Modeling abandonment behavior among patients

Researchers often utilize time-based models of queue abandonment. In such models, researchers determine the length of time until abandonment by drawing from an exogenous distribution with no dependence on the system state. Recent empirical work, however, suggests that queue abandonment times may differ depending on key parameters of the system. We build on these empirical findings herein. Specifically, we study three operational drivers of abandonment – waiting time, queue length, and service rate – within the context of a hospital emergency department (ED) where patients often leave without being seen by a physician. We examine the shape of the hazard function for these patients and identify a dynamic Weibull distribution that is parameterized by queue length and service rate, effectively characterizes abandonment behavior in this context. We conduct a numerical study and demonstrate the benefit of using state-dependent abandonment times. Specifically, we show that a scaled arrival model that overlooks abandonment behavior, a prevailing model in discrete-event simulations of the ED, results in significant bias in resource planning (e.g., staffing levels, bed capacity, etc.) and performs poorly compared to our proposed Weibull model. Our findings have implications for researchers modeling and simulating queue abandonment.