A Stochastic Process Approach to Model Distributed Computing on Complex Networks

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.

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“…requirements of minimum connectivity found in WSNs and other networked systems such as computer networks [30].…”

Section: Partial Connectivity In Consensus Networkmentioning

confidence: 99%

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

2017

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“…Complex networks have become an important subject in science and technology because of their ability to represent and model a large number of complex systems such as society, protein interaction and transportation, among many others [1][2][3]. In computer science, complex networks have been used, for instance, in the study of the topology of the Internet [4], the Web [5], email communications [6], the complexity of software systems [7] and modelling grid computing [8][9][10][11][12]. In the latter field, complex networks were used to represent task execution in grid computing environments, with the tasks being supplied by a master, on demand from worker processors, which were distributed along the network topology.…”

Section: Introductionmentioning

confidence: 99%

A complex network approach to cloud computing

Travieso

Ruggiero²,

Bruno³

et al. 2016

J. Stat. Mech.

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Cloud computing has become an important means to speed up computing. One problem influencing heavily the performance of such systems is the choice of nodes as servers responsible for executing the users' tasks. In this article we report how complex networks can be used to model such a problem. More specifically, we investigate the performance of the processing respectively to cloud systems underlain by Erdős-Rényi and Barabási-Albert topology containing two servers. Cloud networks involving two communities not necessarily of the same size are also considered in our analysis. The performance of each configuration is quantified in terms of two indices: the cost of communication between the user and the nearest server, and the balance of the distribution of tasks between the two servers. Regarding the latter index, the ER topology provides better performance than the BA case for smaller average degrees and opposite behavior for larger average degrees. With respect to the cost, smaller values are found in the BA topology irrespective of the average degree. In addition, we also verified that it is easier to find good servers in the ER than in BA. Surprisingly, balance and cost are not too much affected by the presence of communities. However, for a well-defined community network, we found that it is important to assign each server to a different community so as to achieve better performance.PACS. 89.75.Fb Structures and organization in complex systems -89.20.Ff Computer science and technology -89.20.Hh World Wide Web, Internet

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