Performance Analysis of a Multi-Class, Preemptive Priority Call Center with Time-Varying Arrivals

Abstract

We model a call center as a an $M_{t}/M/n$, preemptive-resume priority queue with time-varying arrival rates and two priority classes of customers. The low priority customers have a dynamic priority where they become high priority if their waiting time exceeds a given service-level time. The performance of the call center is estimated by the mean number in the system and mean virtual waiting time for both classes of customers. We discuss some analytical methods of measuring the performance of call center models, such as Laplace transforms. We also propose a more-robust fluid approximations method to model a call center. The accuracy of the performance measures from the fluid approximation method depend on an asymptotic scheme developed by Halfin and Whitt. Here, the offered load and number of servers are scaled by the same factor, which maintains a constant system utilization. The fluid approximations provide estimates for the mean number in system and mean virtual waiting time. The approximations are solutions of a system of nonlinear differential equations. We analyze the accuracy of the fluid approximations through a comparison with a discrete-event simulation of a call center. We show that for a large enough scale factor, the estimates of the performance measures derived from the fluid approximations method are relatively close to those from the discrete-event simulation. Finally, we demonstrate that these approximations remain relatively close to the simulation estimates as the system state varies between under-loaded and over-loaded status.