A stability conjecture on bandwidth sharing networks

Walton, Neil; Mandjes, Michel

doi:10.1007/s11134-011-9233-2

Cited by 5 publications

(2 citation statements)

References 33 publications

(38 reference statements)

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“…While it seems plausible that the stability of the fluid model for general job sizes implies positive Harris recurrence, there is, to the best of our knowledge, no proof. See also [14,15] for a more extensive discussion on this stability issue. This leads to the next conjecture.…”

Section: Fluid Limitmentioning

confidence: 99%

Stability of Redundancy Systems with Processor Sharing

Raaijmakers¹,

Borst²,

Boxma³

2019

Preprint

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We investigate the stability condition for redundancy-d systems where each of the servers follows a processor-sharing (PS) discipline. We allow for generally distributed job sizes, with possible dependence among the d replica sizes being governed by an arbitrary joint distribution. We establish that the stability condition is characterized by the expectation of the minimum of d replica sizes being less than the mean interarrival time per server. In the special case of identical replicas, the stability condition is insensitive to the job size distribution given its mean, and the stability condition is inversely proportional to the number of replicas. In the special case of i.i.d. replicas, the stability threshold decreases (increases) in the number of replicas for job size distributions that are NBU (NWU). We also discuss extensions to scenarios with heterogeneous servers.

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Section: Fluid Limitmentioning

confidence: 99%

Stability of Redundancy Systems with Processor Sharing

Raaijmakers¹,

Borst²,

Boxma³

2019

Preprint

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“…The stability of network bandwidth sharing under various allocation objectives, with and without Markovian demand assumptions, is discussed by Walton and Mandjes [21]. Their paper surveys the literature on the stability question and illustrates its inherent difficulty.…”

Section: Related Workmentioning

confidence: 99%

Multi-Resource Fairness

Bonald

Roberts

2015

Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems

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Designing efficient and fair algorithms for sharing multiple resources between heterogeneous demands is becoming increasingly important. Applications include compute clusters shared by multi-task jobs and routers equipped with middleboxes shared by flows of different types. We show that the currently preferred objective of Dominant Resource Fairness (DRF) has a significantly less favorable efficiency-fairness tradeoff than alternatives like Proportional Fairness and our proposal, Bottleneck Max Fairness. We propose practical algorithms to realize these sharing objectives and evaluate their performance under a stochastic demand model. It is shown, in particular, that the strategyproofness property that motivated the choice of DRF for an assumed fixed set of jobs or flows, is largely irrelevant when demand is dynamic.

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