Acceptance-Rejection Methods for Generating Random Variates from Matrix Exponential Distributions and Rational Arrival Processes

Abstract

Stochastic models based on matrix exponential structures, like matrix exponential distributions and rational arrival processes, have gained popularity in analytical models recently. However the application of these models in simulation based evaluations is not as widespread yet. One of the possible reasons is the lack of efficient random variates generation methods. In this paper we propose methods for efficient random variates generation for matrix exponential stochastic models based on appropriate representations of the models.

Matching marginal moments and lag autocorrelations with MAPs

“…They can be efficiently applied in several fields of performance evaluation of various systems. Once the traffic is represented by a MAP, it is easy to generate random samples from it ( [11], [13]), which is beneficial in simulations and measurement based performance analysis. It is also well known that queueing models where the arrival and/or service process are given by MAPs can be analyzed in a numerically efficient way by matrix geometric methods [14].…”