Long Term Dependences and Heavy Tails in Traffics and Queues Generated by Memoriless on/off Sources in Series

Abstract : This repport presents the analytical study of a surprising case where a denumerable set of independent and memoriless on/off sources in series creates a traffic with long term dependences. We use Mellin transform to characterize the asymptotic behavior of those dependences. We use similar tools to analyse the queue size of a server subject to these sources in series. This architecture roughly models a shared network like internet. We show that the queue size distribution has a heavy tail. These results agree with the recent experimental datas collected on Web activity.