Modeling and simulating non-stationary, non-Poisson arrival processes
Abstract: 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 which is either more or less variable than Poisson, and may exhibit dependence. We extend techniques that transform a stationary Poisson arrival process into a nonstationary Poisson arrival process by transforming a stationary arrival process into a nonstationary, non-Poisson (NSNP) arrival process. We show that the desired arrival rate is achieved, and that certain variability and dependence properties of the base process are passed on to the transformed process. We also provide techniques for specifying the base process when presented with characteristics of, or data from, an arrival process and illustrate them by modeling e-mail arrival data.
(Joint work with Ira Gerhardt, Manhattan College).