MDS coding is better than replication for job completion times

TL;DR

This paper compares replication and MDS coding strategies in multi-server systems, demonstrating that MDS coding achieves better job completion times with fewer redundant jobs by leveraging algebraic properties.

Contribution

It introduces an MDS coding approach for job distribution, showing it outperforms replication by requiring fewer redundant jobs for improved response times.

Findings

MDS coding reduces the number of redundant jobs needed compared to replication.

MDS coding achieves linear scalability in redundancy.

MDS coding improves response times in multi-server systems.

Abstract

In a multi-server system, how can one get better performance than random assignment of jobs to servers if queue-states cannot be queried by the dispatcher? A replication strategy has recently been proposed where $d$ copies of each arriving job are sent to servers chosen at random. The job's completion time is the first time that the service of any of its copies is complete. On completion, redundant copies of the job are removed from other queues so as not to overburden the system. For digital jobs, where the objects to be served can be algebraically manipulated, and for servers whose output is a linear function of their input, here we consider an alternate strategy: Maximum Distance Separable (MDS) codes. For every batch of $n$ digital jobs that arrive, $n+m$ linear combinations are created over the reals or a large finite field, and each coded job is sent to a random server. The batch completion time is the first time that any $n$ of the $n+m$ coded jobs are served, as the evaluation of $n$ original jobs can be recovered by Gaussian elimination. If redundant jobs can be removed from queues on batch completion, we establish that in order to get the improved response-time performance of sending $d$ copies of each of $n$ jobs via the replication strategy, with the MDS methodology it suffices to send $n+d$ jobs. That is, while replication is multiplicative, MDS is linear.