Scheduling policies for single-hop networks with heavy-tailed traffic

In the first part of the paper, we study the impact of scheduling, in a setting of parallel queues with a mix of heavy-tailed and light-tailed traffic. We analyze queue-length unaware scheduling policies, such as round-robin, randomized, and priority, and characterize their performance. We prove the queue-length instability of Max-Weight scheduling, in the presence of heavy-tailed traffic. Motivated by this, we analyze the performance of Max-Weight-α scheduling, and establish conditions on the α-parameters, under which the system is queue-length stable. We also introduce the Max-Weight-log policy, which provides performance guarantees, without any knowledge of the arriving traffic. In the second part of the paper, we extend the results on Max-Weight and Max-Weight-α scheduling to a single-hop network, with arbitrary topology and scheduling constraints.