Markov renewal models for traffic exhibiting self-similar behaviour

Observations of self-similar behaviour in network traffic have reinforced the notion that Poisson assumptions might facilitate analysis but do not always agree with real world phenomenon. In particular, the traffic processes for these networks are locally bursty while exhibiting long range dependence. We consider three models for network traffic which attempt to capture this behaviour. We are interested in showing how certain properties exhibited in self-similar processes are also observed in classical queueing models. First is the Markov modulated Poisson process which intuitively describes bursty local behaviour but lacks extreme long term correlation. Second, we consider a renewal model for traffic processes in which the interrenewal times have a regular varying distribution. Such renewal models exhibit long range dependence properties. Finally, we consider a Markov renewal process which is a hybrid of the first two models. The benefits of the hybrid include fitting local self-similar behaviour while maintaining long range dependence.