2009
DOI: 10.1287/moor.1090.0409
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Fluid Limits for Shortest Remaining Processing Time Queues

Abstract: We consider a single-server queue with renewal arrivals and i.i.d. service times in which the server uses the shortest remaining processing time policy. To describe the evolution of this queue, we use a measure-valued process that keeps track of the residual service times of all buffered jobs. We propose a fluid model (or formal law of large numbers approximation) for this system and, under mild assumptions, prove the existence and uniqueness of fluid model solutions. Furthermore, we prove a scaling limit theo… Show more

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Cited by 68 publications
(89 citation statements)
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“…Indeed, there is a deep relation between the EDF and SRPT scheduling strategies. Their similarity was first noticed (at least to our knowledge) by Bender, Chakrabarti and Muthukrishnan [5] and then, more explicitly, by Down, Gromoll and Puha [14], who investigated fluid limits for SRPT queues using an auxiliary process similar to the one introduced by Doytchinov, Lehoczky and Shreve [15] in the context of heavy traffic analysis for EDF queues. In fact, in Sect.…”
Section: Introductionmentioning
confidence: 63%
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“…Indeed, there is a deep relation between the EDF and SRPT scheduling strategies. Their similarity was first noticed (at least to our knowledge) by Bender, Chakrabarti and Muthukrishnan [5] and then, more explicitly, by Down, Gromoll and Puha [14], who investigated fluid limits for SRPT queues using an auxiliary process similar to the one introduced by Doytchinov, Lehoczky and Shreve [15] in the context of heavy traffic analysis for EDF queues. In fact, in Sect.…”
Section: Introductionmentioning
confidence: 63%
“…5. Recall that, by Lemmas 13, 14 and Remark 2, for each such network with initial state x n , there is a random timeσ , bounded by a constant γ , such that (14) holds. If (14) implies (15), then the argument given in Sect.…”
Section: Resultsmentioning
confidence: 99%
“…That is, we obtain from our fluid model a fluid level approximation of the amount of time a job of a given size spends in the system, given an arbitrary system configuration at the time of its arrival. This paper is an extended abstract of results in [2]. In [2], a more thorough introduction is provided, as well as all proofs and a detailed analysis of the fluid model behavior.…”
Section: Introductionmentioning
confidence: 99%
“…This paper is an extended abstract of results in [2]. In [2], a more thorough introduction is provided, as well as all proofs and a detailed analysis of the fluid model behavior. There is also a rigorous justification of the fluid model as an approximation to the underlying stochastic model.…”
Section: Introductionmentioning
confidence: 99%
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