On scheduling policies in the presence of heavy-tailed interference

We study the scheduling problem of an asymmetric queueing system in the presence of heavy-tailed interference. The system consists of two parallel queues, competing for one server. One of the queues experiences heavy-tailed OFF periods during the ON/OFF renewal channel process, caused by a heavy-tailed interference to its service link, while the other experiences light-tailed interference. We analyze the throughput characteristic and the expected queue length performance under the priority and max-weight scheduling policies. We show that the expected queue length of the heavy queue cannot be maintained finite even under the most favorable priority policy. The finiteness of the light queue's expected queue length, however, can be guaranteed with service priority, but the system is no longer throughput optimal. We further show that the max-weight scheduling policy does not provide any benefit to the light queue in terms of the steady-state queue length behavior, though the system is always throughput optimal.