Modeling teletraffic arrivals by a Poisson cluster process

In this paper we consider a Poisson cluster process N as a generating process for the arrivals of packets to a server. This process generalizes in a more realistic way the infinite source Poisson model which has been used for modeling teletraffic for a long time. At each Poisson point j, a flow of packets is initiated which is modeled as a partial iid sum process j + Pk i=1 Xji, k Kj , with a random limit Kj which is independent of (Xji) and the underlying Poisson points (j). We study the covariance structure of the increment process of N. In particular, the covariance function of the increment process is not summable if the right tail P(Kj > x) is regularly varying with index (1, 2), the distribution of the Xji's being irrelevant. This means that the increment process exhibits long-range dependence. If var(Kj) < long-range dependence is excluded. We study the asymptotic behavior of the process (N(t))t0 and give conditions on the distribution of Kj and Xji under which th...

• Type: Journal
• Year: 2006
• Where: QUESTA
• Authors: Gilles Faÿ, Bárbara González-Arévalo, Thomas Mikosch, Gennady Samorodnitsky
• Keywords: Increment Process, Poisson, Poisson Points, QUESTA 2006