Generation of self-similar processes for simulation studies of telecommunication networks

It is generally accepted that self-similar processes may provide better models for teletraffic in modern telecommunication networks than Poisson processes. If stochastic self-similarity of teletraffic is not taken into account, it can lead to inaccurate conclusions about the performance of networks. Thus, an important requirement for conducting simulation studies of networks is the ability to generate long synthetic self-similar sequences of incremental processes, to transform them into interevent time intervals, and to do this accurately and quickly. A fast generator for count processes based on wavelets is described. Then a method for transformation of count processes into interevent processes proposed by Leroux and Hassan [1] and an alternative method, that is, inverting the empirical distribution directly, are studied. A case study is discussed to show how long sequences are needed in the steady-state simulation of queueing models with self-similar input processes. This is compared with simulation run lengths of the same queueing models fed by Poisson processes.