Estimating And Simulating Poisson Processes Having Trends Or Multiple Periodicities

this paper we propose methods for estimating and simulating such arrival processes. The scope of this paper encompasses three main objectives. The first objective is to x1. Introduction 2 introduce a time-dependent counting-process model that is sufficiently flexible to represent a wide variety of nonstationary arrival streams arising in large-scale simulation experiments. In particular, we seek a model that accommodates both long-term trends and multiply periodic behavior. The second objective is to formulate and implement a methodology for using our input model in simulation experiments. More specifically, we present methods for estimating model parameters from an observed series of event times and for simulating the arrival process corresponding to a given set of model parameters. The third objective is to carry out and summarize a comprehensive experimental performance evaluation of our estimation and simulation procedures. The proposed arrival process is a nonhomogeneous Poisson process (NHPP) with an Exponential-Polynomial-Trigonometric rate function having Multiple Periodicities---that is, a rate function of the class we shall label EPTMP. Using an exponential rate function is a convenient means of ensuring that the instantaneous arrival rate is always positive. If the arrival rate includes a long-term evolutionary trend, then this trend is naturally represented in the exponent of the rate function by a polynomial component of appropriate degree. Finally if the arrival rate includes some periodic effects, then each of these effects is naturally represented in the exponent of the rate function by a trigonometric component with the appropriate oscillation frequency, oscillation amplitude, and phase delay. In Section 2 of this paper we introduce our NHPP model and..