Heavy-Traffic Analysis of Sojourn Time under the Foreground-Background Scheduling Policy

TL;DR

This paper analyzes the steady-state distribution and mean growth rate of job sojourn times in an M/GI/1 queue under foreground-background scheduling in heavy traffic, using extreme value theory assumptions.

Contribution

It provides new theoretical results on the limiting distribution and mean growth rate of sojourn times in heavy traffic for foreground-background scheduling.

Findings

Derived the limiting distribution of sojourn time in heavy traffic.

Established the growth rate of the mean sojourn time.

Utilized extreme value theory assumptions in the analysis.

Abstract

We consider the steady-state distribution of the sojourn time of a job entering an M/GI/1 queue with the foreground-background scheduling policy in heavy traffic. The growth rate of its mean, as well as the limiting distribution, are derived under broad conditions. Assumptions commonly used in extreme value theory play a key role in both the analysis and the results.