The Annals of Applied Probability

Heavy traffic analysis for EDF queues with reneging

Łukasz Kruk, John Lehoczky, Kavita Ramanan, and Steven Shreve

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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.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 2 (2011), 484-545.

Dates
First available in Project Euclid: 22 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1300800980

Digital Object Identifier
doi:10.1214/10-AAP681

Mathematical Reviews number (MathSciNet)
MR2807965

Zentralblatt MATH identifier
1220.60053

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60G57: Random measures 60J65: Brownian motion [See also 58J65] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]

Keywords
Due dates heavy traffic queueing reneging diffusion limits random measures real-time queues

Citation

Kruk, Łukasz; Lehoczky, John; Ramanan, Kavita; Shreve, Steven. Heavy traffic analysis for EDF queues with reneging. Ann. Appl. Probab. 21 (2011), no. 2, 484--545. doi:10.1214/10-AAP681. https://projecteuclid.org/euclid.aoap/1300800980


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