Optimal Control of Service Systems with Heterogeneous Servers and Priority Customers

We study service systems with parallel servers and random customer arrivals, with a focus on the total waiting cost of customers. Using a Markov decision process (MDP) modeling approach, we analytically characterize the structures of the dynamic server assignment policies for two important systems, one consisting of multiple homogeneous servers and two classes of customers; and the other consisting of two heterogeneous servers and multiple classes of customers. Based on the obtained results, we propose a threshold-type heuristic policy for the generalized system consisting of multiple heterogeneous servers and multiple classes of customers. To design such a heuristic policy, we first develop techniques for the performance evaluation of general threshold-type policies with any given threshold values. We then construct a path to search for the optimal threshold values. Finally, we compare the performance of the best threshold-type heuristic policy with that of the optimal policy, and show that our proposed heuristic policy is computationally efficient yet generates great performance. We compare the system under our threshold-type dynamic server assignment policy with other commonly seen and simple systems (including the dedicated and the work-conserving flexible priority systems), and demonstrate the importance and usefulness of dynamic server assignment control, for service systems having multiple classes of customer arrivals. We also conduct sensitivity analysis to explore the impacts of various system configuration features (including the number of servers; service rate variation; number of customer classes; and system utilization) on the performance regarding waiting-cost minimization.