Stochastic Scheduling ofParallel

We consider the problem of allocating a single server to a system of queues with Poisson arrivals. Each queue represents a class of jobs and possesses a holding cost rate, general service distribution, and a setup cost. The objective is to minimize the expected cost due to the waiting of jobs and the switching of the server. A setup cost is required to eeect an instantaneous switch from one queue to another. We partially characterize an optimal policy and provide a simple heuristic scheduling policy. The heuristic's performance is evaluated in the cases of two and three queues by comparison with a numerically obtained optimal policy. Simulation results are provided to demonstrate the eeectiveness of our heuristic over a wide range of problem instances with four queues.