Optimal patient assignment for W queueing network in a diagnostic facility setting

Quick examination is becoming increasingly critical for the diagnosis of patients. Increasing demand and insufficient diagnostic facilities lead to longer patient waiting times. It is important for hospital managers to reduce the waiting time of high-priority patients. To reduce the patients’ waiting time, the capacity in working time is divided into special time slots for high-priority patients and regular time slots for all patients. Low-priority patients are allowed to be referred to extra time slots by overtime or using the capacity of other hospitals. Two types of patients and three types of capacities form a W queueing network. This paper proposes an average-cost Markov Decision Process (MDP) model to assign the patients to the appropriate queue with the objective of minimising the weighted waiting cost and referral penalty. Structural properties of the optimal control policy under a given capacity are proved via discount-cost MDP. Extensive numerical experiments are performed to show the efficiency of the proposed patient assignment policy and to explore the impact of different parameters on the control policy.