Measurement-based Traac Modeling: Capturing Important Statistics

Measurement-based traac characterization has come to acquire a great deal of importance in high-speed networks. In this paper, we segregate the traac behaviour into the macrody-namics and microdynamics depending on the time scales at which the process is observed. We examine the validity of the Markovian assumption which is commonly made for modeling the macrodynamics of correlated traac in network analysis. A fundamental issue in traac modeling is whether the Markovian assumption has any signiicance on the queueing solutions. Our study compares the queueing solutions obtained using traac models with very diierent underlying structure viz. Markovian vs non-Markovian which are identical only in their second-order and steady-state statistics. Our study suggests that higher-order traac statistics are generally unimportant to queueing solutions. In essence, for a certain class of stationary stochastic processes, the Markovian assumption can be made in traac modeling to simplify the queueing analysis, as long as the important statistics are captured. We also investigate the eeect of the micro-dynamics of the traac on the queueing performance. The microdynamics are associated with the cell interarrival times and bulk arrivals. We show that the second-order statistics of the microdynamics are well captured by white noise in the arrival process power spectrum, which can have a signiicant impact on the queueing performance. A new modeling technique is introduced in which the microdynamics are incorporated into the correlation behaviour of traac to signiicantly simplify the queueing analysis. We demonstrate this technique for several rate traces. Comprehensive numerical and simulation examples are provided to verify this simple eeective modeling technique.