
-
Previous Article
Utility maximization for bandwidth allocation in peer-to-peer file-sharing networks
- JIMO Home
- This Issue
-
Next Article
The (functional) law of the iterated logarithm of the sojourn time for a multiclass queue
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] | |
[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 |
[5] | |
[6] | |
[7] |
http://www.coindesk.com/segregated-witness-bitcoin-block-size-debate/ |
[8] |
S. Kasahara and J. Kawahara, Effect of Bitcoin fee on transaction-confirmation process, arXiv: 1604.00103[cs.CR]. |
[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. |
[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. |
[12] |
J. Poon and T. Dryja, The bitcoin lightning network: Scalable off-chain instant payments, https://lightning.network/lightning-network-paper.pdf, 2016. |
[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 |
[15] |
F. Tschorsch and B. Scheuermann,
Bitcoin and beyond: A technical survey on decentralized digital currencies, Tutorials, 18 (2016), 2084-2123.
|
[16] | |
[17] |
https://www.coindesk.com/segwits-slow-rollout-bitcoins-capacity-hasnt-seen/ |
show all references
References:
[1] | |
[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 |
[5] | |
[6] | |
[7] |
http://www.coindesk.com/segregated-witness-bitcoin-block-size-debate/ |
[8] |
S. Kasahara and J. Kawahara, Effect of Bitcoin fee on transaction-confirmation process, arXiv: 1604.00103[cs.CR]. |
[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. |
[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. |
[12] |
J. Poon and T. Dryja, The bitcoin lightning network: Scalable off-chain instant payments, https://lightning.network/lightning-network-paper.pdf, 2016. |
[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 |
[15] |
F. Tschorsch and B. Scheuermann,
Bitcoin and beyond: A technical survey on decentralized digital currencies, Tutorials, 18 (2016), 2084-2123.
|
[16] | |
[17] |
https://www.coindesk.com/segwits-slow-rollout-bitcoins-capacity-hasnt-seen/ |













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 |
[1] |
Shoji Kasahara, Jun Kawahara. Effect of Bitcoin fee on transaction-confirmation process. Journal of Industrial and Management Optimization, 2019, 15 (1) : 365-386. doi: 10.3934/jimo.2018047 |
[2] |
Yung Chung Wang, Jenn Shing Wang, Fu Hsiang Tsai. Analysis of discrete-time space priority queue with fuzzy threshold. Journal of Industrial and Management Optimization, 2009, 5 (3) : 467-479. doi: 10.3934/jimo.2009.5.467 |
[3] |
Hideaki Takagi. Unified and refined analysis of the response time and waiting time in the M/M/m FCFS preemptive-resume priority queue. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1945-1973. doi: 10.3934/jimo.2017026 |
[4] |
Arnaud Devos, Joris Walraevens, Tuan Phung-Duc, Herwig Bruneel. Analysis of the queue lengths in a priority retrial queue with constant retrial policy. Journal of Industrial and Management Optimization, 2020, 16 (6) : 2813-2842. doi: 10.3934/jimo.2019082 |
[5] |
Shaojun Lan, Yinghui Tang. Performance analysis of a discrete-time $ Geo/G/1$ retrial queue with non-preemptive priority, working vacations and vacation interruption. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1421-1446. doi: 10.3934/jimo.2018102 |
[6] |
Dhanya Shajin, A. N. Dudin, Olga Dudina, A. Krishnamoorthy. A two-priority single server retrial queue with additional items. Journal of Industrial and Management Optimization, 2020, 16 (6) : 2891-2912. doi: 10.3934/jimo.2019085 |
[7] |
Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial and Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049 |
[8] |
Biao Xu, Xiuli Xu, Zhong Yao. Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1599-1615. doi: 10.3934/jimo.2018113 |
[9] |
Zhanyou Ma, Wenbo Wang, Linmin Hu. Performance evaluation and analysis of a discrete queue system with multiple working vacations and non-preemptive priority. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1135-1148. doi: 10.3934/jimo.2018196 |
[10] |
Sofian De Clercq, Koen De Turck, Bart Steyaert, Herwig Bruneel. Frame-bound priority scheduling in discrete-time queueing systems. Journal of Industrial and Management Optimization, 2011, 7 (3) : 767-788. doi: 10.3934/jimo.2011.7.767 |
[11] |
Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discrete-time finite buffer queue. Journal of Industrial and Management Optimization, 2016, 12 (3) : 1121-1133. doi: 10.3934/jimo.2016.12.1121 |
[12] |
Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial and Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167 |
[13] |
Yongjiang Guo, Yuantao Song. The (functional) law of the iterated logarithm of the sojourn time for a multiclass queue. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1049-1076. doi: 10.3934/jimo.2018192 |
[14] |
Tuan Phung-Duc, Ken'ichi Kawanishi. Multiserver retrial queue with setup time and its application to data centers. Journal of Industrial and Management Optimization, 2019, 15 (1) : 15-35. doi: 10.3934/jimo.2018030 |
[15] |
Yutaka Sakuma, Atsushi Inoie, Ken’ichi Kawanishi, Masakiyo Miyazawa. Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time. Journal of Industrial and Management Optimization, 2011, 7 (3) : 593-606. doi: 10.3934/jimo.2011.7.593 |
[16] |
Thomas Demoor, Joris Walraevens, Dieter Fiems, Stijn De Vuyst, Herwig Bruneel. Influence of real-time queue capacity on system contents in DiffServ's expedited forwarding per-hop-behavior. Journal of Industrial and Management Optimization, 2010, 6 (3) : 587-602. doi: 10.3934/jimo.2010.6.587 |
[17] |
Gopinath Panda, Veena Goswami. Effect of information on the strategic behavior of customers in a discrete-time bulk service queue. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1369-1388. doi: 10.3934/jimo.2019007 |
[18] |
Bart Feyaerts, Stijn De Vuyst, Herwig Bruneel, Sabine Wittevrongel. The impact of the $NT$-policy on the behaviour of a discrete-time queue with general service times. Journal of Industrial and Management Optimization, 2014, 10 (1) : 131-149. doi: 10.3934/jimo.2014.10.131 |
[19] |
Michiel De Muynck, Herwig Bruneel, Sabine Wittevrongel. Analysis of a discrete-time queue with general service demands and phase-type service capacities. Journal of Industrial and Management Optimization, 2017, 13 (4) : 1901-1926. doi: 10.3934/jimo.2017024 |
[20] |
Archana Prashanth Joshi, Meng Han, Yan Wang. A survey on security and privacy issues of blockchain technology. Mathematical Foundations of Computing, 2018, 1 (2) : 121-147. doi: 10.3934/mfc.2018007 |
2021 Impact Factor: 1.411
Tools
Metrics
Other articles
by authors
[Back to Top]