Analysis of Scheduling Policies for a M/G/I Queue with Rework

This thesis analyzes a multi-class M/G/1 priority queueing system in which distinct job types require one service cycle and, with non-zero probability, require a second service cycle. The main objective is to find a new heuristic scheduling policy that minimizes the long-run expected holding and preemption costs. Arrival rates, service rates, and the probability of undertaking second service are all class specific. A mean value analysis (MVA) approach was employed to derive the long- run mean time in queue for each job type under each policy, thereby providing the appropriate cost equations. Numerical experiments suggest that the preemptive resume scheduling policy yields the lowest cost most frequently

On the Bias Vector of a Two-Class Preemptive Priority Queue

We give a closed-form expression for the long-run average cost and the bias vector in a two-class exponential preemptive resume priority queue with holding and switching costs. The bias vector is the sum of a quadratic function of the number of customers in each priority class and an exponential function of the number of customers in the high priority class. We use this result to perform a single step of the policy iteration algorithm in the model where the switches of the server from one priority class to the other can be controlled. It is numerically shown that the policy resulting from the application of a single step of the policy iteration algorithm is close to the optimal policy