Analysis of blockchain system based on $$\hbox {M}/(\hbox {M}_1,\hbox {M}_2)/1$$ vacation queueing model | The Journal of Supercomputing Skip to main content
Springer Nature Link
Log in

Analysis of blockchain system based on \(\hbox {M}/(\hbox {M}_1,\hbox {M}_2)/1\) vacation queueing model

  • Published:
The Journal of Supercomputing Aims and scope Submit manuscript

Abstract

With the rapid development of technology, the issues about blockchain are getting more and more attention from scholars. In order to study the operation of the blockchain system, this paper simulated the transaction confirmation process of a blockchain system with two miners. Combining with practice, factors such as adverse transactions, impatience phenomena of transactions, fault repairable conditions of the mining process and a spare miner are considered. An M/(M\(_1\),M\(_2\))/1 vacation queueing model with negative customers, impatient customers, optional services, repairable faults and a spare server is established. The stationary distribution of the system is obtained by using the matrix-geometric solution method, and expressions of the average confirmation time of transactions and other performance indexes are given. The influence of each parameter on the performance indexes of blockchain system is analyzed by using MATLAB software. Revenue function and equilibrium sleep rate of miners are discussed for optimizing the blockchain system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Shen X, Pei QQ, Liu XF (2016) Survey of blockchain. Chin J Netw Inf Secur 2(11):11–20 (in Chinese)

    Google Scholar 

  2. Karthika V, Jaganathan S (2019) A quick synopsis of blockchain technology. Int J Blockchains Cryptocurrencies 1(1):54–66

    Article  Google Scholar 

  3. Nakmoto S (2008) Bitcoin: a peer-to-peer electronic cash system. https://bitcoin.org/bitcoin.pdf

  4. Swan M (2015) Blockchain thinking: the brain as a decentralized autonomous corporation. IEEE Technol Soc Mag 34(4):41–52

    Article  Google Scholar 

  5. Tapscott D, Tapscott A (2017) How blockchain will change organizations. Mit Sloan Manag Rev 58(2):10–13

    Google Scholar 

  6. Zhu XX, He QS, Guo SQ (2018) On the role of blockchain technology in supply chain finance. China Business and Market 32(3):111–119 (in Chinese)

    Google Scholar 

  7. Garcia AR, Garcia PHR (2019) Cryptocurrencies: the communication inside blockchain technology and the cross-border tax law. Int J Blockchains Cryptocurrencies 1(1):22–41

    Article  Google Scholar 

  8. Shah B, Shah N, Shakhla S, Sawant V (2018) Remodeling the healthcare industry by employing blockchain technology. In: 2018 International Conference on Circuits and Systems in Digital Enterprise Technology (ICCSDET) Kottayam, India, pp 1–5

  9. Om P, Bashir A, Vinay T, Surendra S (2019) Key management for blockchain technology. ICT Express. https://doi.org/10.1016/j.icte.2019.08.002

    Article  Google Scholar 

  10. Chen Y, Xie H, Lv K, Wei SJ, Hu CZ (2019) A blockchain-based privacy-preserving distributed database toward user behaviors in social networks. Inf Sci 501:100–117

    Article  Google Scholar 

  11. Zhao Y, Liu Y, Tian A, Yu Y, Du XJ (2019) Blockchain based privacy-preserving software updates with proof-of-delivery for internet of things. J Parallel Distribu Comput 132:141–149

    Article  Google Scholar 

  12. Alberto AB, Alfio L, Giacomo M, Salvatore Q (2019) On the use of blockchain technologies in WiFi networks. Computer Netw. https://doi.org/10.1016/j.comnet.2019.07.011

    Article  Google Scholar 

  13. Liu Y, He D, Obaidat MS, Kumar N, Khan MK, Raymond Choo KK (2020) Blockchain-based identity management systems: a review. J Netw Computer Appl. https://doi.org/10.1016/j.jnca.2020.102731

