Quantitatively Analyzing Relay Networks in Bitcoin
Kai Otsuki, Ryohei Banno† , and Kazuyuki Shudo
Tokyo Institute of Technology
Tokyo, Japan
ootuki.k.aa@m.titech.ac.jp

Abstract—Bitcoin’s throughput is far lower than those ofcentralized systems such as Visa and PayPal. To handle a
comparable number of transactions, Bitcoin’s throughput must
be improved, which will require a reduction in the blockpropagation time. Relay networks have attracted attention asa method to improve throughput. However, the nature andstrength of the effects of relay networks are not yet clear. In
particular, the effects on individual nodes have received little
attention. Thus, this study aims to investigate the effects of relay
networks on the Bitcoin network and its nodes under the current
network state in approximately 2019. We simulate a relay
network under the current network state because simulation
is virtually the only way to obtain data for all nodes. A major
contribution of this study is that it is the first to investigate therelay network effect on the 90th percentile of block propagation
time. Moreover, this study shows that relay networks benefit
not only the system but also the nodes utilizing them. The
utilizing nodes’ blocks were more than six times more likely to beapproved as valid blocks when nonutilizing and utilizing nodes
generated blocks simultaneously. This finding can motivate theuse of nodes in relay networks.
Index Terms—Bitcoin, blockchain, relay network

I. INTRODUCTION
Blockchain has generated extensive study and economic
interest. The total value of Bitcoin, one of the best-known
cryptocurrencies, exceeded 32 billion USD in 2017. Froma technical perspective, blockchain technologies have solved
some challenges; for example, they can manage information
securely and make it almost impossible to tamper with, evenwhen multiple malicious nodes participate in the network.
In addition, blockchain applications do not need a single
management entity. On the other hand, room for improvement remains. One problem with Bitcoin is low transaction
throughput. Transaction throughput is defined by the numberof transactions that a system can handle per second, and it
is a performance indicator for system capacity. Comparedto centralized systems, the throughput of Bitcoin and manyother blockchain technologies is small. Bitcoin’s throughput
is approximately 7 transactions per second (TPS), whereas
centralized systems such as Visa and PayPal have throughputsof 1776 TPS and 700 TPS, on average [1], [2].
Previous work [3], [4] has demonstrated that reducing
the block propagation time can improve throughput while
retaining the same level of security. One method for providing
faster block propagation is utilizing a relay network. A† Current affiliation as of October 2020: Kogakuin University

relay network is an external network that offers faster blockpropagation, and the nodes utilizing it can receive and send
blocks via the network’s relay servers.
Although there are some measurements of relay networks,
measurements of their effects are still needed. Relay network
operators of Bitcoin [5], [6] make their data available to the
public, but they cannot know the entire set of network data
because their data are real data. Thus, it is impossible toknow the relay network effects on the whole network andon individual nodes from their data. [7] examined the effects
of a relay network when all nodes utilized it, but they did
not consider the effects on individual nodes, such as themining success rate, and they did not reveal the relay network
effects when a portion of the nodes utilized it. Moreover,they simulated the Bitcoin network as of 2015 because theirstudy was conducted in approximately that year. In this study,
we designed a realistic relay network model and performed
simulation on the latest Bitcoin network while changing thenumber of nodes utilizing the relay network to examine theeffects of relay networks on the whole network and theindividual nodes.
Our prior study [8] investigated the relay network effects
by simulation. However, there are two significant differences
between this work and the previous work; simulation accuracy
and detailed analysis. In the previous work, the relay networkmodel was quite simple and primitive, and it simulated the
Bitcoin network as of 2015. Simulations of the latest Bitcoin
network are needed because network parameters such as
bandwidth and latency have improved in recent years. In
addition, the simulations in the study [8] were performed withuniform hash power of all nodes to investigate the mining
stats fairly. However, the uniform hash power might haveinfluenced the data, such as the block propagation times andthe orphan block rate. In the present simulation, the hashpower of each node is set based on the real hash power
distribution used in the study [9]. The simulation parameters
including the hash power are set to be realistic and up-to-date.
The parameter settings are discussed in detail in Section 3.
The relay network models in the current and previous study
are shown in Figure 1. In the previous model, the utilizing
nodes were able to send blocks to all the other utilizing nodes
directly, and thus the relay network was somewhat stronger
than the actual relay networks. This study uses a realistic
relay network model that reflects the features of actual relay

Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020

Fig. 1: The comparison of the previous model and the currentone.

