Burstiness in Broadband Integrated Networks

Since broadband integrated networks have to cope with a wide range of bit rates, the notion of burstiness which expresses the irregularity of a ow, has been recognized as a vital question for such networks. In burstiness characterization encountered in the literature, special attention is given to the squared coe cient of variation of interarrival time (Cv2) in a cell arrival process. In order to observe the impact of a bursty ow on a queue, we introduce in this paper a new class of arrival process, the n-stage Markov Modulated Bernoulli Process, MMBPn , for short, and its peculiar case, the n-stage Hyper-Bernoulli process, denoted by HBPn. We numerically solve the MMBPn=D=1=K and we compute in particular the rejection probability and the mean waiting time. For that purpose, a relation between the stationary queue length distribution and arrival time distribution is established. This relation adapts the GASTA equality to the arrival process under consideration. We then discuss the relevance of Cv2 for burstiness characterization through an example : the HBP2=D=1=K queue. We show that Cv becomes signi cant only when local overload occurs, i.e., when the arrival rate is momentarily greater than the server rate. The results are then applied to two basic ATM problems : tra c characterization and bu er dimensioning using bursty inputs.