Simulating a nonstationary Poisson process using bivariate thinning: the case of “typical weekday” arrivals at a consumer electronics store

Abstract

We present a case study in which thinning is applied to simulate time-varying arrivals at a consumer electronics store. The underlying simulation was developed to support an analysis of new staffing schedules for retail sales associates, given proposed changes in store layout and operating procedures. A principal challenge was developing a modeling approach for customer arrivals, where it was understood that the arrival rate varied by time-of-day and by day-of-the-week, as well as seasonally. An analysis of arrival data supported a conjectured "typical weekday" as one basic arrival model. For this model, arrivals were assumed to be nonstationary Poisson, with a piecewise-linear arrival rate independently modulated by hour and by day. Arrival data were filtered and independent hourly and daily thinning factors computed. In the simulation, potential arrivals were generated with a mean equal to the minimum average interarrival rate, determined from the average arrival count for the hour/day time block with unit thinning factors. Candidate arrivals were then thinned using a bivariate acceptance probability equal to the product of the corresponding hourly and daily thinning factors.