Optimal Strategy in Queueing Systems in Emergency Department

The authors' study a noncooperative game problem for queueing control in emergency department (ED). One of the challenges to emergency department (ED) is the control of the urgent patients and the non-urgent patients. The urgent patient which is the primary customer, can be considered as the service interruption in a queueing system. The service interruptions occur frequently and can incur significant delays for the non-urgent patients. Therefore, a non-urgent patient needs to decide whether to join the queue or leave. The scenario is modeled as an M/M/1 queueing game with server interruption where each patient wants to optimize his benefit. It is shown that the individually optimal strategy for joining the queue is characterized by a threshold of queue length. The socially optimal threshold of queue length is also obtained. To bridge the gap between the individually and socially optimal strategies, a pricing mechanism is proposed to toll the service of each non-urgent patient, thus equalizing the two optimal strategies.