    Article  Google Scholar 

  14. Hao W, Zeng J, Dai X, Xiao J (2019) BlockP2P: enabling fast blockchain broadcast with scalable peer-to-peer network topology. In: Miani R, Camargos L, et al. (eds) Green, Pervasive, and Cloud Computing. GPC 2019. Lecture Notes in Computer Science, Springer, Cham, 11484, pp 223–237

  15. Zhou W, Wu X (2006) Survey of P2P technologies. Computer Eng Design 27(1):76–79 (in Chinese)

    Google Scholar 

  16. Raul A, Kalyanaraman S, Yerande K, Devadkar K (2019) Blockchain technology for decentralized data storage on P2P network. In: Wang J, Reddy G, Prasad V, Reddy V (eds) Soft Computing and Signal Processing. Advances in Intelligent Systems and Computing, Springer, Singapore, 900:101-110

  17. Du Y, Li X, Cheng S, Guo Y (2019) Blockchain based distributed network architecture. In: Yu Q (ed) Space Information Networks. SINC 2018. Communications in Computer and Information Science, Springer, Singapore 972, pp 10–14

  18. Wu Y, Li J (2019) Evolution process of blockchain P2P network protocol. Appl Res Comput 36(10):2281–2286 (in Chinese)

    Google Scholar 

  19. Hao W, Zeng J, Dai X et al (2020) Towards a trust-enhanced blockchain P2P topology for enabling fast and reliable broadcast. IEEE Trans Netw Serv Manage 17(2):904–917

    Article  Google Scholar 

  20. Yu C, Jiang X, Yu S, Yang C (2020) Blockchain-based shared manufacturing in support of cyber physical systems: concept, framework, and operation. Robotics Computer Integrated Manuf. https://doi.org/10.1016/j.rcim.2019.101931

    Article  Google Scholar 

  21. Lee Y, Lee KM, Lee SH (2020) Blockchain-based reputation management for custom manufacturing service in the peer-to-peer networking environment. Peer-to-Peer Netw 13:671–683. https://doi.org/10.1007/s12083-019-00730-6

    Article  Google Scholar 

  22. Srivastava R (2019) Mathematical assessment of blocks acceptance in blockchain using Markov model. Int J Blockchains Cryptocurrencies 1(1):42–53

    Article  Google Scholar 

  23. Li QL, Ma JY, Chang YX (2018) Blockchain queueing theory. In: Chen X, Sen A, Li W, Thai M (eds) Computational Data and Social Networks. CSoNet 2018. Lecture Notes in Computer Science, vol 11280. Springer, Cham, pp 25–40

  24. Li QL, Ma JY, Chang YX, Ma FQ, Yu HB (2019) Markov processes in blockchain systems. Comput Social Netw 6(5):1–28

    Google Scholar 

  25. Kasahara S, Kawahara J (2019) Effect of bitcoin fee on transaction confirmation process. J Ind Manage Opt 15(1):365–386

    MathSciNet  MATH  Google Scholar 

  26. Kawase Y, Kasahara S (2017) Transaction-confirmation time for bitcoin: a queueing analytical approach to blockchain mechanism. In: International Conference on Queueing Theory and Network Applications pp. 75–88

  27. Li JJ, Yuan Y, Wang S, Wang FY (2018) Transaction queuing game in bitcoin blockchain. In: IEEE Intelligent Vehicles Symposium, Changshu. https://doi.org/10.1109/IVS.2018.8500403

  28. Taylor PJ, Dargahi T, Dehghantanha A, Parizi RM, Choo KR (2019) A systematic literature review of blockchain cyber security. Digital Commun Netw. https://doi.org/10.1016/j.dcan.2019.01.005

    Article  Google Scholar 

  29. Mohanta BK, Jena D, Panda SS, Sobhanayak S (2019) Blockchain technology: a survey on applications and security privacy challenges. Internet of Things. https://doi.org/10.1016/j.iot.2019.100107

