Abstract
The blockchain paradigm provides a mechanism for content dissemination and distributed consensus on Peer-to-Peer (P2P) networks. While this paradigm has been widely adopted in industry, it has not been carefully analyzed in terms of its network scaling with respect to the number of peers. Applications for blockchain systems, such as cryptocurrencies and IoT, require this form of network scaling. In this paper, we propose a new stochastic network model for a blockchain system. We identify a structural property called one-endedness, which we show to be desirable in any blockchain system as it is directly related to distributed consensus among the peers. We show that the stochastic stability of the network is sufficient for the one-endedness of a blockchain. We further establish that our model belongs to a class of network models, called monotone separable models. This allows us to establish upper and lower bounds on the stability region. The bounds on stability depend on the connectivity of the P2P network through its conductance and allow us to analyze the scalability of blockchain systems on large P2P networks. We verify our theoretical insights using both synthetic data and real data from the Bitcoin network.
- Confirmation. https://en.Bitcoin.it/wiki/Confirmation. Online; accessed 20-October-2019.Google Scholar
- David Aldous, Russell Lyons, et al. Processes on unimodular random networks. Electron. J. Probab, 12(54):1454--1508, 2007.Google Scholar
Cross Ref
- François Baccelli and Serguei Foss. On the saturation rule for the stability of queues. Journal of Applied Probability, 32(2):494--507, 1995.Google Scholar
Cross Ref
- Francois Baccelli, Mir-Omid Haji-Mirsadeghi, and Ali Khezeli. Eternal family trees and dynamics on unimodular random graphs. Unimodularity in Randomly Generated Graphs, 719:85, 2018.Google Scholar
Cross Ref
- François Baccelli, Mir-Omid Haji-Mirsadeghi, James T Murphy III, et al. Doeblin trees. Electronic Journal of Probability, 24, 2019.Google Scholar
- François Baccelli, Fabien Mathieu, Ilkka Norros, and Rémi Varloot. Can p2p networks be super-scalable? In 2013 Proceedings IEEE INFOCOM, pages 1753--1761. IEEE, 2013.Google Scholar
Cross Ref
- François Baccelli and Antonio Sodre. Renewal population dynamics and their eternal family trees. arXiv preprint arXiv:1803.08081, 2018.Google Scholar
- Vivek Bagaria, Sreeram Kannan, David Tse, Giulia Fanti, and Pramod Viswanath. Prism: Deconstructing the blockchain to approach physical limits. In Proceedings of the 2019 ACM SIGSAC Conference on Computer and Communications Security, pages 585--602. ACM, 2019.Google Scholar
Digital Library
- Itai Benjamini and Oded Schramm. Recurrence of distributional limits of finite planar graphs. In Selected Works of Oded Schramm, pages 533--545. Springer, 2011.Google Scholar
Cross Ref
- Blockchair. Bitcoin database dump. https://gz.blockchair.com/Bitcoin/blocks/. Online; accessed 20-Janurary-2020.Google Scholar
- Shaileshh Bojja Venkatakrishnan, Giulia Fanti, and Pramod Viswanath. Dandelion: Redesigning the bitcoin network for anonymity. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 1(1):22, 2017.Google Scholar
- Vitalik Buterin et al. Ethereum white paper. GitHub repository, pages 22--23, 2013.Google Scholar
- Flavio Chierichetti, Silvio Lattanzi, and Alessandro Panconesi. Rumour spreading and graph conductance. In Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms, pages 1657--1663. SIAM, 2010.Google Scholar
Digital Library
- Christian Decker and RogerWattenhofer. Information propagation in the bitcoin network. In IEEE P2P 2013 Proceedings, pages 1--10. IEEE, 2013.Google Scholar
- Alexandros G Dimakis, Anand D Sarwate, and Martin J Wainwright. Geographic gossip: Efficient aggregation for sensor networks. In Proceedings of the 5th international conference on Information processing in sensor networks, pages 69--76, 2006.Google Scholar
- Ittay Eyal, Adem Efe Gencer, Emin Gün Sirer, and Robbert Van Renesse. Bitcoin-ng: A scalable blockchain protocol. In 13th {USENIX} symposium on networked systems design and implementation ({NSDI} 16), pages 45--59, 2016.Google Scholar
- Ittay Eyal and Emin Gün Sirer. Majority is not enough: Bitcoin mining is vulnerable. Communications of the ACM, 61(7):95--102, 2018.Google Scholar
Digital Library
