Dynamic Scheduling of a Multiclass Queue: Discount Optimality

We consider a single-server queuing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and we assume a linear cost structure. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (nonpreemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy that is optimal, and a simple algorithm for its computation is presented.