Fluid approximation and perturbation analysis of a dynamic priority call center

We analyze a call center with multiclass calls and dynamic priority service discipline, in which a lower priority customer becomes high priority when its waiting time exceeds a given service level threshold. For each priority queue, the service discipline is first come, first served. Based on a fluid approximation of the system, we apply infinitesimal perturbation analysis (EPA) to derive estimators for the derivative of the queue lengths with respect to the threshold parameter. We establish unbiasedness of the estimators, and report numerical results via simulation.