Fluid queues and regular variation

Boxma, Onno

doi:10.1016/s0166-5316(96)90052-8

Cited by 17 publications

(6 citation statements)

References 11 publications

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“…Remarks: (i) In Boxma (1996) [BOX96,BOX97], a precise asymptotics of the embeded queue distribution was obtained for multiplexing On-Off sources one of which had regularly varying On periods while the others had exponentially distributed On periods. A similar setting with intermediately varying On periods was investigated in [RSS97].…”

Section: Then the Queue Asymptotics Of This Queueing System Is Equal mentioning

confidence: 99%

Asymptotic results for multiplexing subexponential on-off processes

Jelenković

Lazar

1999

Adv. Appl. Probab.

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Consider an aggregate arrival process A N obtained by multiplexing N On-Off processes with exponential Off periods of rate λ and subexponential On periods τ on . As N goes to infinity, with λN → Λ, A N approaches an M/G/∞ type process. Both for finite and infinite N , we obtain the asymptotic characterization of the arrival process activity period.Using these results we investigate a fluid queue with the limiting M/G/∞ arrival process A ∞ t and capacity c. When On periods are regularly varying (with non-integer exponent), we derive a precise asymptotic behavior of the queue length random variable Q P t observed at the beginning of the arrival process activity periodswhere ρ = EA ∞ t < c; r (c ≤ r) is the rate at which the fluid is arriving during an On period. The asymptotic (time average) queue distribution lower bound is obtained under more general assumptions on On periods than regular variation.In addition, we analyze a queueing system in which one On-Off process, whose On period belongs to a subclass of subexponential distributions, is multiplexed with independent exponential processes with aggregate expected rate Ee t . This system is shown to be asymptotically equivalent to the same queueing system with the exponential arrival processes being replaced by their total mean value Ee t .

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Section: Then the Queue Asymptotics Of This Queueing System Is Equal mentioning

confidence: 99%

Asymptotic results for multiplexing subexponential on-off processes

Jelenković

Lazar

1999

Adv. Appl. Probab.

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“…It is undertaken in [8,29,52]; in all three papers the restrictive assumption is made that P[A 11 > x] is regularly varying, and the last paper considers the Pareto distribution within the class of regularly varying functions. In each of these papers, starting-point i s F ormula (2.2.19) of [15], that follows from (5.1) and (5.2) after some manipulations (take r = 1 for simplicity):…”

Section: Several Long-tailed On-period Distributions -Lower Boundsmentioning

confidence: 99%

“…By allowing just one set of sources to have activity period distributions with a nonexponential tail, one may use Proposition 5.8 combined with the method exposed in [8,9], to study the tail behaviour of B 1 and W.…”

Section: Several Long-tailed On-period Distributions -Lower Boundsmentioning

confidence: 99%

Fluid queues with long-tailed activity period distributions

Boxma

Dumas

1998

Computer Communications

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This is a survey paper on uid queues, with a strong emphasis on recent attempts to represent phenomena like long-range dependence. The central model of the paper is a uid queueing system fed by N independent sources that alternate between silence and activity periods. The distribution of the activity periods of at least one source is assumed to be long-tailed, which may give rise to long-range dependence. We consider the e ect of this tail behaviour on the steady-state distributions of the bu er content at embedded points in time and at arbitrary time, and on the busy period distribution. Both exact results and bounds are discussed.

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“…We believe -but couldn't prove yet -that, in general, Similar observations have been made for fluid-flow models [2]. Of course, in order for a result like (12) or (13) to be of 'practical' value, one should also be able to derive the constant of proportionality, i.e., the 'intercept' of the curve m-(q-2 ).…”

Section: A Second Approachmentioning

confidence: 65%

Traffic characteristics and queueing behavior of discrete-time on-off sources

Laevens

Bruneel

2000

IFIP Advances in Information and Communication Technology

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In this paper, some results are presented from an attempt to study -in a discrete-time setting -the phenomenon of long-range dependence. For a well-known source model, traffic characteristics such as the power spectral density and the index of dispersion for counts are analyzed. Based on these characteristics, the distinction between short-range and long-range dependence is touched upon. The traffic generated by a superposition of sources is also studied, whereby the case of an infinite number of sources gets special attention. In this, the discrete-time version of the M/G/oo queue model is called upon. Finally, some results pertaining to the queueing behavior of such traffic are discussed.

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Fluid queues and regular variation

Cited by 17 publications

References 11 publications

Asymptotic results for multiplexing subexponential on-off processes

Asymptotic results for multiplexing subexponential on-off processes

Fluid queues with long-tailed activity period distributions

Traffic characteristics and queueing behavior of discrete-time on-off sources

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