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Transient Moments of the TCP Window Size Process

Part of: Stochastic processes Markov processes Computer system organization Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Andreas H. Löpker  and
Johan S. H. van Leeuwaarden
Andreas H. Löpker*
Affiliation:
EURANDOM
Johan S. H. van Leeuwaarden*
Affiliation:
EURANDOM and Eindhoven University of Technology
*
∗Postal address: EURANDOM, PO Box 513, 5600 MB Eindhoven, The Netherlands.
∗Postal address: EURANDOM, PO Box 513, 5600 MB Eindhoven, The Netherlands.
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Abstract

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The TCP window size process can be modeled as a piecewise-deterministic Markov process that increases linearly and experiences downward jumps at Poisson times. We present a transient analysis of this window size process. Our main result is the Laplace transform of the transient moments. Formulae for the integer and fractional moments are derived, as well as an explicit characterization of the speed of convergence to steady state. Central to our approach are the infinitesimal generator and Dynkin's martingale.

Keywords

Piecewise-deterministic Markov processDynkin's martingaleoptional stoppingTCPwindow sizeAIMDstationary distributiontransient momentsexponential functionaldifference equationmixing time

MSC classification

Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J35: Transition functions, generators and resolvents 60K10: Applications (reliability, demand theory, etc.) 90B20: Traffic problems 90B15: Network models, stochastic 90B18: Communication networks 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60G44: Martingales with continuous parameter 68M20: Performance evaluation; queueing; scheduling
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 1 , March 2008 , pp. 163 - 175
Copyright
Copyright © Applied Probability Trust 2008 

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