End-to-end Analysis of Packet Inter-arrival Times of CBR Flows

In this paper, we develop a simple model for the end-to-end analysis of packet inter-arrival times of CBR flows in differentiated services networks. Our model illustrates that at high network utilization levels: (1) the packet inter-arrival times of CBR flows becomes heavy-tailed once the flows traverse through a large number of hops, and (2) the aggregate of such CBR flows is self-similar, long-rage dependent Fractional Brownian Motion (FBM). We validate our model through simulations and examine the region of applicability—with respect to network utilization, heterogeneity of CBR flows, and number of hops that a CBR flow traverses—of our model. We find that although the model predicts the behavior of CBR flows in the asymptotic case, for flows that contribute significant amount ( 10%) to the cumulative bit rate of the CBR aggregate, the observations yielded by the model hold at relatively low levels of network utilization (40-50%), small number of network hops (6-8), and moderate levels of heterogeneity in the packet sizes and bandwidth requirements of the CBR flows.