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NHPP process associated with heavy tail interarrivals in network traffic

Packet arrival processes for data network are not consistent with Poisson processes. It has been established that arrival process is self-similar and the number of TCP connections initiated by a user session is heavy-tailed. The heavy tail or long tail distributions yield better model for data packet arrival models than exponential models. In particular it is observed that the Weibull, Pareto and Lognormal distribution give a good fit for the interarrival times for Web applications, LAN, MAN, WAN etc. We show that for Weibull interarrivals, the counting process formed is a Duane process, a less known counting process. In this paper we show that if packet interarrivals are modeled according to Lognormal distribution which is a example of a class of heavy-tail distributions, than the corresponding renewal process is not a Poisson process. We give a new result of approximate mean arrival rate of counting process for Lognormal interarrivals. We show that packet arrival process of heavy-tailed distributed interarrivals form Non Homogeneous Poisson Process and thus mean packet arrival rate is not constant but it is time varying.