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Priority queueing analysis of transaction-confirmation time for Bitcoin
Graduate School of Information Science, Nara Institute of Science and Technology, Takayama 8916-5, Ikoma, Nara 6300192, Japan |
In Bitcoin system, a transaction is given a priority value according to its attributes such as the remittance amount and fee, and transactions with high priorities are likely to be confirmed faster than those with low priorities. In this paper, we analyze the transaction-confirmation time for Bitcoin system. We model the transaction-confirmation process as a queueing system with batch service, M/$ \mbox{G}^B $/1. We consider the joint distribution of numbers of transactions in system and the elapsed service time, deriving the mean transaction-confirmation time. Using the result, we derive the recursive formulae of mean transaction-confirmation times of an M/$ \mbox{G}^B $/1 queue with priority service discipline. In numerical examples, we show the effect of the maximum block size on the mean transaction-confirmation time, investigating the accuracy region of our queueing model. We also discuss how the increase in micropayments, which are likely to be given low priorities, affects the transaction-confirmation time.
References:
[1] |
A. M. Antonopoulos, Mastering Bitcoin, O'Reilly, 2014. Google Scholar |
[2] |
M. L. Chaudhry and J. G. C. Templeton,
The queuing system M/GB/1 and its ramifications, European Journal of Operational Research, 6 (1981), 56-60.
doi: 10.1016/0377-2217(81)90328-3. |
[3] |
M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, John Wiley & Sons, 1983. |
[4] |
http://www.meti.go.jp/committee/kenkyukai/sansei/fintech\_kadai/pdf/003\_02\_00.pdf Google Scholar |
[5] |
http://www.coindesk.com/1mb-block-size-today-bitcoin/ Google Scholar |
[6] | |
[7] |
http://www.coindesk.com/segregated-witness-bitcoin-block-size-debate/ Google Scholar |
[8] |
S. Kasahara and J. Kawahara, Effect of Bitcoin fee on transaction-confirmation process, arXiv: 1604.00103[cs.CR]. Google Scholar |
[9] |
Y. Kawase and S. Kasahara, Transaction-Confirmation Time for Bitcoin: A Queueing Analytical Approach to Blockchain Mechanism, The 12th International Conference on Queueing Theory and Network Applications (QTNA2017), Qinhuangdao, China, August 21-23, 2017. Google Scholar |
[10] |
M. Möser and R. Böhome,
Trends, tips, tolls: A longitudinal study of bitcoin transaction fees, Financial Cryptography and Data Security, Lecture Notes in Computer Science, Springer, 8976 (2015), 19-33.
doi: 10.1007/978-3-662-48051-9_2. |
[11] |
S. Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System, 2008. Available from: https://bitcoin.org/bitcoin.pdf. Google Scholar |
[12] |
J. Poon and T. Dryja, The bitcoin lightning network: Scalable off-chain instant payments, https://lightning.network/lightning-network-paper.pdf, 2016. Google Scholar |
[13] |
H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vol. 2. Finite systems. North-Holland Publishing Co., Amsterdam, 1993. |
[14] |
https://github.com/bitcoin/bips/blob/master/bip-0141.mediawiki Google Scholar |
[15] |
F. Tschorsch and B. Scheuermann, Bitcoin and beyond: A technical survey on decentralized digital currencies, Tutorials, 18 (2016), 2084-2123. Google Scholar |
[16] | |
[17] |
https://www.coindesk.com/segwits-slow-rollout-bitcoins-capacity-hasnt-seen/ Google Scholar |
show all references
References:
[1] |
A. M. Antonopoulos, Mastering Bitcoin, O'Reilly, 2014. Google Scholar |
[2] |
M. L. Chaudhry and J. G. C. Templeton,
The queuing system M/GB/1 and its ramifications, European Journal of Operational Research, 6 (1981), 56-60.
