Throughput Optimal Scheduling Over Time-Varying Channels in the Presence of Heavy-Tailed Traffic

We study the problem of scheduling over timevarying links in a network that serves both heavy-tailed and light-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic (the heavy queue), and the other receives light-tailed traffic (the light queue). The queues are connected to the server through time-varying ON/OFF links, which model fading wireless channels. We first show that the policy that gives complete priority to the light-tailed traffic guarantees the best possible tail behavior of both queue backlog distributions, whenever the queues are stable. However, the priority policy is not throughput maximizing, and can cause undesirable instability effects in the heavy queue. Next, we study the class of throughput optimal max-weight-alpha scheduling policies. We discover a threshold phenomenon, and show that the steadystate light queue backlog distribution is heavy-tailed for arrival rates above a threshold value, and light-tailed otherwise. We also obtain the exact tail coefficient of the light queue backlog distribution under max-weight-alpha scheduling. Finally, we study a log-max-weight scheduling policy, which is throughput optimal, and ensures that the light queue backlog distribution is light-tailed.