networks. Our current model is explained in detail in Section
3. In the detailed analysis, we quantitatively investigate theeffects of the relay network and present not only the results
but also their causes. For example, we thoroughly discuss
the reason why the orphan block rates of the utilizing nodes
are much smaller than those of the non-utilizing nodes in
Section 4. Moreover, many new findings are obtained. For
instance, this paper is the first to quantitatively investigate
the effects on the 90% block propagation time. The relay
network is found to have a larger influence on the 50%
block propagation time than on the 90% block propagation
time. Moreover, this paper compares the orphan block rates
with those in a previous study by Gervais et al. [7] anddemonstrates that the effect of relay networks on the orphan
block rate is smaller in the present network. With respect tothe effect on the individual nodes, although our previous study[8] suggested that the orphan block rate of utilizing nodes issmaller than that of non-utilizing nodes, this study ensuresthat the effect is maintained in the current realistic model
under the latest network. Moreover, a more detailed analysis,
which is shown in table VI, reveals that the utilizing nodes’
blocks are more than six times more likely to be approved asvalid blocks when non-utilizing and utilizing nodes generate
blocks simultaneously. This is one of our new findings.
This paper reveal the effects of the relay network on the
network and the individual nodes and provides a detailed
numerical analysis of the effects.
II. B ITCOIN AND R ELAY N ETWORKS
This paper aims to identify the effects of relay networks,
which are a recognized method for improving block propagation times. Herein, we describe block propagation in
the Bitcoin network and the challenges it faces and thenexplain relay networks. These descriptions will be useful forunderstanding this study.
A. Transaction handling
Nodes will issue a transaction when they send coins. The
coin transmission is completed when a block including thetransaction is confirmed. When nodes issue transactions, they

propagate them to the network through adjacent nodes. Whennodes receive transactions, they save the transaction andthen try to mine blocks including those transactions. For
security reasons, block generation requires a great deal ofcomputation. If nodes succeed in block generation and theblocks are confirmed, then they will receive mining rewards,
which is the main incentive for nodes to participate in the
Bitcoin network [10]. When nodes are able to mine blocks,
they propagate these blocks to the network. When nodes
obtain blocks, they confirm them, and the blocks will beappended to their ledger if they are valid. At this stage,
the transactions included in the block are confirmed. The
number of confirmed transactions per second is called thetransaction throughput, and this number is used to evaluate
system capacity.
B. Orphan blocks
The blocks that are not included in the longest chain of theledger are called orphan blocks. Orphan blocks are importantfor both the system and its nodes. Prior works [3], [7] havereported that orphan blocks have a negative influence on
security. Therefore, decreasing orphan blocks is importantfrom a security perspective. For miners, orphan blocks arebad because they cannot receive mining rewards for orphan
blocks; orphan blocks only waste their computation power.
For both the whole system and its nodes, decreasing orphan
blocks is significant. Previous works [3], [7] show that
improving the block propagation time is necessary to decrease
the number of orphan blocks.
C. Transaction throughput
Bitcoin’s major challenge is to improve its transaction
throughput. Indeed, its throughput falls behind that of centralized systems. Basically, there are two ways to improvethroughput [4]: increase the block size or to reduce the blockinterval. However, improvement of the block propagation
time is needed in both cases [3] because both cases areaccompanied by an increase in orphan blocks. In other words,
improving the block propagation time makes it possible toimplement these methods while maintaining security.
D. Relay networks
Several types of relay networks [5], [6], [11] have beenused in the Bitcoin network. Relay networks have attracted
attention as a method to improve the block propagation time,
and their effectiveness has been discussed [7], [8], [12].
Four projects listed in Table I are well-known in Bitcoin.
These relay networks differ from each other, but the basic
structure is common to some extent across them. Figure 2
depicts this structure. Relay networks are external networks
and are composed of relay servers as shown in Figure 2. These
servers are deployed in each region. For example, Falcon [5]relay servers are placed in the US, Germany, Brazil, Japan,
Australia and several other regions. The following provides
an overview of block distribution by relay networks. First,

Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020

TABLE I: Summary of relay network projects.
Project
BFRN [6]Falcon [5]FIBRE [11]bloXroute [13]

Year
2014
2016
2016
2018

# servers
8
10
6
Unknown

Developer
Matt Corallo et al.
Cornell University research teamMatt Corallo et al.
Uri Klarman et al.

