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Effect of Bitcoin fee on transaction-confirmation process

  • * Corresponding author: Shoji Kasahara

    * Corresponding author: Shoji Kasahara 

The first author is supported in part by SCAT Foundation, and Japan Society for the Promotion of Science under Grant-in-Aid for Scientific Research (B) No. 15H04008

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  • 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.

    Mathematics Subject Classification: Primary: 68M20, 60K25; Secondary: 90B22.


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  • Figure 1.  Trend of fee-amount distribution over time

    Figure 2.  Trend of transaction-arrival rates of two priority classes

    Figure 3.  Relative frequency and exponential probability density function of block-generation time

    Figure 4.  Comparison of analysis and simulation for the transaction-confirmation time: Two-priority case

    Figure 5.  Mean transaction-confirmation time: classless case

    Figure 6.  Mean transaction-confirmation time: two-priority case. ($\lambda_H = 0.90466$)

    Figure 7.  Mean transaction-confirmation time: high priority case. The ratio of $\lambda_H$ to $\lambda_L$ is fixed, and the overall arrival rate $\lambda$ changes

    Figure 8.  Mean transaction-confirmation time: low priority case. The ratio of $\lambda_H$ to $\lambda_L$ is fixed, and the overall arrival rate $\lambda$ changes

    Table 1.  Block-generation time

    Mean [s]544.09
    Variance $2.9277 \times 10^{5}$
    Maximum [s]6,524
    Minimum [s]0
    Median [s]377
     | Show Table
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    Table 2.  Number of transactions in a block

    Mean [transactions]529.27
    Variance $2.5152 \times 10^5$
    Maximum [transactions]12,239
    Minimum [transactions]0
    Median [transactions]386
     | Show Table
    DownLoad: CSV

    Table 3.  Transaction size in byte

    Variance $3.7445\times 10^6$
     | Show Table
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    Table 4.  Cumulative frequency of fee amount for transactions

     | Show Table
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    Table 5.  Transaction-type statistics

    Number of transactions61,353,01457,058,9474,294,067
    Mean TCT [s]1075.0874.133744.1
    Variance of TCT $1.8989 \times 10^8$ $8.4505 \times 10^7$ $1.5826 \times 10^9$
    Maximum of TCT $3.1045\times 10^7$ $3.1045\times 10^7$ $2.6244\times 10^7$
    Minimum of TCT000
    Median of TCT510502640
    Mean arrival rate0.972750.904660.068082
     | Show Table
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    Table 6.  Comparison of analysis and measurement for the transaction-confirmation time

    Transaction TypeArrival RateMeasurementAnalysis
     | Show Table
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