# Coflow Scheduling in Input-Queued Switches: Optimal Delay Scaling and Algorithms

## TL;DR

This paper investigates optimal coflow-level delay in input-queued switches, deriving lower bounds, analyzing existing policies, and proposing a new coflow-aware batching policy that achieves optimal delay scaling.

## Contribution

It introduces a throughput-optimal coflow scheduling policy that achieves the best delay scaling, filling a gap in existing coflow-agnostic approaches.

## Key findings

- Lower bounds on coflow delay depend on flow size variability
- Existing policies do not achieve optimal delay scaling
- The proposed CAB policy achieves optimal delay scaling

## Abstract

A coflow is a collection of parallel flows belonging to the same job. It has the all-or-nothing property: a coflow is not complete until the completion of all its constituent flows. In this paper, we focus on optimizing \emph{coflow-level delay}, i.e., the time to complete all the flows in a coflow, in the context of an $N\times N$ input-queued switch. In particular, we develop a throughput-optimal scheduling policy that achieves the best scaling of coflow-level delay as $N\rightarrow\infty$. We first derive lower bounds on the coflow-level delay that can be achieved by any scheduling policy. It is observed that these lower bounds critically depend on the variability of flow sizes. Then we analyze the coflow-level performance of some existing coflow-agnostic scheduling policies and show that none of them achieves provably optimal performance with respect to coflow-level delay. Finally, we propose the Coflow-Aware Batching (CAB) policy which achieves the optimal scaling of coflow-level delay under some mild assumptions.