Time-dependent analysis for refused admissions in clinical wards

For capacity planning issues in health care, such as the allocation of hospital beds, the admissions rate of patients is commonly assumed to be constant over time. In addition to the purely random fluctuations, there is also typically a predictable pattern in the number of arriving patients. For example, roughly 2/3 of the admitted patients at an Intensive Care Unit arrives during office hours. Also, most of the scheduled admissions occur during weekdays instead of during the weekend. Using approximations based on the infinite-server queue, we analyze an Mt/H/s/s model to determine the impact of the time-dependent arrival pattern on the required number of operational beds and fraction of refused admissions for clinical wards. In particular, the results show that the effect of the daily pattern is rather limited for clinical wards in contrast to the week-weekend pattern, for which the difference in the fraction of refused admissions across the week is considerable. We also show that an increased variability in length of stay distribution has a stabilizing effect on the time-dependent required number of beds. Finally, we demonstrate a method to determine the required number of beds across the week.