Scheduling Control for Many-Server Queues When Customers Change Class

We consider a two class, many-server queueing system which allows for customer abandonment and class changes. With the objective to minimize the long-run average holding cost, we formulate a stochastic queueing control problem. Instead of solving this directly, we apply a fluid scaling to obtain a deterministic counterpart to the problem. By considering the equilibrium of the deterministic solution, we can solve the resulting control problem, referred to as the equilibrium control problem (ECP), and use the solution to propose a priority policy for the original stochastic queueing system. We prove that in an overloaded system, under a fluid scaling, our policy is asymptotically optimal as it attains the lower bound formed by the solution of the ECP