Fig. 2: Relay network structure.

utilizing nodes send blocks to relay servers in the same region
when they discover the blocks. Then, relay servers propagate
the blocks to other servers; block transmissions between
servers are basically faster than normal transmissions. For
instance, FIBRE [11] uses an UDP-based protocol, topology
optimization and other methods to realize rapid transmission.
Finally, the utilizing nodes can receive blocks from the relay
servers with which they connect. Therefore, relay networks
decrease propagation times between continents and can provide blocks with a large number of nodes simultaneously.
III. METHODOLOGYThis paper investigates relay network effects on theblockchain network and individual nodes when an ideal relay
network is utilized in the network. Simulation is an appropriate and realistic approach for this examination because it isvirtually impossible to obtain real data of individual nodes inpeer-to-peer networks. This section describes our simulation
settings and relay network model. At the end of this section,
we explain how we analyze the simulation results.
A. Simulation
In this paper, SimBlock [14], which is a relatively new
blockchain network simulator, was utilized. SimBlock has
been used in several studies [8], [9], [15], and the simulator
parameters, such as bandwidth and latency, have been updated[9]. Therefore, this simulator provides a simulation under thelatest network state. The simulation parameter settings areshown in table II. The number of Bitcoin nodes was 10,000
based on data obtained from [16]. The block interval andblock size followed those of Gervais et al. [7]. Bandwidthand latency were obtained from Nagayama et al. [9]; thesevalues were the most recent internet values.

TABLE II: Parameter settings.
# of nodes
Block interval
Block size
Hash Power# of connections
Geographical distribution
Bandwidth
Delay

10000
10 min535 KB
Distribution according to Aoki et al. [14]Distribution according to Miller et al. [17]Distribution according to Gervais et al. [7]6 regional bandwidth according to Nagayama et al. [9]6 regional delay according to Nagayama et al. [9]In this simulator, the transmission time is determined by themessage size, latency and bandwidth. Bandwidth is chosen as
the smaller of the upstream bandwidth of the sender or thedownstream bandwidth of the receiver.
Simulations were conducted while changing the utilization
rate of the relay network, that is, the rate of nodes utilizing therelay network. In detail, 100%, 50%, 25%, 12%, 6%, 3%, 1%
and 0% were chosen as the utilization rates. Each simulation
terminated when 1000 non-orphan blocks were generated.
B. Relay network model
For simulations, the relay network must be modeled, andthis paper aimed to capture the effects of relay networks when
they worked ideally. Basically, each relay network is quite
different; specifically, their protocol, the number of deployed
servers and their servers’ capacities differ. Therefore, it isunrealistic to create a relay network model that reflects theirtraits identically. However, their ideal operation is basicallycommon and obvious. Ideally, relay networks are expected topropagate blocks to nodes in different regions in three steps.
First, nodes send blocks to one of the relay servers with which
the nodes connect. The second step is transmission between
regions; these connections are between relay servers and are
faster than normal for the reasons mentioned in the previous
section. Finally, the relay servers provide blocks with theirconnecting nodes in parallel. These three steps are basicallythe minimal steps for intercontinental transmission.
We aimed to simulate such a relay network when working
ideally. Figure 3 shows the model. This model assumes thatrelay servers are deployed in each region and utilizing nodes
receive/send blocks from/to the relay server in the same
region. The model also assumes that the connections between
these relay servers provide 10 times broader upward bandwidth than normal connections. In general, the connections
between relay servers are faster than normal connections forthe aforementioned reasons, and the model provides fast blockpropagation in the form of broader upload bandwidth. Next,
when the relay servers receive blocks, they can send thoseblocks to all utilizing nodes in the same region simultaneously
because the model simulates relay networks when they are
working ideally. This simultaneous transmission is madepossible by a server load distribution with a large bandwidth.

Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020

Fig. 3: Our relay network model.
Fig. 4: 50th percentile of block propagation times.
C. Evaluation indices
Relay network effects on the Bitcoin network and individual nodes are examined in this paper. To evaluate theeffects on the blockchain network, 50% and 90% of theblock propagation time and orphan block rate were chosen,
respectively. These variables are commonly used in manystudies [3], [7], [8], [12], [15], [18], and they are appropriate
parameters for evaluating effects. In particular, although the90th percentile of block propagation time is important and has
been investigated in many studies [12], [18], previous relay
network measurements [7], [8] did not focus on it.
Moreover, this paper focuses on the number of generated
blocks and the orphan block rate and compares them forutilizing nodes and -utilizing nodes to clarify the effects on
individual nodes. The number of generated blocks is definedas the number of generated blocks per node, which is an
important value for miners because they participate in theblockchain network to obtain mining rewards [10]. The otherparameter, the orphan block rate of each node group, is therate of each node’s orphan blocks in all generated blocks;
it is a significant value because nodes cannot obtain mining
rewards for orphan blocks, and computational power is wasted
in many blockchains, such as Bitcoin [10]. In other words, if
relay networks decrease their orphan blocks, this would be areason for nodes to utilize them.
IV. RESULTThis section examines the effects of relay networks basedon the experimental results. As mentioned in the previous
section, the block propagation time, orphan block rate andmining statistics were investigated. This section focuses oneach individually.
A. Propagation time
Data obtained in previous studies [8], [12] indicate thatrelay networks decrease the block propagation time. Our
results suggested two effects.
First, they showed an improvement in block propagation
time, consistent with previous studies. Figure 4 and Figure
5 depict the 50th and 90th percentiles of block propagation

