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Volume 2017, Article ID 4832740, 11 pages
Research Article

Distributed Sequential Consensus in Networks: Analysis of Partially Connected Blockchains with Uncertainty

1Media Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA
2Harvard T. H. Chan School of Public Health, Harvard University, Boston, MA 02115, USA
3BISITE Research Group, University of Salamanca, Edificio Multiusos I+D+i, 37008 Salamanca, Spain

Correspondence should be addressed to Francisco Prieto-Castrillo; ude.tim@oteirpf

Received 9 July 2017; Revised 13 September 2017; Accepted 10 October 2017; Published 1 November 2017

Academic Editor: Dimitri Volchenkov

Copyright © 2017 Francisco Prieto-Castrillo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work presents a theoretical and numerical analysis of the conditions under which distributed sequential consensus is possible when the state of a portion of nodes in a network is perturbed. Specifically, it examines the consensus level of partially connected blockchains under failure/attack events. To this end, we developed stochastic models for both verification probability once an error is detected and network breakdown when consensus is not possible. Through a mean field approximation for network degree we derive analytical solutions for the average network consensus in the large graph size thermodynamic limit. The resulting expressions allow us to derive connectivity thresholds above which networks can tolerate an attack.