- Michalis Faloutsos, Petros Faloutsos, and Christos Faloutsos. On power-law relationships of the internet topology. In ACM SIGCOMM computer communication review, volume 29, pages 251--262. ACM, 1999.Google Scholar
- Giulia Fanti, Shaileshh Bojja Venkatakrishnan, Surya Bakshi, Bradley Denby, Shruti Bhargava, Andrew Miller, and Pramod Viswanath. Dandelion++: Lightweight cryptocurrency networking with formal anonymity guarantees. Proceedings of the ACM on Measurement and Analysis of Computing Systems, 2(2):29, 2018.Google Scholar
Digital Library
- Serguei Foss and Takis Konstantopoulos. An overview of some stochastic stability methods (<special issue> network design, control and optimization). Journal of the Operations Research Society of Japan, 47(4):275--303, 2004.Google Scholar
Cross Ref
- Nikolaos Fountoulakis and Konstantinos Panagiotou. Rumor spreading on random regular graphs and expanders. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pages 560--573. Springer, 2010.Google Scholar
- Nikolaos Fountoulakis, Konstantinos Panagiotou, and Thomas Sauerwald. Ultra-fast rumor spreading in social networks. In Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms, pages 1642--1660. SIAM, 2012.Google Scholar
Digital Library
- Maria Frolkova and Michel Mandjes. A bitcoin-inspired infinite-server model with a random fluid limit. Stochastic Models, 35(1):1--32, 2019.Google Scholar
Cross Ref
- Ayalvadi Ganesh. Rumor spreading on graphs, 2015.Google Scholar
- Juan Garay, Aggelos Kiayias, and Nikos Leonardos. The bitcoin backbone protocol: Analysis and applications. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 281--310. Springer, 2015.Google Scholar
Cross Ref
- Adem Efe Gencer, Soumya Basu, Ittay Eyal, Robbert Van Renesse, and Emin Gün Sirer. Decentralization in bitcoin and ethereum networks. In International Conference on Financial Cryptography and Data Security, pages 439--457. Springer, 2018.Google Scholar
Cross Ref
- Arthur Gervais, Ghassan Karame, Karl WÃ'st, Vasileios Glykantzis, Hubert Ritzdorf, and Srdjan Capkun. On the security and performance of proof of work blockchains. In Proceedings of the 23nd ACM SIGSAC Conference on Computer and Communication Security (CCS). ACM, 2016.Google Scholar
Digital Library
- Johannes Göbel, Holger Paul Keeler, Anthony E Krzesinski, and Peter G Taylor. Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay. Performance Evaluation, 104:23--41, 2016.Google Scholar
Cross Ref
- Rudolf Halin. Über unendliche wege in graphen. Mathematische Annalen, 157(2):125--137, 1964.Google Scholar
Cross Ref
- Stratis Ioannidis, Augustin Chaintreau, and Laurent Massoulié. Optimal and scalable distribution of content updates over a mobile social network. In IEEE INFOCOM 2009, pages 1422--1430. IEEE, 2009.Google Scholar
Cross Ref
- Svante Janson, Tomasz Luczak, and Andrzej Rucinski. Random graphs, volume 45. John Wiley & Sons, 2011.Google Scholar
- Sanjit Kaul, Roy Yates, and Marco Gruteser. Real-time status: How often should one update? In 2012 Proceedings IEEE INFOCOM, pages 2731--2735. IEEE, 2012.Google Scholar
Cross Ref
- Yoshiaki Kawase and Shoji Kasahara. Transaction-confirmation time for bitcoin: a queueing analytical approach to blockchain mechanism. In International Conference on Queueing Theory and Network Applications, pages 75--88. Springer, 2017.Google Scholar
Cross Ref
- Frank P Kelly. Reversibility and stochastic networks. Cambridge University Press, 2011.Google Scholar
Digital Library
- Michael Krivelevich, Benny Sudakov, Van H Vu, and Nicholas C Wormald. Random regular graphs of high degree. Random Structures & Algorithms, 18(4):346--363, 2001.Google Scholar
Digital Library
- Yoad Lewenberg, Yonatan Sompolinsky, and Aviv Zohar. Inclusive block chain protocols. In International Conference on Financial Cryptography and Data Security, pages 528--547. Springer, 2015.Google Scholar
Cross Ref
- Quan-Lin Li, Jing-Yu Ma, and Yan-Xia Chang. Blockchain queue theory. In International Conference on Computational Social Networks, pages 25--40. Springer, 2018.Google Scholar
Cross Ref
- Quan-Lin Li, Jing-Yu Ma, Yan-Xia Chang, Fan-Qi Ma, and Hai-Bo Yu. Markov processes in blockchain systems. arXiv preprint arXiv:1904.03598, 2019.Google Scholar
- Russell Lyons and Yuval Peres. Probability on trees and networks, volume 42. Cambridge University Press, 2017.Google Scholar
