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

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. 1 BACKGROUND We are perhaps all too familiar with the regular ebb and flow of demand in service systems. Examples abound-the seasonal crush of holiday shopping, the daily grind of morning and evening rush hours, savings on evening and weekend telephone calls, the wisdom of dinner-hour reservations at your favorite restaurant, the annoyance of rolling electricity brownouts, and the economy of airfares for Saturday-night layovers. Indeed, WSC is scheduled during the early weeks of December at least in part because of the slack demand (and favorable scheduling and pricing) of hotel facilities at this time of year. Given the ubiquity and impact of such systems, it is not surprising that there is a significant literature on simulating input processes that vary in intensity over time The purpose of this paper is to add a case study to this literature, based on recent experience. The study also provides a unique, bivariate extension of the standard thinning technique developed by Lewis and Shedler (1979) for generating nonstationary Poisson arrivals. The client for this case was a major chain of consumer electronics outlets. In response to slipping market share, the corporate office proposed a change in retail store layout and operating procedures intended to streamline customer service. The study objective was to determine the potential impact of the new operating procedures on the workload of sales …