OPTIMAL SCHEDULING IN A MACHINE WITH STOCHASTIC VARYING PROCESSING RATE

We address the problem of allocating the capacity of a machine among j obs of different classes when the machine processing rate varies stoch astically over time. We establish that the policy that always allocate s the maximum available processing rate to the class having the maximu m weight minimizes, pathwise, a weighted sum of the remaining service requirements of the different classes, at any point in time. This resu lt is based on the application of elementary forward induction argumen ts and holds over the class of all policies (e.g., including randomize d policies). As an easy corollary of this result we generalize a recen t work by Hirayama and Kijima [5] on the optimality of the muc-rule in a multiclass G/M/1 queueing system in which the server processing rat e varies stochastically with time. To the best of our knowledge, our p roof is the first one in this context that only uses direct pathwise a rguments.