International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Semi-Markov Based Dependability Modeling of Bitcoin Nodes Under Eclipse Attacks and State-Dependent Mitigation

Chencheng Zhou
Department of Electrical and Computer Engineering, University of Massachusetts, Dartmouth, MA, USA.

Liudong Xing
Department of Electrical and Computer Engineering, University of Massachusetts, Dartmouth, MA, USA.

Qisi Liu
Department of Electrical and Computer Engineering, University of Massachusetts, Dartmouth, MA, USA.

Honggang Wang
Department of Electrical and Computer Engineering, University of Massachusetts, Dartmouth, MA, USA.


Received on October 30, 2020
Accepted on December 21, 2020


The block chain technology has immense potential in many different applications, including but not limited to cryptocurrencies, financial services, smart contracts, supply chains, healthcare services, and energy trading. Due to the critical nature of these applications, it is pivotal to model and evaluate dependability of the block chain-based systems, contributing to their reliable and robust operation. This paper models and analyzes the dependability of Bitcoin nodes subject to Eclipse attacks and state-dependent mitigation activities. Built upon the block chain technology, the Bitcoin is a peer-to-peer cryptocurrency system enabling an individual user to trade freely without the involvement of banks or any other types of intermediate agents. However, a node in the Bitcoin is vulnerable to the Eclipse attack, which aims to monopolize the information flow of the victim node. A semi-Markov process (SMP) based approach is proposed to model the Eclipse attack behavior and possible mitigation activities that may prevent the attack from being successful during the attack process. The SMP model is then evaluated to determine the steady-state dependability of the Bitcoin node. Numerical examples are provided to demonstrate the influence of the time to restart the Bitcoin software and time to detect and delete the malicious message on the Bitcoin node dependability.

Keywords- Bitcoin, Block chain, Dependability, Eclipse attack, Semi-Markov process (SMP).


Zhou, C., Xing, L., Liu, Q., & Wang, H. (2021). Semi-Markov Based Dependability Modeling of Bitcoin Nodes Under Eclipse Attacks and State-Dependent Mitigation. International Journal of Mathematical, Engineering and Management Sciences, 6(2), 480-492.

Conflict of Interest

The authors confirm that there is no conflict of interest to declare for this publication.


This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. The authors would like to thank the editor and anonymous reviewers for their comments that help improve the quality of this work.


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