Fluid approximations for a priority call center with time-varying arrivals

We model a call center as a 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 measured by the mean number in system for the two customer classes. A fluid approximation is proposed to estimate the mean number in system for each class. The quality of the approximation is tested by comparing it with a stochastic simulation model of the system. Finally, using the fluid approximations, we discuss how to compute the mean number in system for each class and estimate the overall staffing level, or number of agents.