Queueing network model for obstetric patient flow in a hospital

A queueing network is used to model the flow of patients in a hospital using the observed admission rate of patients and the histogram for the length of stay for patients in each ward. A complete log of orders for every movement of all patients from room to room covering two years was provided to us by the Medical Information Department of the University of Tsukuba Hospital in Japan. We focused on obstetric patients, who are generally hospitalized at random times throughout the year, and we analyzed the patient flow probabilistically. On admission, each obstetric patient is assigned to a bed in one of the two wards: one for normal delivery and the other for high-risk delivery. Then, the patient may be transferred between the two wards before discharge. We confirm Little's law of queueing theory for the patient flow in each ward. Next, we propose a new network model of M/G/ ∞ and M/M/ m queues to represent the flow of these patients, which is used to predict the probability distribution for the number of patients staying in each ward at the nightly census time. Although our model is a very rough and simplistic approximation of the real patient flow, the predicted probability distribution shows good agreement with the observed data. The proposed method can be used for capacity planning of hospital wards to predict future patient load in each ward.