Optimal scheduling in a machine with stochastic varying processing rate

Addresses the problem of allocating the capacity of a machine among jobs of different classes when the machine processing rate varies stochastically over time. The authors establish that the policy that always allocates the maximum available processing rate to the class having the maximum weight minimizes, pathwise, a weighted sum of the remaining service requirements of the different classes, at any point in time. This result is based on the application of elementary forward induction arguments and holds over the class of all policies (e.g., including randomized policies). As an easy corollary of this result the authors generalize work by Hirayama and Kijima (1992) on the optimality of the μc-rule in a multiclass G/M/1 queueing system in which the server processing rate varies stochastically with time. To the best of the authors´ knowledge, their proof is the first one in this context that only uses direct pathwise arguments