Stability for Two-class Multiserver-job Systems

TL;DR

This paper derives the first analytical stability region for a two-class, non-dropping multiserver-job system with FCFS scheduling, revealing insights into server wastage and the effects of service rates.

Contribution

It provides the first closed-form stability condition for FCFS multiserver-job systems with classes having distinct service distributions.

Findings

Identifies significant server wastage during queueing.

Shows nonmonotonic effects of service rates on wastage.

Provides analytical insights into system stability and efficiency.

Abstract

Multiserver-job systems, where jobs require concurrent service at many servers, occur widely in practice. Much is known in the dropping setting, where jobs are immediately discarded if they require more servers than are currently available. However, very little is known in the more practical setting where jobs queue instead. In this paper, we derive a closed-form analytical expression for the stability region of a two-class (non-dropping) multiserver-job system where each class of jobs requires a distinct number of servers and requires a distinct exponential distribution of service time, and jobs are served in first-come-first-served (FCFS) order. This is the first result of any kind for an FCFS multiserver-job system where the classes have distinct service distributions. Our work is based on a technique that leverages the idea of a "saturated" system, in which an unlimited number of jobs are always available. Our analytical formula provides insight into the behavior of FCFS multiserver-job systems, highlighting the huge wastage (idle servers while jobs are in the queue) that can occur, as well as the nonmonotonic effects of the service rates on wastage.