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A Markov chain approximation for the analysis of banyan networks

Author:

Arif MerchantAuthors Info & Claims

SIGMETRICS '91: Proceedings of the 1991 ACM SIGMETRICS conference on Measurement and modeling of computer systems

April 1991

Pages 60 - 67

https://doi.org/10.1145/107971.107979

Published: 02 April 1991 Publication History

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Abstract

This paper analyzes the delay suffered by messages in a clocked, packet-switched, square Banyan network with k x k output-buffered switches by approximating the flow processes in the network with Markov chains. We recursively approximate the departure process of buffers of the n^th stage in terms of thqt at the n -- l^st stage. We show how to construct the transition matrix for the Markov chain at each stage of the network and how to solve for the stationary distribution of the delay in the queues of that stage. The analytical results are compared with simulation results for several cases. Finally, we give a method based on this approximation and the technique of coupling to compute upper bounds on the time for the system to approach steady state.

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Cited By

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Vasiliadis DRizos GSimos T(2019)Simulation for Multistage Interconnection Networks Using Relaxed Blocking ModelRecent Progress in Computational Sciences and Engineering10.1201/9780429070655-136(570-575)Online publication date: 7-May-2019
https://doi.org/10.1201/9780429070655-136
Vasiliadis DRizos GVassilakis CGlavas E(2011)Modelling and performance evaluation of a novel internal-priority routing scheme for finite-buffered multistage interconnection networksInternational Journal of Parallel, Emergent and Distributed Systems10.1080/17445760.2010.53921826:5(381-397)Online publication date: Oct-2011
https://doi.org/10.1080/17445760.2010.539218
Vasiliadis DRizos GMargariti STsiantis L(2007)Comparative study of blocking mechanisms for packet switched Omega networksProceedings of the 6th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications10.5555/1355643.1355647(18-22)Online publication date: 16-Feb-2007
https://dl.acm.org/doi/10.5555/1355643.1355647
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Index Terms

A Markov chain approximation for the analysis of banyan networks
1. Computing methodologies
  1. Modeling and simulation
    1. Model development and analysis
      1. Modeling methodologies
2. Networks
  1. Network types
    1. Packet-switching networks

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A Markov chain approximation for the analysis of banyan networks

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Published In

SIGMETRICS '91: Proceedings of the 1991 ACM SIGMETRICS conference on Measurement and modeling of computer systems

April 1991

228 pages

ISBN:0897913922

DOI:10.1145/107971

Chairman:
Tom W. Keller
IBM Corp, Austin, TX

ACM SIGMETRICS Performance Evaluation Review Volume 19, Issue 1
May 1991
223 pages
ISSN:0163-5999
DOI:10.1145/107972
Editor:
Tom W. Keller
IBM Corp., Austin, TX
Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 02 April 1991

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SIGMETRICS91

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SIGMETRICS

SIGMETRICS91: ACM SIGMETRICS Conference on Measurement & Modeling of Computer Systems

May 21 - 24, 1991

California, San Diego, USA

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Overall Acceptance Rate 459 of 2,691 submissions, 17%

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Cited By

View all

Vasiliadis DRizos GSimos T(2019)Simulation for Multistage Interconnection Networks Using Relaxed Blocking ModelRecent Progress in Computational Sciences and Engineering10.1201/9780429070655-136(570-575)Online publication date: 7-May-2019
https://doi.org/10.1201/9780429070655-136
Vasiliadis DRizos GVassilakis CGlavas E(2011)Modelling and performance evaluation of a novel internal-priority routing scheme for finite-buffered multistage interconnection networksInternational Journal of Parallel, Emergent and Distributed Systems10.1080/17445760.2010.53921826:5(381-397)Online publication date: Oct-2011
https://doi.org/10.1080/17445760.2010.539218
Vasiliadis DRizos GMargariti STsiantis L(2007)Comparative study of blocking mechanisms for packet switched Omega networksProceedings of the 6th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications10.5555/1355643.1355647(18-22)Online publication date: 16-Feb-2007
https://dl.acm.org/doi/10.5555/1355643.1355647
Vasiliadis DRizos GMargariti STsiantis L(2007)Comparative study of blocking mechanisms for packet switched Omega networksProceedings of the 6th WSEAS International Conference on Electronics, Hardware, Wireless and Optical Communications10.5555/1353572.1353576(18-22)Online publication date: 16-Feb-2007
https://dl.acm.org/doi/10.5555/1353572.1353576
Vasiliadis DRizos GVassilakis CGlavas E(2007)Performance Evaluation of Two-Priority Network Schema for Single-Buffered Delta Networks2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications10.1109/PIMRC.2007.4394153(1-7)Online publication date: Sep-2007
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Vasiliadis DRizos GVassilakis C(2007)Performance Analysis of blocking Banyan SwitchesInnovative Algorithms and Techniques in Automation, Industrial Electronics and Telecommunications10.1007/978-1-4020-6266-7_20(107-111)Online publication date: 2007
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Molokov DShaaban MHeliotis JSavakis A(2006)The Design, Modeling and Simulation of Switching Fabrics for an ATM Network SwitchAdvances in Computer, Information, and Systems Sciences, and Engineering10.1007/1-4020-5261-8_43(275-282)Online publication date: 2006
https://doi.org/10.1007/1-4020-5261-8_43
Lai W(2000)Performing Permutations on Interconnection Networks by Regularly Changing Switch StatesIEEE Transactions on Parallel and Distributed Systems10.1109/71.87794011:8(829-837)Online publication date: 1-Aug-2000
https://dl.acm.org/doi/10.1109/71.877940
Datta SSitaraman RLeiserson CCuller D(1997)The performance of simple routing algorithms that drop packetsProceedings of the ninth annual ACM symposium on Parallel algorithms and architectures10.1145/258492.258508(159-169)Online publication date: 1-Jun-1997
https://dl.acm.org/doi/10.1145/258492.258508
Rehrmann RMonien BLüling RDiekmann RBlelloch G(1996)On the communication throughput of buffered multistage interconnection networksProceedings of the eighth annual ACM symposium on Parallel Algorithms and Architectures10.1145/237502.237521(152-161)Online publication date: 24-Jun-1996
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