Queuing theory with heavy tails and network traffic modeling
Yu Li · HAL (Le Centre pour la Communication Scientifique Directe) · 2018
Traditional queuing theory fails to model network traffic because of the different nature of Internet. To be more precise, Internet traffic exhibits heavy tail phenomenon , the inter arrival time is not exponential and the traffic volume is not poissonian. Most of network traffic models are empirically established in absence of mathematical description. In this paper we establish a queuing theory with heavy tails and present a mathematical model of network traffic. In this model traffic ratio is Pareto distributed and volume traffic has a shifted logarithm Erlang distribution, or more generally, a logarithm Gamma distribution. Furthermore, we derive the distribution of inter arrival times.