Delay Stability of Back-Pressure Policies in the Presence of Heavy-Tailed Traffic

We study multihop networks with flow-scheduling constraints, no constraints on simultaneous activation of different links, potentially multiple source-destination routes, and a mix of heavy-tailed and light-tailed traffic. In this setting, we analyze the delay performance of the widely studied class of Back-Pressure scheduling policies, known for their throughput optimality property, using as a performance criterion the notion of delay stability, i. e., whether the expected end-to-end delay in steady state is finite. Our analysis highlights the significance of "bottleneck links," i. e., links that are allowed to serve the source queues of heavy-tailed flows. The main idea is that traffic that has to pass through bottleneck links experiences large delays under Back-Pressure. By means of simple examples, we provide insights into how the network topology, the routing constraints, and the link capacities may facilitate or hinder the ability of light-tailed flows to avoid bottlenecks. Our delay-stability analysis is greatly simplified by the use of fluid approximations, allowing us to derive analytical results that would have been hard to obtain through purely stochastic arguments. Finally, we show how to achieve the best performance with respect to the delay stability criterion, by using a parameterized version of the Back-Pressure policy.