Optimal Heavy-Traffic Queue Length Scaling in an Incompletely Saturated Switch

TL;DR

This paper analyzes the MaxWeight scheduling algorithm's performance in switch networks with partial port saturation, demonstrating its optimal queue length scaling even when ports saturate at different rates.

Contribution

It extends previous results by proving optimal heavy-traffic queue length scaling for MaxWeight in incompletely saturated switches with heterogeneous port saturation rates.

Findings

MaxWeight achieves optimal queue length scaling in incomplete saturation scenarios.

The drift technique effectively analyzes complex switch configurations.

Results apply to Internet routers and data center networks.

Abstract

We consider an input queued switch operating under the MaxWeight scheduling algorithm. This system is interesting to study because it is a model for Internet routers and data center networks. Recently, it was shown that the MaxWeight algorithm has optimal heavy-traffic queue length scaling when all ports are uniformly saturated. Here we consider the case when an arbitrary number of ports are saturated (which we call the incompletely saturated case), and each port is allowed to saturate at a different rate. We use a recently developed drift technique to show that the heavy-traffic queue length under the MaxWeight scheduling algorithm has optimal scaling with respect to the switch size even in these cases.