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A martingale-envelope and applications

Authors:

Felix Poloczek,

Florin CiucuAuthors Info & Claims

ACM SIGMETRICS Performance Evaluation Review, Volume 41, Issue 3

Pages 43 - 45

https://doi.org/10.1145/2567529.2567543

Published: 10 January 2014 Publication History

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Abstract

In the framework of stochastic network calculus we present a new envelope-based approach which uses martingales to characterize a queueing system. We show that this setting allows a simple handling of multiplexing and scheduling: whereas multiplexing of several sources results in multiplication of the corresponding martingales, per-flow analysis in a scheduled system can be done by shifting the martingales to a certain point in time. Applying this calculus to Markov Arrival Processes, it is shown that the performance bounds can become reasonably tight.

References

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E. Buffet and N. G. Duffield. Exponential upper bounds via martingales for multiplexers with Markovian arrivals. Journal of Applied Probability, 31(4):1049--1060, 1994.

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G. Choudhury, D. Lucantoni, and W. Whitt. Squeezing the most out of ATM. IEEE Transactions on Communications, 44(2):203--217, Feb. 1996.

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F. Ciucu, F. Poloczek, and J. Schmitt. Sharp Bounds in Stochastic Network Calculus. ArXiv e-prints, Mar. 2013.

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F. Ciucu and J. Schmitt. Perspectives on network calculus: no free lunch, but still good value. SIGCOMM Comput. Commun. Rev., 42(4):311--322, Aug. 2012.

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N. G. Duffield. Exponential bounds for queues with Markovian arrivals. Queueing Systems, 17(3-4):413--430, Sept. 1994.

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A martingale-envelope and applications

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Published In

cover image ACM SIGMETRICS Performance Evaluation Review

ACM SIGMETRICS Performance Evaluation Review Volume 41, Issue 3

December 2013

111 pages

ISSN:0163-5999

DOI:10.1145/2567529

Editor:
Giuliano Casale
Imperial College London, London

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Association for Computing Machinery

New York, NY, United States

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Published: 10 January 2014

Published in SIGMETRICS Volume 41, Issue 3

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