Traffic modeling: matching the power spectrum and distribution

Abstract

This paper examines the validity of the Markovian assumption which is commonly made for modeling of correlated traffic in network analyses. Indeed, real traffic is likely to be nonMarkovian. A fundamental issue in traffic modeling is whether the Markovian assumption has any significance on the queueing solutions. Our study compares the queueing solutions obtained using traffic models with very different underlying structure viz. Markovian vs. nonMarkovian. The Markovian model is represented by a circulant modulated rate process (CMRP). The nonMarkovian model is represented by an ARMA process with or without nonlinear modifications. The two models can be made identical in their second-order and steady-state statistics, but with significantly different higher-order statistics. Comprehensive studies with different rational power spectra and distributions show that the queueing results using these two traffic models match very closely. Our study suggests that higher-order traffic statistics are generally unimportant to queueing solutions. In essence, for a certain class of stationary stochastic processes, the Markovian assumption can be made in traffic modeling to simplify the queueing analysis, as long as the important statistics are captured.