Zero Queueing for Multi-Server Jobs

TL;DR

This paper studies multi-server job queueing systems in large-scale cloud environments, deriving conditions for zero queueing and introducing a novel Lyapunov drift analysis method applicable to complex queueing models.

Contribution

It provides the first stability and queueing probability results for multi-server jobs under large-scale regimes, with a new Lyapunov drift technique.

Findings

Derived conditions for zero queueing in multi-server systems.

Analyzed stability and queueing probabilities in large-scale regimes.

Introduced a novel Lyapunov drift analysis method.

Abstract

Cloud computing today is dominated by multi-server jobs. These are jobs that request multiple servers simultaneously and hold onto all of these servers for the duration of the job. Multi-server jobs add a lot of complexity to the traditional one-job-per-server model: an arrival might not "fit" into the available servers and might have to queue, blocking later arrivals and leaving servers idle. From a queueing perspective, almost nothing is understood about multi-server job queueing systems; even understanding the exact stability region is a very hard problem. In this paper, we investigate a multi-server job queueing model under scaling regimes where the number of servers in the system grows. Specifically, we consider a system with multiple classes of jobs, where jobs from different classes can request different numbers of servers and have different service time distributions, and jobs are served in first-come-first-served order. The multi-server job model opens up new scaling regimes where both the number of servers that a job needs and the system load scale with the total number of servers. Within these scaling regimes, we derive the first results on stability, queueing probability, and the transient analysis of the number of jobs in the system for each class. In particular we derive sufficient conditions for zero queueing. Our analysis introduces a novel way of extracting information from the Lyapunov drift, which can be applicable to a broader scope of problems in queueing systems.