A unified algorithm for finite and infinite buffer content distribution of Markov fluid models

This article analyzes a generic class of queuing systems with server vacation. The special feature of the models considered is that the duration of the vacations explicitly depends on the buffer content evolution during the previous active period (i.e., the time elapsed since the previous vacation). During both active periods and vacations, the buffer content evolves as a Lévy process. For two specific classes of models, the Laplace–Stieltjes transform of the buffer content distribution at switching epochs between successive vacations and active periods, and in steady state, is derived.

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Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources

Advances in Applied Probability ◽

10.1017/s0001867800009861 ◽

2000 ◽

Vol 32 (01) ◽

pp. 244-255 ◽

Cited By ~ 7

Author(s):

V. Dumas ◽

A. Simonian

Keyword(s):

Lower Bound ◽

Finite Number ◽

Upper Bound ◽

Content Distribution ◽

Upper Bounds ◽

Lower And Upper Bounds ◽

Fluid Queue ◽

Asymptotic Bounds ◽

Multiplicative Factor ◽

Buffer Content

We consider a fluid queue fed by a superposition of a finite number of On/Off sources, the distribution of the On period being subexponential for some of them and exponential for the others. We provide general lower and upper bounds for the tail of the stationary buffer content distribution in terms of the so-called minimal subsets of sources. We then show that this tail decays at exponential or subexponential speed according as a certain parameter is smaller or larger than the ouput rate. If we replace the subexponential tails by regularly varying tails, the upper bound and the lower bound are sharp in that they differ only by a multiplicative factor.

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A TANDEM FLUID QUEUE WITH GRADUAL INPUT

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964802161031 ◽

2002 ◽

Vol 16 (1) ◽

pp. 29-45 ◽

Cited By ~ 6

Author(s):

Werner R.W. Scheinhardt ◽

Bert Zwart

Keyword(s):

Steady State ◽

Content Distribution ◽

Fluid Model ◽

Sample Path ◽

Fluid Queue ◽

Finite Buffers ◽

Martingale Methods ◽

Buffer Content

For a two-node tandem fluid model with gradual input, we compute the joint steady-state buffer-content distribution. Our proof exploits martingale methods developed by Kella and Whitt. For the case of finite buffers, we use an insightful sample-path argument to extend an earlier proportionality result of Zwart to the network case.

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Content Distribution Stochastic Fluid Models for Multi-regions P2P Networks

Content Computing - Lecture Notes in Computer Science ◽

10.1007/978-3-540-30483-8_10 ◽

2004 ◽

pp. 82-87

Author(s):

Zhiqun Deng ◽

Dejun Mu ◽

Guanzhong Dai ◽

Wanlin Zhu

Keyword(s):

Content Distribution ◽

Fluid Models ◽

P2p Networks ◽

Stochastic Fluid Models ◽

Stochastic Fluid

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BOUNDS FOR FLUID MODELS DRIVEN BY SEMI-MARKOV INPUTS

Probability in the Engineering and Informational Sciences ◽

10.1017/s026996489913403x ◽

1999 ◽

Vol 13 (4) ◽

pp. 429-475 ◽

Cited By ~ 12

Author(s):

N. Gautam ◽

V. G. Kulkarni ◽

Z. Palmowski ◽

T. Rolski

Keyword(s):

Lower Bounds ◽

Markov Processes ◽

Fluid Model ◽

Loss Probability ◽

Telecommunication Networks ◽

Upper And Lower Bounds ◽

Fluid Models ◽

Output Capacity ◽

Buffer Content ◽

Semi Markov Processes

In this paper we consider an infinite buffer fluid model whose input is driven by independent semi-Markov processes. The output capacity of the buffer is a constant. We derive upper and lower bounds for the limiting distribution of the stationary buffer content process. We discuss examples and applications where the results can be used to determine bounds on the loss probability in telecommunication networks.

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Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources

Advances in Applied Probability ◽

10.1239/aap/1013540032 ◽

2000 ◽

Vol 32 (1) ◽

pp. 244-255 ◽

Cited By ~ 9

Author(s):

V. Dumas ◽

A. Simonian

Keyword(s):

Lower Bound ◽

Finite Number ◽

Upper Bound ◽

Content Distribution ◽

Upper Bounds ◽

Lower And Upper Bounds ◽

Fluid Queue ◽

Asymptotic Bounds ◽

Multiplicative Factor ◽

Buffer Content

We consider a fluid queue fed by a superposition of a finite number of On/Off sources, the distribution of the On period being subexponential for some of them and exponential for the others. We provide general lower and upper bounds for the tail of the stationary buffer content distribution in terms of the so-called minimal subsets of sources. We then show that this tail decays at exponential or subexponential speed according as a certain parameter is smaller or larger than the ouput rate. If we replace the subexponential tails by regularly varying tails, the upper bound and the lower bound are sharp in that they differ only by a multiplicative factor.

Download Full-text