    Article  Google Scholar 

  30. Chicarino V, Albuquerque C, Jesus E, Rocha A (2020) On the detection of selfish mining and stalker attacks in blockchain networks. Ann Telecommun 75:143–152

    Article  Google Scholar 

  31. Xu X, Wang X, Song X, Li X (2018) Fluid model modulated by an M/M/1 working vacation queue with negative customer. Acta Mathe Appl Sinica, English Ser 34:404–415

    Article  MathSciNet  Google Scholar 

  32. Yue DQ, Ma JW, Ma JM, Yu J (2009) Analysis of a repairable queueing system with spare servers. J Shandong Univ (Nat Sci) 44(3):39–44 (in Chinese)

    MathSciNet  MATH  Google Scholar 

  33. Feng YG (2011) \(\text{ M}^{X}\)/(\(\text{ G}_1,\text{ G}_2\))/1 queueing system with balking and negative customer arrivers under single vacation policy. J Fuyang Teachers College (Nat Sci) 28(2):18–21+106 (in Chinese)

  34. Sedlmeir J, Buhl HU, Fridgen G, Keller R (2020) The energy consumption of blockchain technology: beyond myth. Bus Inf Syst Eng. https://doi.org/10.1007/s12599-020-00656-x

    Article  Google Scholar 

  35. Ghosh E, Das B (2020) A study on the issue of blockchain’s energy consumption. In: Chakraborty M, Chakrabarti S, Balas V (eds) Proceedings of International Ethical Hacking Conference 2019. eHaCON 2019. Advances in Intelligent Systems and Computing, Springer, Singapore 1065, pp. 63–75

  36. Hassani H, Huang X, Silva ES (2019) Big data and blockchain. Fusing big data, blockchain and cryptocurrency. Palgrave Pivot, Cham, pp 7–48

    Chapter  Google Scholar 

  37. Yin CX, Jin SF (2018) An energy-saving strategy based on multi-server vacation queuing theory in cloud data center. J Supercomput 74:6766–6784

    Article  Google Scholar 

  38. Li C, Tang J, Luo YL (2018) Multi-queue scheduling of heterogeneous jobs in hybrid geo-distributed cloud environment. J Supercomput 74:5263–5292

    Article  Google Scholar 

  39. Schellhaas H (1999) A modified kolmogorov-smirnov test for a rectangular distribution with unknown parameters: computation of the distribution of the test statistic. Stat Pap 40(3):343–349

    Article  MathSciNet  Google Scholar 

  40. Tian NS, Yue DQ (2002) The quasi birth and death process and matrix-geometric solution. Science Press, Beijing (in Chinese)

    Google Scholar 

  41. Wu DA, Takagi H (2006) M/G/1 queue with multiple working vacations. Perform Eval 63(7):654–681

    Article  Google Scholar 

  42. Yu SL, Liu ZM, Wu JB (2006) Equilibrium strategies of the unobservable M/M/1 queue with balking and delayed repairs. Appl Math Comput 290:56–65

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61973261, 61872311, Natural Science Foundation of Hebei Province under Grant Nos. A2020203010, A2018203088, Key Foundation of Higher Education Science and Technology Research of Hebei Province under Grant No. ZD2017079.

Author information

Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, 066004, China

    Jiaqi Fan, Zhanyou Ma, Yang Zhang & Changzhen Zhang

Authors
  1. Jiaqi Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhanyou Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yang Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Changzhen Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhanyou Ma.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fan, J., Ma, Z., Zhang, Y. et al. Analysis of blockchain system based on \(\hbox {M}/(\hbox {M}_1,\hbox {M}_2)/1\) vacation queueing model. J Supercomput 77, 3673–3694 (2021). https://doi.org/10.1007/s11227-020-03408-6

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11227-020-03408-6

Keywords

Search

Navigation