Effect of Bitcoin fee on transaction-confirmation process

Shoji Kasahara; Jun Kawahara

doi:10.3934/jimo.2018047

Article Contents

2019, Volume 15, Issue 1: 365-386. Doi: 10.3934/jimo.2018047

This issue Previous Article Pricing decisions for complementary products in a fuzzy dual-channel supply chain Next Article A class of two-stage distributionally robust games

Effect of Bitcoin fee on transaction-confirmation process

Shoji Kasahara^, and
Jun Kawahara

Graduate School of Information Science, Nara Institute of Science and Technology, Takayama 8916-5, Ikoma, Nara 6300192, Japan

* Corresponding author: Shoji Kasahara
* Corresponding author: Shoji Kasahara

Received: June 2017

Revised: October 2017

Early access: April 2018

Published: January 2019

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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Abstract

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.

Keywords:

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

Citation:

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Figure 1. Trend of fee-amount distribution over time

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

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

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

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Figure 5. Mean transaction-confirmation time: classless case

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

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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

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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

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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

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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

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Table 3. Transaction size in byte

Mean	571.34
Variance	$3.7445\times 10^6$
Maximum	999657
Minimum	62
Median	259

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Table 4. Cumulative frequency of fee amount for transactions

BTC	Frequency
0	1378501
0.00001	3050709
0.0001	42881857
0.001	60723356
0.01	61219997
0.1	61236481
1	61236972
10	61237045

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Table 5. Transaction-type statistics

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	$1.8989 \times 10^8$	$8.4505 \times 10^7$	$1.5826 \times 10^9$
Maximum of TCT	$3.1045\times 10^7$	$3.1045\times 10^7$	$2.6244\times 10^7$
Minimum of TCT	0	0	0
Median of TCT	510	502	640
Mean arrival rate	0.97275	0.90466	0.068082

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Table 6. Comparison of analysis and measurement for the transaction-confirmation time

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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