Admission Control in a Two Class Loss System with Periodically Varying Parameters and Abandonments

Gabriel Zayas-Cabán
Industrial and Systems Engineering

University of Wisconsin, Madison, WI, USA

Mark E. Lewis

School of Operations Research & Information Engineering
Cornell University
Ithaca, NY 14853


Motivated by service systems, such as telephone call centers and emergency departments, we consider admission control for a two-class multi-server loss system with periodically varying parameters and customers who may abandon from service. Assuming mild conditions for the parameters, a dynamic programming formulation is developed. We show that under the infinite horizon discounted problem, there exists an optimal threshold policy and provide conditions for a customer class to be preferred for each fixed time, extending stationary results to the non-stationary setting. We approximate the non-stationary problem by discretizing the time horizon into equally spaced intervals and examine how policies for this approximation change as a function of time and parameters numerically.  We compare the performance of these approximations with several admission policies used in practice in a discrete-event simulation study. We show that simpler admission policies that ignore non-stationarity or abandonments lead to significant losses in rewards.