Internet Traffic Modeling: Markovian Approach to Self-Similar Traffic and Prediction of Loss Probability for Finite Queues

It has been reported that IP packet traffic exhibits the self-similar nature and causes the degradation of network performance. Therefore it is crucial for the appropriate buffer design of routers and switches to predict the queueing behavior with self-similar input. It is well known that the fitting methods based on the second-order statistics of counts for the arrival process are not sufficient for predicting the performance of the queueing system with self-similar input. However recent studies have revealed that the loss probability of finite queuing system can be well approximated by the Markovian input models. This paper studies the time-scale impact on the loss probability of MMPP/D/1/K system where the MMPP is generated so as to match the variance of the self-similar process over specified time-scales. We investigate the loss probability in terms of system size, Hurst parameters and time-scales. We also compare the loss probability of resulting MMPP/D/1/K with simulation. Numerical results show that the loss probability of MMPP/D/1/K are not significantly affected by time-scale and that the loss probability is well approximated with resulting MMPP/D/1/K. key words: internet traÆc modeling, self-similarity, tting, MMPP/D/1/K, loss probability