Timely Distributed Computation with Stragglers

TL;DR

This paper analyzes the age of information in a distributed computation system with stragglers, comparing uncoded and various coded schemes, and finds that MM-MDS coding asymptotically outperforms others in minimizing age.

Contribution

It introduces a comprehensive analysis of age performance for different coding schemes in distributed systems with stragglers, identifying optimal codes for age minimization.

Findings

MM-MDS coded scheme outperforms others asymptotically

Characterization of optimal codes for minimal average age

Analysis under exponential transmission delays and shifted exponential computation times

Abstract

We consider a status update system in which the update packets need to be processed to extract the embedded useful information. The source node sends the acquired information to a computation unit (CU) which consists of a master node and $n$ worker nodes. The master node distributes the received computation task to the worker nodes. Upon computation, the master node aggregates the results and sends them back to the source node to keep it \emph{updated}. We investigate the age performance of uncoded and coded (repetition coded, MDS coded, and multi-message MDS (MM-MDS) coded) schemes in the presence of stragglers under i.i.d.~exponential transmission delays and i.i.d~shifted exponential computation times. We show that asymptotically MM-MDS coded scheme outperforms the other schemes. Furthermore, we characterize the optimal codes such that the average age is minimized.