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Effect of Bitcoin fee on transaction-confirmation process
Graduate School of Information Science, Nara Institute of Science and Technology, Takayama 8916-5, Ikoma, Nara 6300192, Japan |
In Bitcoin system, transactions are prioritized according to transaction fees. Transactions without fees are given low priority and likely to wait for confirmation. Because the demand of micro payment in Bitcoin is expected to increase due to low remittance cost, it is important to quantitatively investigate how transactions with small fees of Bitcoin affect the transaction-confirmation time. In this paper, we analyze the transaction-confirmation time by queueing theory. We model the transaction-confirmation process of Bitcoin as a priority queueing system with batch service, deriving the mean transaction-confirmation time. Numerical examples show how the demand of transactions with low fees affects the transaction-confirmation time. We also consider the effect of the maximum block size on the transaction-confirmation time.
References:
[1] |
E. Androulaki, G. O. Karame, M. Roeschlin, T. Scherer and S. Capkun,
Evaluating user privacy in Bitcoin, The 17th International Conference on Financial Cryptography and Data Security, (2013), 34-51.
doi: 10.1007/978-3-642-39884-1_4. |
[2] |
A. M. Antonopoulos, Mastering Bitcoin, O'Reilly, 2014. Google Scholar |
[3] |
T. Bamert, C. Decker, L. Elsen, R. Wattenhofer and S. Welten,
Have a snack, pay with Bitcoins, 2013 IEEE Thirteenth International Conference on Peer-to-Peer Computing, (2013), 1-5.
doi: 10.1109/P2P.2013.6688717. |
[4] |
R. Böhme, N. Christin, B. Edelman and T. Moore, Bitcoin: Economics, technology, and governance, Journal of Economic Perspectives, 29 (2015), 213-238. Google Scholar |
[5] |
J. Bonneau, A. Miller, J. Clark, A. Narayanan, J. A. Kroll and E. W. Felten,
SoK: Research perspectives and challenges for Bitcoin and cryptocurrencies, IEEE Symposium on Security and Privacy, (2015), 104-121.
doi: 10.1109/SP.2015.14. |
[6] |
M. L. Chaudhry and J. G. C. Templeton,
The queuing system M/$ \mbox{G}^{\text B} $/1 and its ramifications, European Journal of Operational Research, 6 (1981), 56-60.
doi: 10.1016/0377-2217(81)90328-3. |
[7] |
M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, John Wiley & Sons, 1983. |
[8] |
C. Decker and R. Wattenhofer,
Information propagation in the Bitcoin network, 13th IEEE International Conference on Peer-to-Peer Computing, (2013), 1-10.
doi: 10.1109/P2P.2013.6688704. |
[9] |
J. Göbel, H. P. Keeler, A. E. Krzesinski and P. G. Taylor, Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay, Performance Evaluation, 104 (2016), 23-41. Google Scholar |
[10] |
G. O. Karame, E. Androulaki and S. Capkun,
Double-spending fast payments in Bitcoin, The 2012 ACM Conference on Computer and Communications Security, (2012), 906-917.
doi: 10.1145/2382196.2382292. |
[11] |
A. Kiayias and G. Panagiotakos, Speed-security tradeoffs in blockchain protocols, IACR: Cryptology ePrint Archive, 2015. Google Scholar |
[12] |
S. Kotz and S. Nadarajah,
Extreme Value Distributions Theory and Applications, Imperial College Press, 2000. |
[13] |
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. |
[14] |
S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system, (2008). Available from https://bitcoin.org/bitcoin.pdf. Google Scholar |
[15] |
R. Peter, A transaction fee market exists without a block size limit, (2015). Available from https://scalingbitcoin.org/papers/feemarket.pdf Google Scholar |
[16] |
Y. Sompolinsky and A. Zohar, Accelerating Bitcoin's transaction processing. Fast money grows on trees, not chains, IACR: Cryptology ePrint Archive, 2013, Available from https://eprint.iacr.org/2013/881. Google Scholar |
[17] |
Y. Sompolinsky and A. Zohar,
Secure high-rate transaction processing in Bitcoin, 19th International Conference on Financial Cryptography and Data Security, 8975 (2015), 507-527.
|
[18] |
H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, North-Holland Publishing Co., Amsterdam, 1993. |
[19] |
F. Tschorsch and B. Scheuermann,
Bitcoin and beyond: A technical survey on decentralized digital currencies, IEEE Communications Surveys & Tutorials, 18 (2016), 2084-2123.
doi: 10.1109/COMST.2016.2535718. |
[20] |
R. W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice Hall, 1989. |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] |
show all references
References:
[1] |
E. Androulaki, G. O. Karame, M. Roeschlin, T. Scherer and S. Capkun,
Evaluating user privacy in Bitcoin, The 17th International Conference on Financial Cryptography and Data Security, (2013), 34-51.
doi: 10.1007/978-3-642-39884-1_4. |
[2] |
A. M. Antonopoulos, Mastering Bitcoin, O'Reilly, 2014. Google Scholar |
[3] |
T. Bamert, C. Decker, L. Elsen, R. Wattenhofer and S. Welten,
Have a snack, pay with Bitcoins, 2013 IEEE Thirteenth International Conference on Peer-to-Peer Computing, (2013), 1-5.
doi: 10.1109/P2P.2013.6688717. |
[4] |
R. Böhme, N. Christin, B. Edelman and T. Moore, Bitcoin: Economics, technology, and governance, Journal of Economic Perspectives, 29 (2015), 213-238. Google Scholar |
[5] |
J. Bonneau, A. Miller, J. Clark, A. Narayanan, J. A. Kroll and E. W. Felten,
SoK: Research perspectives and challenges for Bitcoin and cryptocurrencies, IEEE Symposium on Security and Privacy, (2015), 104-121.
