Heavy traffic analysis for EDF queues with reneging

TL;DR

This paper analyzes the heavy-traffic behavior of an EDF queue with reneging, showing how the system's reneged work fraction can be approximated and minimized, with results validated through simulations.

Contribution

It provides a measure-valued process description and heavy-traffic limit analysis for EDF queues with reneging, extending previous work to include reneging behavior.

Findings

Reneged work fraction is minimized by EDF policy.

Heavy traffic limit is a doubly reflected Brownian motion.

Explicit formulas compare reneged and late work fractions.

Abstract

This paper presents a heavy-traffic analysis of the behavior of a single-server queue under an Earliest-Deadline-First (EDF) scheduling policy in which customers have deadlines and are served only until their deadlines elapse. The performance of the system is measured by the fraction of reneged work (the residual work lost due to elapsed deadlines) which is shown to be minimized by the EDF policy. The evolution of the lead time distribution of customers in queue is described by a measure-valued process. The heavy traffic limit of this (properly scaled) process is shown to be a deterministic function of the limit of the scaled workload process which, in turn, is identified to be a doubly reflected Brownian motion. This paper complements previous work by Doytchinov, Lehoczky and Shreve on the EDF discipline in which customers are served to completion even after their deadlines elapse. The fraction of reneged work in a heavily loaded system and the fraction of late work in the corresponding system without reneging are compared using explicit formulas based on the heavy traffic approximations. The formulas are validated by simulation results.