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2011 Diffusion limits for shortest remaining processing time queues
H. Christian Gromoll, Łukasz Kruk, Amber L. Puha
Stoch. Syst. 1(1): 1-16 (2011). DOI: 10.1214/10-SSY016


We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.


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H. Christian Gromoll. Łukasz Kruk. Amber L. Puha. "Diffusion limits for shortest remaining processing time queues." Stoch. Syst. 1 (1) 1 - 16, 2011.


Published: 2011
First available in Project Euclid: 24 February 2014

zbMATH: 1291.60187
MathSciNet: MR2948916
Digital Object Identifier: 10.1214/10-SSY016

Primary: 60F17, 60K25
Secondary: 60G57, 68M20, 90B22

Rights: Copyright © 2011 INFORMS Applied Probability Society


Vol.1 • No. 1 • 2011
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