Balanced Nonadaptive Redundancy Scheduling

TL;DR

This paper analyzes redundancy scheduling in distributed systems, introducing a block design-based policy that outperforms traditional methods by reducing waiting times through improved graph expansion properties.

Contribution

It proposes a novel block design-based scheduling policy and provides an analytical framework using combinatorics and graph theory to evaluate its performance.

Findings

Block design scheduling reduces average waiting time by up to 25% compared to random.

The proposed policy outperforms round-robin, halving waiting times.

Graph expansion properties explain the improved performance.

Abstract

Distributed computing systems implement redundancy to reduce the job completion time and variability. Despite a large body of work about computing redundancy, the analytical performance evaluation of redundancy techniques in queuing systems is still an open problem. In this work, we take one step forward to analyze the performance of scheduling policies in systems with redundancy. In particular, we study the pattern of shared servers among replicas of different jobs. To this end, we employ combinatorics and graph theory and define and derive performance indicators using the statistics of the overlaps. We consider two classical nonadaptive scheduling policies: random and round-robin. We then propose a scheduling policy based on combinatorial block designs. Compared with conventional scheduling, the proposed scheduling improves the performance indicators. We study the expansion property of the graphs associated with round-robin and block design-based policies. It turns out the superior performance of the block design-based policy results from better expansion properties of its associated graph. As indicated by the performance indicators, the simulation results show that the block design-based policy outperforms random and round-robin scheduling in different scenarios. Specifically, it reduces the average waiting time in the queue to up to 25% compared to the random policy and up to 100% compared to the round-robin policy.