Large-scale parallel server system with multi-component jobs

TL;DR

This paper analyzes large-scale parallel server systems with multi-component jobs, proving asymptotic independence of server workloads and encompassing models like redundancy queues using mean-field techniques.

Contribution

It introduces a broad model for parallel server systems with multi-component jobs, establishing asymptotic independence and including popular redundancy queue models as special cases.

Findings

Proves steady-state workload independence as system size grows

Includes models like cancel-on-start and cancel-on-completion redundancy

Uses mean-field limits based on monotonicity and work conservation

Abstract

A broad class of parallel server systems is considered, for which we prove the steady-state asymptotic independence of server workloads, as the number of servers goes to infinity, while the system load remains sub-critical. Arriving jobs consist of multiple components. There are multiple job classes, and each class may be of one of two types, which determines the rule according to which the job components add workloads to the servers. The model is broad enough to include as special cases some popular queueing models with redundancy, such as cancel-on-start and cancel-on-completion redundancy. Our analysis uses mean-field process representation and the corresponding mean-field limits. In essence, our approach relies almost exclusively on three fundamental properties of the model: (a) monotonicity, (b) work conservation, (c) the property that, on average, "new arriving workload prefers to go to servers with lower workloads."