End-to-end Model for a Flow in the Internet

We develop an end-to-end model for packet inter-arrival times of flows in the Internet. Our model illustrates that under asymptotic conditions of high network utilization, (1) packet inter-arrival times of flows become heavy-tailed after they traverse a large number of hops, and (2) the aggregate of such flows is a long-range dependent self-similar process. We validate our model through extensive simulations and derive the region of applicability—with respect to non-asymptotic settings of network utilization, heterogeneity in traffic composition, and number of hops that a flow traverses—of our model. We find that for flows that contribute significant amount ( 10%) to the cumulative bit rate of the aggregate, the observations yielded by the model hold at relatively low levels of network utilization (30-40%), small number of network hops (4-6), and moderate levels of heterogeneity in packet sizes and bandwidth requirements of flows.