research-article

The Distribution of Waiting Times in Clocked Multistage Interconnection Networks

Authors:

A. WeissAuthors Info & Claims

IEEE Transactions on Computers, Volume 37, Issue 11

Pages 1337 - 1352

https://doi.org/10.1109/12.8700

Published: 01 November 1988 Publication History

Abstract

Analyzes the random delay experienced by a message traversing a buffered, multistage packet-switching banyan network. The authors find the generating function for the distribution of waiting time at the first stage of the network for a very general class of traffic, assuming messages have discrete sizes. For example, traffic can be uniform or nonuniform, messages can have different sizes, and messages can arrive in batches. For light-to-moderate loads, the authors conjecture that delays experienced at the various stages of the network are nearly the same and are nearly independent. This allows us to approximate the total delay distribution. Better approximations for the distribution of waiting times at later stages of the network are attained by assuming that in the limit a sort of spatial steady state is achieved. Extensive simulations confirm the formulas and conjectures.

References

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Cited By

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Prasad RWinzer PBorst SThottan M(2007)Queuing Delays in Randomized Load Balanced NetworksProceedings of the IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications10.1109/INFCOM.2007.54(400-408)Online publication date: 1-May-2007
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Tscha Y(2003)Scheduling length for switching element disjoint multicasting in Banyan-type switching networksJournal of Systems Architecture: the EUROMICRO Journal10.1016/S1383-7621(02)00135-248:6-7(175-191)Online publication date: 1-Jan-2003
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The Distribution of Waiting Times in Clocked Multistage Interconnection Networks

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Published In

cover image IEEE Transactions on Computers

IEEE Transactions on Computers Volume 37, Issue 11

November 1988

174 pages

ISSN:0018-9340

Editor:
Ming T. Liu

Issue’s Table of Contents

Copyright © Copyright © 1988 IEEE. All Rights Reserved.

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IEEE Computer Society

United States

Publication History

Published: 01 November 1988

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Cited By

Wang XChan HShi ERay ILi NKruegel C(2015)Circuit ORAMProceedings of the 22nd ACM SIGSAC Conference on Computer and Communications Security10.1145/2810103.2813634(850-861)Online publication date: 12-Oct-2015
https://dl.acm.org/doi/10.1145/2810103.2813634
Prasad RWinzer PBorst SThottan M(2007)Queuing Delays in Randomized Load Balanced NetworksProceedings of the IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications10.1109/INFCOM.2007.54(400-408)Online publication date: 1-May-2007
https://dl.acm.org/doi/10.1109/INFCOM.2007.54
Tscha Y(2003)Scheduling length for switching element disjoint multicasting in Banyan-type switching networksJournal of Systems Architecture: the EUROMICRO Journal10.1016/S1383-7621(02)00135-248:6-7(175-191)Online publication date: 1-Jan-2003
https://dl.acm.org/doi/10.1016/S1383-7621%2802%2900135-2
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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Koppelman D(1996)A Family of Interconnection Networks for Nonuniform TrafficIEEE Transactions on Parallel and Distributed Systems10.1109/71.5037737:5(486-492)Online publication date: 1-May-1996
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Meliksetian DChen C(1993)A Markov-modulated Bernoulli process approximation for the analysis of Banyan NetworksACM SIGMETRICS Performance Evaluation Review10.1145/166962.16700521:1(183-194)Online publication date: 1-Jun-1993
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Meliksetian DChen COwicki SMuntz D(1993)A Markov-modulated Bernoulli process approximation for the analysis of Banyan NetworksProceedings of the 1993 ACM SIGMETRICS conference on Measurement and modeling of computer systems10.1145/166955.167005(183-194)Online publication date: 1-Jun-1993
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Abraham SPadmanabhan K(1992)Effect of data access delays and system partitionability on the dynamic performance of a shared memory multiprocessorProceedings of the 1992 ACM/IEEE conference on Supercomputing10.5555/147877.148111(674-682)Online publication date: 1-Dec-1992
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Meliksetian DChen C(1992)Performance analysis of communications in static interconnection networksACM SIGMETRICS Performance Evaluation Review10.1145/149439.13314820:1(249-250)Online publication date: 1-Jun-1992
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Sivaram R(1992)Queuing delays for uniform and nonuniform traffic patterns in a MINACM SIGSIM Simulation Digest10.1145/141426.14142822:1(17-27)Online publication date: 1-Jul-1992
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