Heavy tailed M/G/1-PS queues with impatience and admission control in packet networks

Boyer, Jacqueline; Guillemin, Fabrice; Pierpoint, Robert; Zwart, Bert

doi:10.1109/infcom.2003.1208671

Cited by 14 publications

(13 citation statements)

References 18 publications

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“…Secondly, our results demonstrate that the negative performance impact of the heavy-tailed class can be reduced by limiting the number of simultaneously active users in the system. These findings reinforce some of the arguments made in [4,11] in favor of admission control for TCP flows. It is worth observing that in practice TCP time-out effects and user impatience may indirectly induce a limit on the maximum number of active flows (although the actual mechanics are quite different).…”

Section: Introductionsupporting

confidence: 89%

“…They further showed that the result is sharp, in the sense that the tail equivalence does not hold for Weibull distributions with a larger index parameter. Recently, Boyer et al [4] obtained a tail equivalence result for heavy-tailed PS queues with impatient users and admission control. In contrast to the remarkably explicit results for heavy-tailed PS queues, the delay asymptotics for light-tailed service requirements have remained largely intractable.…”

Section: Introductionmentioning

confidence: 99%

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Bandwidth sharing with heterogeneous service requirements

Borst

Queija

Zwart

2003

Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress - ITC-18

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C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a PNA Probability, Networks and Algorithms Probability, Networks and AlgorithmsBandwidth Sharing with Heterogeneous Service Requirements S.C Borst, R. Núñez-Queija, A.P. Zwart Bandwidth Sharing with Heterogeneous Service Requirements ABSTRACT We consider a system with two heterogeneous traffic classes. The users from both classes randomly generate service requests, one class having light-tailed properties, the other one exhibiting heavy-tailed characteristics. The heterogeneity in service requirements reflects the extreme variability in flow sizes observed in the Internet, with a vast majority of small transfers ('mice') and a limited number of exceptionally large flows ('elephants'). The active traffic flows share the available bandwidth in a Processor-Sharing (PS) fashion. The PS discipline has emerged as a natural paradigm for modeling the flow-level performance of bandwidth-sharing protocols like TCP. The number of simultaneously active traffic flows is limited by a threshold on the maximum system occupancy. We obtain the exact asymptotics of the transfer delays incurred by the users from the light-tailed class. The results show that the threshold mechanism significantly reduces the detrimental performance impact of the heavy-tailed class. REPORT PNA-R0312 DECEMBER 15, 2003 AbstractWe consider a system with two heterogeneous traffic classes. The users from both classes randomly generate service requests, one class having light-tailed properties, the other one exhibiting heavy-tailed characteristics. The heterogeneity in service requirements reflects the extreme variability in flow sizes observed in the Internet, with a vast majority of small transfers ('mice') and a limited number of exceptionally large flows ('elephants'). The active traffic flows share the available bandwidth in a Processor-Sharing (PS) fashion. The PS discipline has emerged as a natural paradigm for modeling the flow-level performance of bandwidth-sharing protocols like TCP. The number of simultaneously active traffic flows is limited by a threshold on the maximum system occupancy. We obtain the exact asymptotics of the transfer delays incurred by the users from the light-tailed class. The results show that the threshold mechanism significantly reduces the detrimental performance impact of the heavy-tailed class.2000 Mathematics Subject Classification: 60K25 (primary), 68M20, 90B18, 90B22 (secondary).

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Section: Introductionsupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Bandwidth sharing with heterogeneous service requirements

Borst

Queija

Zwart

2003

Providing Quality of Service in Heterogeneous Environments, Proceedings of the 18th International Teletraffic Congress - ITC-18

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“…Define (5) Note that by definition R(x) = R 1 (x). With similar arguments as before, it is not difficult to show that (4) lim…”

Section: The Mig/1 Ps Queuesupporting

confidence: 62%

“…The large-deviations results of the present paper aim to give some insight into the introduction of admission control for elastic traffic in broadband packet networks; we refer to the paper Boyer et al [4] for more discussion in this direction. From a technical point of view, the main point of that paper is to make use of the relation IP'…”

Section: P' (V> X) Rv 1p' (B > X(1 -P))mentioning

confidence: 93%

Tail asymptotics for processor-sharing queues

2004

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ABSTRACT. The basic queueing system considered in this paper is the MIG/1 processor sharing (PS) queue with or without impatience and with finite or infinite capacity. Under some mild assumptions, a criterion for the validity of the RSR (Reduced Service Rate) approximation is established when service times are heavy tailed. This result is applied to various models based on MIG/1 processor sharing queues.

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“…figures 12,14,16,21). This is due to the fact that max-min fairness gives an absolute priority to flows with small bit rates.…”

Section: Resultsmentioning

confidence: 99%

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

et al. 2006

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We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processorsharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.

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Heavy tailed M/G/1-PS queues with impatience and admission control in packet networks

Cited by 14 publications

References 18 publications

Bandwidth sharing with heterogeneous service requirements

Bandwidth sharing with heterogeneous service requirements

Tail asymptotics for processor-sharing queues

A queueing analysis of max-min fairness, proportional fairness and balanced fairness

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