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Transforming Renewal Processes for Simulation of Nonstationary Arrival Processes

Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208
i-gerhardt{at}northwestern.edu
nelsonb{at}northwestern.edu

Simulation models of real-life systems often assume stationary (homogeneous) Poisson arrivals. Therefore, when nonstationary arrival processes are required, it is natural to assume Poisson arrivals with a time-varying arrival rate. For many systems, however, this provides an inaccurate representation of the arrival process that is either more or less variable than Poisson. In this paper we extend techniques that transform a stationary Poisson arrival process into a nonstationary Poisson arrival process (NSPP) by transforming a stationary renewal process into a nonstationary, non-Poisson (NSNP) arrival process. We show that the desired arrival rate is achieved and that when the renewal base process is either more or less variable than Poisson, then the NSNP process is also more or less variable, respectively, than an NSPP. We also propose techniques for specifying the renewal base process when presented properties of, or data from, an arrival process and illustrate them by modeling real arrival data.

Key words: arrival counting process; phase-type distribution; nonstationary Poisson process
History: received July 2008; revised October 2008; accepted November 2008.