On scheduling algorithms robust to heavy-tailed traffic

Adaptive CSMA algorithms have attracted considerable attention, due to their throughput optimality, utility maximizing properties, and amenability to simple distributed implementation. In this paper, we investigate the impact of heavy-tailed traffic on the performance of a queue length based adaptive CSMA algorithm. Specifically, we consider two conflicting links that share a channel using adaptive CSMA. One of the links serves heavy-tailed traffic, while the other link serves light-tailed traffic. Our main contribution is in demonstrating a threshold phenomenon in the relationship between the arrival rates and the queue backlog distributions. In particular, we show that when the arrival rate of the light-tailed traffic is less than a threshold value, the light-tailed traffic experiences a light-tailed queue backlog at steady state, whereas for arrival rates above the same threshold, the light-tailed traffic experiences a heavy-tailed queue backlog. Comparing this result to a corresponding result for max-weight scheduling [8], we conclude that adaptive CSMA is potentially more robust to bursty traffic, compared to max-weight scheduling.