On the long time behavior of the TCP window size process

被引：37

作者：

Chafai, Djalil ^{[2
]}

Malrieu, Florent ^{[1
]}

Paroux, Katy ^{[3
]}

机构：

[1] Univ Rennes 1, CNRS, UMR 6625, Inst Rech Math Rennes IRMAR, F-35042 Rennes, France

[2] Univ Paris Est Marne La Vallee, CNRS, UMR 8050, Lab Anal & Math Appl, F-77454 Champs Sur Marne 2, France

[3] Univ Franche Comte, CNRS, UMR 6623, Math Lab, F-25030 Besancon, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2010年 / 120卷 / 08期

关键词：

Network protocols; Queueing theory; Additive Increase Multiplicative Decrease processes (AIMD); Piecewise Deterministic Markov Processes (PDMP); Exponential ergodicity; Coupling; DETERMINISTIC MARKOV-PROCESSES; EXPONENTIAL FUNCTIONALS; PERPETUITIES; ERGODICITY; ALGORITHMS; STABILITY; MODELS;

D O I：

10.1016/j.spa.2010.03.019

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The TCP window size process appears in the modeling of the famous transmission control protocol used for data transmission over the Internet. This continuous time Markov process takes its values in [0, infinity), and is ergodic and irreversible. It belongs to the additive increase-multiplicative decrease class of processes. The sample paths are piecewise linear deterministic and the whole randomness of the dynamics comes from the jump mechanism. Several aspects of this process have already been investigated in the literature. In the present paper, we mainly get quantitative estimates for the convergence to equilibrium, in terms of the W(1) Wasserstein coupling distance, for the process and also for its embedded chain. (C) 2010 Elsevier B.V. All rights reserved.

引用

页码：1518 / 1534

页数：17

共 23 条

[1] Ane C., 2000, INEGALITES SOBOLEV L
[2] [Anonymous], 1996, STATIONARY BEHAV IDE
[3] Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincare
Bakry, Dorninique
Cattiaux, Patrick
Guillin, Arnaud
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2008, 254 (03) : 727 - 759
[4] A single channel on/off model with TCP-like control
Borkovec, M
Dasgupta, A
Resnick, S
Samorodnitsky, G
[J]. STOCHASTIC MODELS, 2002, 18 (03) : 333 - 367
[5] Stability and ergodicity of piecewise deterministic Markov processes
Costa, O. L. V.
Dufour, F.
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2008, 47 (02) : 1053 - 1077
[6] DAVIS MHA, 1984, J ROY STAT SOC B MET, V46, P353
[7] A Markovian analysis of additive-increase multiplicative-decrease algorithms
Dumas, V
Guillemin, F
Robert, P
[J]. ADVANCES IN APPLIED PROBABILITY, 2002, 34 (01) : 85 - 111
[8] Perpetuities with thin tails
Goldie, CM
Grubel, R
[J]. ADVANCES IN APPLIED PROBABILITY, 1996, 28 (02) : 463 - 480
[9] Goldie CM, 2000, ANN PROBAB, V28, P1195
[10] INTERACTING MULTI-CLASS TRANSMISSIONS IN LARGE STOCHASTIC NETWORKS
Graham, Carl
Robert, Philippe
[J]. ANNALS OF APPLIED PROBABILITY, 2009, 19 (06) : 2334 - 2361

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