Randomized longest-queue-first scheduling for large-scale buffered systems

TL;DR

This paper introduces diffusion approximations for large-scale parallel queues using a randomized longest-queue-first scheduling algorithm, demonstrating accurate performance predictions and computational advantages through new mean-field limit theorems.

Contribution

It develops the first diffusion approximations for queueing systems in the large-buffer mean-field regime, allowing analysis of performance and complexity trade-offs.

Findings

Diffusion approximations are accurate for moderate system sizes.

The randomized algorithm emulates the longest-queue-first with less computational effort.

Trade-offs between performance and complexity are characterized.

Abstract

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing the number of sampled buffers $d=d(n)$ to depend on the number of buffers $n$, which yields an asymptotic `decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of $n$ and $d(n)$. To our knowledge, we are the first to derive diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized longest-queue-first algorithm emulates the longest-queue-first algorithm, yet is computationally more attractive. The analysis of the system performance as a function of $d(n)$ is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized longest-queue-first scheduling algorithm.