Statistical analysis of the traffic generated by the superposition of N independent interrupted poisson processes

Abstract

This paper concentrates on the statistical characterization of the traffic generated by the superposition of N independent and homogeneous Interrupted Poisson processes. The superposed traffic is considered here as a candidate for modeling bursty and correlated arrival processes, such is the case for the aggregate packet arrival process at an ATM multiplexer. More precisely, we approximate the traffic generated by N ^r multimedia sources by the superposition of homogeneous interrupted Poisson processes, whose number, N, as well as their three parameters can be estimated using some statistical matching methods. In this paper, the main part of our analysis focuses on the appropriateness of the proposed model, from a statistical point of view through the theoretical investigation of its variability and correlation behaviors. In particular, we pay a special attention to a statistical problem that has not been yet investigated properly, namely the theoretical investigation of the dependence among the successive packet inter-arrival times in the superposition process. Based on some numerical examples, our analysis shows that as we increase the number of component processes, the burstiness of the superposition traffic decreases while the correlation among the packet inter-arrival times increases. We will also highlight a statistical matching method that can be applied to estimate the parameters of the proposed model.