Scheduling in switched queueing networks with heavy-tailed trac

Abstract

We study scheduling problems arising in switched queueing networks, a class of stochastic systems that are often used to model data communication networks, such as uplinks and downlinks of cellular networks, networks of data switches, and ad hoc wireless networks. Motivated by empirical evidence of self-similarity and long-range dependence, the networks that we consider receive a mix of heavy-tailed and light-tailed trac. In this setting we evaluate the delay performance of the widely-studied class of Max-Weight scheduling policies. As performance metric we use the notion of delay stability, i.e., whether the steady-state expected delay in a queue is finite or not. Max-Weight policies are known to have excellent stability properties, and also to achieve good delay performance under light-tailed trac. Classical results from queueing theory imply that heavy-tailed queues are delay unstable under any policy, so we focus on the potential impact of heavy tails on light-tailed queues. The main insight derived from this thesis is that the Max-Weight policy performs poorly in the presence of heavy tails, whereas a suitably modified version of Max-Weight achieves much better overall performance. More specifically: (i) under the Max-Weight scheduling policy, any light-tailed queue that conflicts (i.e., cannot be served simultaneously) with a heavy-tailed queue is delay unstable; (ii) delay instability may propagate to light-tailed queues that do not conflict with heavy-tailed queues. The latter can happen through a "domino effect," if a light-tailed queue conflicts with a queue that has become delay unstable because it conflicts with a heavy-tailed queue. The extent of this phenomenon depends on the arrival rates; (iii) under the parameterized Max-Weight- scheduling policy, all light-tailed queues are delay stable provided the -parameters are chosen suitably. On the methodological side, we show how fluid approximations can be combined with renewal theory in order to prove delay instability results. Moreover, we show how fluid approximations can be combined with stochastic Lyapunov theory in order to prove delay stability results. Finally, we identify a class of piecewise linear Lyapunov functions that are suitable for obtaining exponential bounds on queue-length asymptotics, in the presence of heavy-tailed trac.