doi: 10.1016/0377-2217(81)90328-3. |
[3] |
M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, John Wiley & Sons, 1983. |
[4] |
http://www.meti.go.jp/committee/kenkyukai/sansei/fintech\_kadai/pdf/003\_02\_00.pdf Google Scholar |
[5] |
http://www.coindesk.com/1mb-block-size-today-bitcoin/ Google Scholar |
[6] | |
[7] |
http://www.coindesk.com/segregated-witness-bitcoin-block-size-debate/ Google Scholar |
[8] |
S. Kasahara and J. Kawahara, Effect of Bitcoin fee on transaction-confirmation process, arXiv: 1604.00103[cs.CR]. Google Scholar |
[9] |
Y. Kawase and S. Kasahara, Transaction-Confirmation Time for Bitcoin: A Queueing Analytical Approach to Blockchain Mechanism, The 12th International Conference on Queueing Theory and Network Applications (QTNA2017), Qinhuangdao, China, August 21-23, 2017. Google Scholar |
[10] |
M. Möser and R. Böhome,
Trends, tips, tolls: A longitudinal study of bitcoin transaction fees, Financial Cryptography and Data Security, Lecture Notes in Computer Science, Springer, 8976 (2015), 19-33.
doi: 10.1007/978-3-662-48051-9_2. |
[11] |
S. Nakamoto, Bitcoin: A Peer-to-Peer Electronic Cash System, 2008. Available from: https://bitcoin.org/bitcoin.pdf. Google Scholar |
[12] |
J. Poon and T. Dryja, The bitcoin lightning network: Scalable off-chain instant payments, https://lightning.network/lightning-network-paper.pdf, 2016. Google Scholar |
[13] |
H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vol. 2. Finite systems. North-Holland Publishing Co., Amsterdam, 1993. |
[14] |
https://github.com/bitcoin/bips/blob/master/bip-0141.mediawiki Google Scholar |
[15] |
F. Tschorsch and B. Scheuermann, Bitcoin and beyond: A technical survey on decentralized digital currencies, Tutorials, 18 (2016), 2084-2123. Google Scholar |
[16] | |
[17] |
https://www.coindesk.com/segwits-slow-rollout-bitcoins-capacity-hasnt-seen/ Google Scholar |













Period | Classless [s] | Low priority [s] | High priority [s] | |
1st | (2013/10/1-2014/9/30) | 1060.67797 | 1947.47115 | 1044.25043 |
2nd | (2014/10/1-2015/9/30) | 1171.98866 | 4887.56496 | 1070.32818 |
overall | (2013/10/1-2015/9/30) | 1124.13286 | 3888.06977 | 1059.06133 |
Period | Classless [s] | Low priority [s] | High priority [s] | |
1st | (2013/10/1-2014/9/30) | 1060.67797 | 1947.47115 | 1044.25043 |
2nd | (2014/10/1-2015/9/30) | 1171.98866 | 4887.56496 | 1070.32818 |
overall | (2013/10/1-2015/9/30) | 1124.13286 | 3888.06977 | 1059.06133 |
Transaction Type | Arrival Rate | Measurement [s] | Analysis[s] |
Classless | 0.9709120529 | 1124.13286 | 1112.025339 |
High Priority | 0.9349109906 | 1059.06133 | 1108.773595 |
Low Priority | 0.0360010622 | 3888.06977 | 1196.469817 |
Transaction Type | Arrival Rate | Measurement [s] | Analysis[s] |
Classless | 0.9709120529 | 1124.13286 | 1112.025339 |
High Priority | 0.9349109906 | 1059.06133 | 1108.773595 |
Low Priority | 0.0360010622 | 3888.06977 | 1196.469817 |
Period | 1st 2013/10-2014/09 |
2nd 2014/10-2015/09 |
Overall 2013/10-2015/09 |
Classless | 3.72401 | 15.32505 | 10.17893 |
Period | 1st 2013/10-2014/09 |
2nd 2014/10-2015/09 |
Overall 2013/10-2015/09 |
Classless | 3.72401 | 15.32505 | 10.17893 |
Period | 1st 2013/10-2014/09 |
2nd 2014/10-2015/09 |
Overall 2013/10-2015/09 |
Low Priority | 1.66569 | 3.90654 | 3.01387 |
High Priority | 3.70045 | 14.94895 | 9.99103 |
Period | 1st 2013/10-2014/09 |
2nd 2014/10-2015/09 |
Overall 2013/10-2015/09 |
Low Priority | 1.66569 | 3.90654 | 3.01387 |
High Priority | 3.70045 | 14.94895 | 9.99103 |
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