Heavy Traffic Queue Length Behavior in Switches with Reconfiguration Delay

TL;DR

This paper analyzes the queue length behavior of optical switches with reconfiguration delays under the Adaptive MaxWeight policy, providing delay bounds and asymptotic queue length estimates in heavy traffic conditions.

Contribution

It introduces a weak state space collapse analysis for Adaptive MaxWeight with reconfiguration delay and derives tight queue length bounds in heavy traffic.

Findings

Weak state space collapse observed in steady-state.

Derived delay bounds depend on expected schedule duration.

Asymptotically tight queue length bounds in heavy traffic.

Abstract

Optical switches have been drawing attention due to their large data bandwidth and low power consumption. However, scheduling policies need to account for the schedule reconfiguration delay of optical switches to achieve good performance. The Adaptive MaxWeight policy achieves optimal throughput for switches with nonzero reconfiguration delay, and has been shown in simulation to have good delay performance. In this paper, we analyze the queue length behavior of a switch with nonzero reconfiguration delay operating under the Adaptive MaxWeight. We first show that the Adaptive MaxWeight policy exhibits a weak state space collapse behavior in steady-state, which could be viewed as an inheritance of the MaxWeight policy in a switch with zero reconfiguration delay. We then use the weak state space collapse result to obtain a steady state delay bound under the Adaptive MaxWeight algorithm in heavy traffic by applying a recently developed drift technique. The resulting delay bound is dependent on the expected schedule duration. We then derive the relation between the expected schedule duration and the steady state queue length through drift analysis, and obtain asymptotically tight queue length bounds in the heavy traffic regime.