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.
Highlights
A key ingredient of our analysis is a mapping on the space of measure-valued functions which, when applied to the DLS system, yields another system whose difference from the reneging system vanishes in heavy traffic. This mapping can be viewed as a generalization of the scalar double reflection map to measure-valued processes, and, using its continuity properties, we identify the heavy traffic limit of the reference and the reneging systems
The results of this paper suggest a simple formula for the fraction of lost work in the EDF system with reneging
We identify the heavy traffic limit of the workload in the reneging system
Summary
Maria Curie-Sklodowska University and Polish Academy of Sciences, Carnegie Mellon University, Brown University and Carnegie Mellon University. This paper presents a heavy-traffic analysis of the behavior of a singleserver 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. 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.
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