- Laurent Massoulié and Milan Vojnovi?. Coupon replication systems. In ACM SIGMETRICS Performance Evaluation Review, volume 33, pages 2--13. ACM, 2005.Google Scholar
- Milena Mihail, Christos Papadimitriou, and Amin Saberi. On certain connectivity properties of the internet topology. In 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings., pages 28--35. IEEE, 2003.Google Scholar
Cross Ref
- Jelena Misic, Vojislav B Misic, Xiaolin Chang, Saeideh Gholamrezazadeh Motlagh, and Zulfiker M Ali. Modeling of bitcoin's blockchain delivery network. IEEE Transactions on Network Science and Engineering, 2019.Google Scholar
Cross Ref
- Satoshi Nakamoto. Bitcoin: A peer-to-peer electronic cash system. 2008.Google Scholar
- Mark Newman. Networks. Oxford university press, 2018.Google Scholar
- Konstantinos Panagiotou and Leo Speidel. Asynchronous rumor spreading on random graphs. Algorithmica, 78(3):968-- 989, 2017.Google Scholar
Digital Library
- Nikolaos Papadis, Sem Borst, AnwarWalid, Mohamed Grissa, and Leandros Tassiulas. Stochastic models and wide-area network measurements for blockchain design and analysis. In IEEE INFOCOM 2018-IEEE Conference on Computer Communications, pages 2546--2554. IEEE, 2018.Google Scholar
Cross Ref
- Rafael Pass, Lior Seeman, and Abhi Shelat. Analysis of the blockchain protocol in asynchronous networks. In Annual International Conference on the Theory and Applications of Cryptographic Techniques, pages 643--673. Springer, 2017.Google Scholar
Cross Ref
- Rafael Pass and Elaine Shi. Fruitchains: A fair blockchain. In Proceedings of the ACM Symposium on Principles of Distributed Computing, pages 315--324. ACM, 2017.Google Scholar
Digital Library
- Mathew Penrose et al. Random geometric graphs, volume 5. Oxford university press, 2003.Google Scholar
- Sergei Popov. Iota whitepaper. Technical White Paper, year= 2017, 2017.Google Scholar
- Dongyu Qiu and Rayadurgam Srikant. Modeling and performance analysis of bittorrent-like peer-to-peer networks. In ACM SIGCOMM computer communication review, volume 34, pages 367--378. ACM, 2004.Google Scholar
- Sridharan Ranganathan, Alan D George, Robert W Todd, and Matthew C Chidester. Gossip-style failure detection and distributed consensus for scalable heterogeneous clusters. Cluster Computing, 4(3):197--209, 2001.Google Scholar
Digital Library
- Saulo Ricci, Eduardo Ferreira, Daniel Sadoc Menasche, Artur Ziviani, Jose Eduardo Souza, and Alex Borges Vieira. Learning blockchain delays: a queueing theory approach. ACM SIGMETRICS Performance Evaluation Review, 46(3):122-- 125, 2019.Google Scholar
Digital Library
- Sujay Sanghavi, Bruce Hajek, and Laurent Massoulié. Gossiping with multiple messages. IEEE Transactions on Information Theory, 53(12):4640--4654, 2007.Google Scholar
Digital Library
- Devavrat Shah et al. Gossip algorithms. Foundations and Trends® in Networking, 3(1):1--125, 2009.Google Scholar
Digital Library
- Yonatan Sompolinsky and Aviv Zohar. Secure high-rate transaction processing in bitcoin. In International Conference on Financial Cryptography and Data Security, pages 507--527. Springer, 2015.Google Scholar
Cross Ref
- David Tse and Pramod Viswanath. Fundamentals of wireless communication. Cambridge university press, 2005.Google Scholar
- Valery Ugrinovskii. Conditions for detectability in distributed consensus-based observer networks. IEEE Transactions on Automatic Control, 58(10):2659--2664, 2013.Google Scholar
Cross Ref
- Remco Van Der Hofstad. Random graphs and complex networks. Available on http://www. win. tue. nl/rhofstad/NotesRGCN. pdf, 11, 2009.Google Scholar
- Lei Yang, Vivek Bagaria, Gerui Wang, Mohammad Alizadeh, David Tse, Giulia Fanti, and Pramod Viswanath. Prism: Scaling bitcoin by 10,000 x. arXiv preprint arXiv:1909.11261, 2019.Google Scholar
- Xiangying Yang and Gustavo De Veciana. Service capacity of peer to peer networks. In IEEE INFOCOM 2004, volume 4, pages 2242--2252. IEEE, 2004.Google Scholar
Cross Ref
- Ji Zhu and Bruce Hajek. Stability of a peer-to-peer communication system. IEEE Transactions on Information Theory, 58(7):4693--4713, 2012. Proc.Google Scholar
Digital Library
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Stability and Scalability of Blockchain Systems
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