Optimal control of M/M/S queueing systems

Abstract

This thesis characterizes the optimal operating policy of multi-server queueing system subject to Poisson arrival process and exponentially distributed service times (M/M/S queue). Optimal policy minimizes the long-run total expected discounted cost to the system. The cost components 9f the system are taken as the server cost and the holding cost which is considered as the lost profit from the business or the lost production with respect to the type of the system. Markov Decision Theory is used in the characterization of the controlled process. Generator is the basic tool of the formulation. Application of some solution procedures is very easy for this type of formulation. Two different algorithms are presented to obtain the optimal policy: Successive approximation algorithm and policy improvement algorithm. Optimal policy for a simple maintenance problem is found using these two methods. Computational experiments on the computer indicate that the policy improvement method converges to the optimal policy more quickly. The theoretic results are extended to tandem queueing systems at the end.