A Two-Time-Scale Approach to Time-Varying Queues in Hospital Inpatient Flow Management

摘要: We analyze a time-varying Mperi/Geo2timeScale/N queueing system. The arrival process is periodic Poisson. service time of customer has components in different scales: length stay (LOS) days and departure (hdis) hours. This system been used to study patient flows from the emergency department (ED) hospital inpatient wards. In that setting, LOS simply number she spends ward her hdis discharge hour on day discharge. develop new analytical framework can perform exact analysis this novel two steps: first midnight count obtain its stationary distribution, then time-dependent compute various performance measures. also approximation tools significantly reduce computational time. particular, via Stein's method, we derive explicit expressions approximate distribution count. provide error bounds for these approximations numerically demonstrate they are remarkably accurate systems with sizes load conditions. Our theoretical numerical have produced insights be improve flow management. find term affects overnight wait caused by mismatch between daily arrivals discharges, whereas intra-day non-synchronization patterns. Thus, reducing or increasing capacity impact average significantly; shifting timing earlier times alleviate peak congestion morning mainly performance.