamically adjusting service rates under the described maintenance policy.</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>