Modeling IP traffic: joint characterization of packet arrivals and packet sizes using BMAPs

Abstract

This paper proposes a traffic model and a parameter fitting procedure that are capable of achieving accurate prediction of the queuing behavior for IP traffic exhibiting long-range dependence. The modeling process is a discrete-time batch Markovian arrival process (dBMAP) that jointly characterizes the packet arrival process and the packet size distribution. In the proposed dBMAP, packet arrivals occur according to a discrete-time Markov modulated Poisson process (dMMPP) and each arrival is characterized by a packet size with a general distribution that may depend on the phase of the dMMPP. The fitting procedure is designed to provide a close match of both the autocovariance and the marginal distribution of the packet arrival process, using a dMMPP; a packet size distribution is fitted individually to each state of the dMMPP. A major feature of the procedure is that the number of states of the fitted dBMAP is not fixed a priori; it is determined as part of the procedure itself. In this way, the procedure allows establishing a compromise between the accuracy of the fitting and the number of parameters, while maintaining a low computational complexity. We apply the inference procedure to several traffic traces exhibiting long-range dependence. Very good results were obtained since the fitted dBMAPs match closely the autocovariance, the marginal distribution and the queuing behavior of the measured traces. Our results also show that ignoring the packet size distribution and its correlation with the packet arrival process can lead to large errors in terms of queuing behavior.