Modeling patient arrivals in community clinics

Abstract

We develop improved methods for modeling and simulating the streams of patients arriving at a community clinic. In previous practice, random (unscheduled) patient arrivals were often assumed to follow an ordinary Poisson process (so the corresponding patient interarrival times were randomly sampled from an exponential distribution); and for scheduled arrivals, each patient's tardiness (i.e., the deviation from the scheduled appointment time) was often assumed to be randomly sampled from a normal distribution. A thorough analysis of patient arrival times, obtained from detailed workflow observations in nine community clinics, indicates these assumptions are not generally valid, and the tardiness data sets for this study are best modeled by unbounded Johnson distributions. We also propose a nonhomogeneous Poisson process to model the random patient arrivals; we review a nonparametric approach to estimating the associated mean-value function; and we describe an algorithm for generating random patient arrivals from the estimated model. The adequacy of this model of random patient arrivals can be assessed by standard goodness-of-fit tests. These findings are important since testable scheduling optimization strategies must be based upon accurate models for both random and scheduled patient arrivals. The impacts on modeling, as well as implications for practice management, are discussed.