Fluid Limits for Processor-Sharing Queues with Impatience

Gromoll, H. Christian; Pierpoint, Robert; Zwart, Bert

doi:10.1287/moor.1070.0298

Cited by 51 publications

(66 citation statements)

References 26 publications

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“…State descriptors of this kind were proposed in Gromoll and Kruk (2007) and Gromoll et al (2008) for processor sharing queues with soft and firm deadlines, respectively. Let…”

Section: Basic Performance Processesmentioning

confidence: 99%

Edge minimality of EDF resource sharing networks

Kruk

2017

Math Meth Oper Res

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We consider a general real-time network with soft customer deadlines, in which users require service from several shared resources simultaneously. We call the service protocol for such a network edge minimal (locally edge minimal) if it minimizes globally (resp., locally) in time, in a suitable sense, the system resource idleness with respect to customers with lead times not greater than any given threshold value on all the routes of the network. We show that the preemptive Earliest-Deadline-First (EDF) service discipline is edge minimal. Moreover, we characterize the preemptive EDF policy as a protocol making the underlying network locally edge minimal. Our arguments are pathwise, independent on the network topology and requiring very mild assumptions, or even no assumptions, on the model stochastic primitives. Application of our characterization to fluid model analysis for EDF resource sharing networks is also discussed.

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“…State descriptors of this kind were proposed in Gromoll and Kruk (2007) and Gromoll et al (2008) for processor sharing queues with soft and firm deadlines, respectively. Let…”

Section: Basic Performance Processesmentioning

confidence: 99%

Edge minimality of EDF resource sharing networks

Kruk

2017

Math Meth Oper Res

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“…Puha and Williams [17] and Gromoll [11] established the analogue results for the PS queue. Recent developments include the analysis of PS queues with impatience [13], [14].…”

Section: Literaturementioning

confidence: 99%

The fluid limit of the multiclass processor sharing queue

Tahar

Jean-Marie

2012

Queueing Syst

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Consider a single server queueing system with several classes of customers, each having its own renewal input process and its own general service times distribution. Upon completing service, customers may leave, or reenter the queue, possibly as customers of a different class. The server is operating under the egalitarian processor sharing discipline. Building on prior work by Gromoll et al. [12] and Puha et al.[16], we establish the convergence of a properly normalized state process to a fluid limit. We show the existence of a unique solution to this fluid limit model, both for a stable and an overloaded queue. We also describe the asymptotic behavior of the trajectories of the fluid limit.

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“…It is studied in Gromoll et al [8] and shown to have a unique solution that is bounded away from zero outside t = 0, see Corollary 3.8. So the norm z(·) 1 is unique.…”

Section: Theorem 1 For Any Initial State Z(0) a Fms Exists And Is Umentioning

confidence: 99%

“…To establish convergence of fluid limits to the invariant point, we use an equivalent description of fluid limits, which is a generalisation of the approximating equation suggested by Gromoll et al [8] for a single-stage-service PS queue. We also discuss the method of of Lyapunov functions since the model treated in this paper is an instant of a more general open problem: no Lyapunov function is known for a PS-queue with routing and impatience.…”

Section: Introductionmentioning

confidence: 99%

Fluid Limit of a Ps-Queue With Multistage Service

Frolkova¹,

Zwart

2017

Prob. Eng. Inf. Sci.

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The PS-model treated in this paper is motivated by freelance job websites where multiple freelancers compete for a single job. In the context of such websites, multistage service of a job means collection of applications from multiple freelancers. Under Markovian stochastic assumptions, we develop fluid limit approximations for the PS-model in overload. Based on this approximation, we estimate what proportion of freelancers get the jobs they apply for. In addition, the PS-model studied here is an instant of PS with routing and impatience, for which no Lyapunov function is known, and we suggest some partial solutions.

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Fluid Limits for Processor-Sharing Queues with Impatience

Cited by 51 publications

References 26 publications

Edge minimality of EDF resource sharing networks

Edge minimality of EDF resource sharing networks

The fluid limit of the multiclass processor sharing queue

Fluid Limit of a Ps-Queue With Multistage Service

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