Faster Data-access in Large-scale Systems: Network-scale Latency Analysis under General Service-time Distributions

TL;DR

This paper analyzes and compares the mean latency of split-and-replicate and erasure-coded cloud storage systems under various service time distributions, proposing a load-balancing scheme and providing bounds and numerical validation.

Contribution

It introduces a novel load-balancing scheme for large-scale storage, compares coded and replicated systems, and provides latency bounds under general service time distributions.

Findings

Coded systems with high redundancy have similar or lower latency than split-and-replicate systems.

Coded systems outperform unsplit-replicated systems by at least 20%.

Latency bounds are derived for low redundancy erasure-coded systems under exponential service times.

Abstract

In cloud storage systems with a large number of servers, files are typically not stored in single servers. Instead, they are split, replicated (to ensure reliability in case of server malfunction) and stored in different servers. We analyze the mean latency of such a split-and-replicate cloud storage system under general sub-exponential service time. We present a novel scheduling scheme that utilizes the load-balancing policy of the \textit{power of $d$ $(\geq 2)$} choices. An alternative to split-and-replicate is to use erasure-codes, and recently, it has been observed that they can reduce latency in data access (see \cite{longbo_delay} for details). We argue that under high redundancy (integer redundancy factor strictly greater than or equal to 2) regime, the mean latency of a coded system is upper bounded by that of a split-and-replicate system (with same replication factor) and the gap between these two is small. We validate this claim numerically under different service distributions such as exponential, shift plus exponential and the heavy-tailed Weibull distribution and compare the mean latency to that of an unsplit-replicated system. We observe that the coded system outperforms the unsplit-replication system by at least $20\%$. Furthermore, we consider the mean latency for an erasure coded system with low redundancy (fractional redundancy factor between 1 and 2), a scenario which is more pragmatic, given the storage constraints (\cite{rashmi_thesis}). However under this regime, we restrict ourselves to the special case of exponential service time distribution and use the randomized load balancing policy namely \textit{batch-sampling}. We obtain an upper bound on mean delay that depends on the order statistics of the queue lengths, which, we further smooth out via a discrete to continuous approximation.