On the Validity of Some Markovian Models in ATM Tra c Modelling

Markov modulated models are often used to model tra c in a network. How well the processes really capture the essentials of real tra c is less known. We review some of these models and apply a number of associated tting methods to an Ethernet tra c in di erent timescales. The tted models are then used as input to a bu er where bu er occupancies are used as a measure of the goodness of the models. Also, the ability of a tting method to correctly model the tra c when applied to tra c generated from a model that the tting method was intended for is examined. 1 Markovian Models for ATM Tra c 1.1 Markovian Models Models of bursty tra c are frequently used to dimension bu ers in ATM networks. Among the more common models we nd the Markov modulated Poisson processes (MMPPs) and Markov modulated Bernoulli processes (MMBPs). The two processes are doubly stochastic point processes where the rate of a Poisson (Bernoulli) process is governed by an underlying Markov chain in continuous (discrete) time. Arrivals and state transitions of the modulating chain are statistically independent. The processes are fully characterised by the number s of states in the modulating chain, the transition rates (probabilities) qu;v, and arrival rates (probabilities) ru, u; v 2 f1; : : : ; sg. The reason why these models are frequently employed is probably because of their ability to match various tra c statistics and their mathematical tractability. However, little is known about their actual relevance when it comes to not only producing a tra c that is generally bursty, but producing a tra c that is essentially \equivalent" to real tra c.