Delay analysis of a single server queue with Poisson cluster arrival process arising in ATM networks

Poisson cluster processes (PCPs) can be used to model arrival processes in ATM (asynchronous transfer mode) networks. These processes are bursty, and there is a strong correlation between the successive arrivals. Different approximation methods which capture the burstiness and the correlation between the successive events on the average waiting time for the PCP/D/1 queue are examined. The notion of effective batchiness is introduced, and its properties are given. In particular, it is shown that, in light traffic, the correlation between arrivals has little effect on the average wait, and it approaches to that of the classical M/D/1 queue, i.e. a minimum effective batchiness of 1. In heavy traffic, the average wait approaches to that of the M/sup x//D/1 queue, i.e. a batch Poisson arrival which results in the maximum effective batchiness given in terms of the first two moments of the cluster size.<>