Optimal Control of Service Systems with Heterogeneous Servers and Priority Customers

We study non-preemptive queueing systems consisting multiple classes of customers with different waiting cost rates and multiple servers with heterogeneous service rates. We compare two common-in-practice systems (dedicated system and work-conserving flexible priority system) and characterize conditions for each one to be more favorable. Under the objective of minimizing discounted total waiting cost, we develop a Markov decision process formulation and analytically characterize the structure of the optimal dynamic server assignment policy. We prove that, the optimal policy is of a threshold type with intentional idleness. We also invent an approach to compute the optimal threshold values. Through numerical experiments, we quantify the advantage of the optimal policy.