A Stochastic Queueing Model for Capacity Allocation in the Hierarchical Healthcare Delivery System

Abstract

We use the capacity allocation as a demand management tool to optimize the patient flow distribution on a hierarchical healthcare delivery system, which is a mixture of patient choice and gatekeeping. Capacity allocation for such service system can be challenging because of the inherent stochastic referral process and patients’ heterogeneous delay sensitivities. In this research, a stochastic queueing-based model is proposed to find the optimal allocation of the limited service capacity of the second level of experts. Considering the impact of the deficiency of the skill level and the amount of gatekeepers, the stochastic referral process is modeled with a tandem queue. By solving a fixed-point problem, we show that there is an unique optimal allocation and corresponding equilibrium demand. We carry out numerical studies and find that providing two alternatives for patients can be better than gatekeeper system, when the capacity of the gatekeeper is moderate compared to patients’ potential demand. Results also indicate that the optimal allocation is robust in terms of the referral rate and the mistreatment rate when two rates are less than corresponding thresholds.