On the performance of broadcast based consensus under non-zero-mean stochastic disturbances

Yang Yang, Rick S. Blum
{"title":"On the performance of broadcast based consensus under non-zero-mean stochastic disturbances","authors":"Yang Yang, Rick S. Blum","doi":"10.1109/SPAWC.2011.5990402","DOIUrl":null,"url":null,"abstract":"The broadcast-based consensus algorithm is one special type of randomized consensus algorithm, and is amenable to practical implementation in wireless networks. This paper focuses on the performance analysis of this broadcast-based consensus algorithm in the presence of non-zero-mean stochastic perturbations. It is demonstrated that as the algorithm proceeds, the deviation of the node states from their average will converge, in expectation, to a fixed value, which is determined by the Laplacian matrix of the network, the mixing parameter, and the mean of the stochastic perturbations. Asymptotic upper and lower bounds on the total mean-square deviation are derived, which describe the range of distances over which the node states deviate from consensus. These bounds can facilitate evaluation of the applicability of this algorithm in practice. In addition, performance of the broadcast-based consensus algorithm under zero-mean stochastic disturbances is also analyzed, and results regarding its convergence and mean-square deviation are given. The theoretical results presented in this work hold true regardless of the statistics of the stochastic disturbances, and are valid for arbitrary network topology as long as the topology is connected.","PeriodicalId":102244,"journal":{"name":"2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications","volume":"06 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SPAWC.2011.5990402","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

Abstract

The broadcast-based consensus algorithm is one special type of randomized consensus algorithm, and is amenable to practical implementation in wireless networks. This paper focuses on the performance analysis of this broadcast-based consensus algorithm in the presence of non-zero-mean stochastic perturbations. It is demonstrated that as the algorithm proceeds, the deviation of the node states from their average will converge, in expectation, to a fixed value, which is determined by the Laplacian matrix of the network, the mixing parameter, and the mean of the stochastic perturbations. Asymptotic upper and lower bounds on the total mean-square deviation are derived, which describe the range of distances over which the node states deviate from consensus. These bounds can facilitate evaluation of the applicability of this algorithm in practice. In addition, performance of the broadcast-based consensus algorithm under zero-mean stochastic disturbances is also analyzed, and results regarding its convergence and mean-square deviation are given. The theoretical results presented in this work hold true regardless of the statistics of the stochastic disturbances, and are valid for arbitrary network topology as long as the topology is connected.
非零均值随机扰动下基于广播的一致性算法的性能研究
基于广播的共识算法是一种特殊类型的随机化共识算法,适合在无线网络中实际实现。本文重点分析了这种基于广播的共识算法在非零均值随机扰动下的性能。结果表明,随着算法的进行,节点状态与其平均值的偏差在期望上收敛到一个固定值,该值由网络的拉普拉斯矩阵、混合参数和随机扰动的平均值决定。导出了总均方偏差的渐近上界和下界,它描述了节点状态偏离一致的距离范围。这些边界便于在实际中评价算法的适用性。此外,还分析了基于广播的一致性算法在零均值随机干扰下的性能,并给出了其收敛性和均方差的结果。无论随机扰动的统计量如何,本文的理论结果都是正确的,并且只要拓扑是连通的,对任意网络拓扑都是有效的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信