doi: 10.1109/SP.2015.14. |
[6] |
M. L. Chaudhry and J. G. C. Templeton,
The queuing system M/$ \mbox{G}^{\text B} $/1 and its ramifications, European Journal of Operational Research, 6 (1981), 56-60.
doi: 10.1016/0377-2217(81)90328-3. |
[7] |
M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, John Wiley & Sons, 1983. |
[8] |
C. Decker and R. Wattenhofer,
Information propagation in the Bitcoin network, 13th IEEE International Conference on Peer-to-Peer Computing, (2013), 1-10.
doi: 10.1109/P2P.2013.6688704. |
[9] |
J. Göbel, H. P. Keeler, A. E. Krzesinski and P. G. Taylor, Bitcoin blockchain dynamics: The selfish-mine strategy in the presence of propagation delay, Performance Evaluation, 104 (2016), 23-41. Google Scholar |
[10] |
G. O. Karame, E. Androulaki and S. Capkun,
Double-spending fast payments in Bitcoin, The 2012 ACM Conference on Computer and Communications Security, (2012), 906-917.
doi: 10.1145/2382196.2382292. |
[11] |
A. Kiayias and G. Panagiotakos, Speed-security tradeoffs in blockchain protocols, IACR: Cryptology ePrint Archive, 2015. Google Scholar |
[12] |
S. Kotz and S. Nadarajah,
Extreme Value Distributions Theory and Applications, Imperial College Press, 2000. |
[13] |
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. |
[14] |
S. Nakamoto, Bitcoin: A peer-to-peer electronic cash system, (2008). Available from https://bitcoin.org/bitcoin.pdf. Google Scholar |
[15] |
R. Peter, A transaction fee market exists without a block size limit, (2015). Available from https://scalingbitcoin.org/papers/feemarket.pdf Google Scholar |
[16] |
Y. Sompolinsky and A. Zohar, Accelerating Bitcoin's transaction processing. Fast money grows on trees, not chains, IACR: Cryptology ePrint Archive, 2013, Available from https://eprint.iacr.org/2013/881. Google Scholar |
[17] |
Y. Sompolinsky and A. Zohar,
Secure high-rate transaction processing in Bitcoin, 19th International Conference on Financial Cryptography and Data Security, 8975 (2015), 507-527.
|
[18] |
H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, North-Holland Publishing Co., Amsterdam, 1993. |
[19] |
F. Tschorsch and B. Scheuermann,
Bitcoin and beyond: A technical survey on decentralized digital currencies, IEEE Communications Surveys & Tutorials, 18 (2016), 2084-2123.
doi: 10.1109/COMST.2016.2535718. |
[20] |
R. W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice Hall, 1989. |
[21] | |
[22] | |
[23] | |
[24] | |
[25] | |
[26] |








Mean [s] | 544.09 |
Variance | |
Maximum [s] | 6,524 |
Minimum [s] | 0 |
Median [s] | 377 |
Mean [s] | 544.09 |
Variance | |
Maximum [s] | 6,524 |
Minimum [s] | 0 |
Median [s] | 377 |
Mean [transactions] | 529.27 |
Variance | |
Maximum [transactions] | 12,239 |
Minimum [transactions] | 0 |
Median [transactions] | 386 |
Mean [transactions] | 529.27 |
Variance | |
Maximum [transactions] | 12,239 |
Minimum [transactions] | 0 |
Median [transactions] | 386 |
Mean | 571.34 |
Variance | |
Maximum | 999657 |
Minimum | 62 |
Median | 259 |
Mean | 571.34 |
Variance | |
Maximum | 999657 |
Minimum | 62 |
Median | 259 |
BTC | Frequency |
0 | 1378501 |
0.00001 | 3050709 |
0.0001 | 42881857 |
0.001 | 60723356 |
0.01 | 61219997 |
0.1 | 61236481 |
1 | 61236972 |
10 | 61237045 |
BTC | Frequency |
0 | 1378501 |
0.00001 | 3050709 |
0.0001 | 42881857 |
0.001 | 60723356 |
0.01 | 61219997 |
0.1 | 61236481 |
1 | 61236972 |
10 | 61237045 |
Statistic | Classless | H | L |
Number of transactions | 61,353,014 | 57,058,947 | 4,294,067 |
Mean TCT [s] | 1075.0 | 874.13 | 3744.1 |
Variance of TCT | | | |
Maximum of TCT | | | |
Minimum of TCT | 0 | 0 | 0 |
Median of TCT | 510 | 502 | 640 |
Mean arrival rate | 0.97275 | 0.90466 | 0.068082 |
Statistic | Classless | H | L |
Number of transactions | 61,353,014 | 57,058,947 | 4,294,067 |
Mean TCT [s] | 1075.0 | 874.13 | 3744.1 |
Variance of TCT | | | |
Maximum of TCT | | | |
Minimum of TCT | 0 | 0 | 0 |
Median of TCT | 510 | 502 | 640 |
Mean arrival rate | 0.97275 | 0.90466 | 0.068082 |
Transaction Type | Arrival Rate | Measurement | Analysis |
Classless | 0.97275 | 1,075.0 | 568.10 |
H | 0.90466 | 874.13 | 562.16 |
L | 0.068082 | 3,744.1 | 647.05 |
Transaction Type | Arrival Rate | Measurement | Analysis |
Classless | 0.97275 | 1,075.0 | 568.10 |
H | 0.90466 | 874.13 | 562.16 |
L | 0.068082 | 3,744.1 | 647.05 |
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