Choosing Arrival Process Models for Service Systems: Tests of a Nonhomogeneous Poisson Process

• Activity Number: 113
• Type: Invited
• Date/Time: Monday, August 10, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Song-Hee Hailey Kim* and Ward Whitt
• Companies: Yale School of Management and Columbia University
• Keywords: nonhomogeneous Poisson process ; service system arrival processes ; data transformations for statistical tests ; power of statistical tests ; Kolmogorov-Smirnov statistical test

Abstract

Service systems such as call centers and hospitals typically have strongly time-varying arrivals, and a natural model for their arrival process for performance analysis is a nonhomogeneous Poisson process (NHPP). As this is such a common modeling approach, it is important to perform statistical tests with data to confirm that an NHPP is actually appropriate. We compare alternative methods that test the NHPP assumption, with a focus on examining the tests' power, and find that a careful data transformation significantly improves the power of tests. We also discuss important issues that need to be taken into account when applying above tests to real arrival data: (1) data rounding, e.g., to seconds, (2) over-dispersion caused by combining data from multiple days with different arrival rate, and (3) choosing subintervals over which the rate varies too much.