Queue Length Asymptotics for Generalized Max-Weight Scheduling in the presence of Heavy-Tailed Traffic

TL;DR

This paper analyzes the asymptotic behavior of queue lengths under generalized max-weight scheduling with heavy-tailed traffic, revealing worst-case tail behavior and proposing a new policy with better tail decay.

Contribution

It provides an exact asymptotic characterization of queue length tails under max-weight-alpha policies and introduces the log-max-weight policy with improved tail decay.

Findings

Max-weight-alpha leads to heavy, power-law tails for light queues.

Log-max-weight policy achieves exponential tail decay.

Max-weight scheduling can be worst-case for queue tail behavior.

Abstract

We investigate the asymptotic behavior of the steady-state queue length distribution under generalized max-weight scheduling in the presence of heavy-tailed traffic. We consider a system consisting of two parallel queues, served by a single server. One of the queues receives heavy-tailed traffic, and the other receives light-tailed traffic. We study the class of throughput optimal max-weight-alpha scheduling policies, and derive an exact asymptotic characterization of the steady-state queue length distributions. In particular, we show that the tail of the light queue distribution is heavier than a power-law curve, whose tail coefficient we obtain explicitly. Our asymptotic characterization also contains an intuitively surprising result - the celebrated max-weight scheduling policy leads to the worst possible tail of the light queue distribution, among all non-idling policies. Motivated by the above negative result regarding the max-weight-alpha policy, we analyze a log-max-weight (LMW) scheduling policy. We show that the LMW policy guarantees an exponentially decaying light queue tail, while still being throughput optimal.