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

Abstract

Abstract-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.

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

“…Specifically, it was shown in [12] that when the heavy-tailed traffic has an infinite variance, the light-tailed traffic experiences an infinite expected delay under max-weight scheduling, due to competition from the heavytailed traffic. The authors also studied a more general max-weight-α policy, wherein by increasing the preference afforded to the light queue, it is possible to make the expected delay of the light-tailed traffic finite.…”

“…To our knowledge, [12] was the first paper to study the performance of the max-weight family of scheduling policies, when heavy-tailed and light-tailed traffic compete for service. Specifically, it was shown in [12] that when the heavy-tailed traffic has an infinite variance, the light-tailed traffic experiences an infinite expected delay under max-weight scheduling, due to competition from the heavytailed traffic.…”

When heavy-tailed and light-tailed flows compete: The response time tail under generalized max-weight scheduling

“…The first steps towards filling this gap have been provided by the recent work of Markakis et al in [15] and Jagannathan et al [16], [17], which analyze a scenario where heavy-tailed and light-tailed flows interact through a generalized max-weight policy. Our present paper builds on these papers; in particular, our model is borrowed from [16].…”

“…Our goal now is to understand how max-weight scheduling and its variants perform under such an extreme form of asymmetry. We begin by considering the most well studied subclass of generalized max-weight policies: max-weight-α policies [15], which includes the classical maxweight policy as a special case. We then consider the class of log-max-weight policies.…”

“…Max-weight-α scheduling: The max-weight-α policy [15], [17] is a generalization of the classical max-weight policy, and is characterized by two positive parameters α L and α H . In each slot, the max-weight-α policy serves the queue that wins the comparison…”