time, respectively. In both figures, decreases in propagation
time were observed in all three node groups. Regarding nonutilizing nodes and all nodes, block propagation times steadilydecreased as the utilization rate rose. In fact, Table III and IV
show that the 50th and 90th percentiles of propagation timedecreased by approximately 100 ms and 200 ms, respectively,
for both groups when comparing the 0% and 3% cases. Similar to the other node groups, an improvement in the utilizing
nodes was observed. Therefore, relay networks improve theblock propagation times of non-utilizing nodes and all nodes
in addition to improving those of the utilizing nodes.
Second, an interesting observation is that the graph shapesof the non-utilizing and utilizing nodes resemble each other,which seems to indicate that the degree of improvementin these two groups was approximately the same. In fact,
the differences in value for non-utilizing and utilizing nodes
were kept within approximately 800 ms to 1000 ms in allcases according to Table III. The differences in the 90th
percentile were within approximately 1500 ms to 2000 ms
at any utilization rate, as shown in Table IV. However, notethat the times of the utilizing nodes were always better thanthose of the non-utilizing nodes. Thus, the utilizing nodes
maintain their advantage, although the degree of improvement
is similar to that of non-utilizing nodes.
Moreover, the comparison of the 50th and 90th percentilesof propagation time reveals an interesting phenomenon. The
differences between the 50th percentiles of non-utilizing andutilizing nodes were within approximately 800 ms to 1000
ms in all cases according to Table III. On the other hand, thedifferences in the 90th percentile were within approximately
1500 ms to 2000 ms, as shown in Table IV. This seems
to suggest that relay networks have a smaller influence on
the 90th percentile than the 50th percentile. Relay networks
quickly disseminate blocks to nodes that are in the vicinity of
their relay servers, and nodes that are distant from them haveto rely on the Bitcoin network to obtain blocks, which seems
to contribute to the differences between the 90th percentile
and the 50th percentile.

Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020

TABLE IV: 90th percentile of block propagation times(msec).
UR1
Group
Utilizing
Non-utilizing
All

0%

1%

3%

6%

12%

25%

50%

100%

N/A
5317
5317

3660
5307
5302

3171
5126
5106

2972
4905
4862

2719
4691
4573

2511
4338
4100

2318
3831
2903

2154
N/A
2154

50%
0.43

100%
0.34

1 utilization rate

TABLE V: Orphan block rate.
Utilization rate
Orphan block rate

0%
0.95

1%
0.93

3%
0.89

6%
0.79

12%
0.76

25%
0.63

Fig. 5: 90th percentile of block propagation times.
TABLE III: 50th percentile of block propagation times(msec).
UR1
Group
Utilizing
Non-utilizing
All

0%

1%

3%

6%

12%

25%

50%

100%

N/A
3854
3854

3050
3853
3851

2763
3741
3730

2590
3576
3555

2365
3378
3316

2160
3081
2993

1969
2692
2366

1837
N/A
1837

1 utilization rate

B. Orphan block rate
Previous studies [7], [8] have indicated that relay networks
decrease the orphan block rate. According to Gervais et al.
[7], the orphan block rate was approximately 7.5% of the original value when all nodes participated in the relay network.
Table V shows our results. We found that the improvement
increased as the utilization rate rose, and the orphan block
rate was approximately 36% of the original value when theutilization rate was 100%. In other words, our result indicatesthat the relay network improved the orphan block rate, but the
improvement was smaller than the improvement observed in
the study of Gervais et al. [7]. Two factors seem to contributeto this difference.
First, the number of Bitcoin nodes in our simulation waslarger than that in the previous study. In general, the morenodes that participate in the network, the more time isrequired to propagate data. As a result, orphan blocks are
more likely to emerge.
Second, the original orphan block rate of our study wasmuch better than that used in the previous work. Theseexperiments simulated the latest Bitcoin network, and the
network is much faster than the network of the first study.
As a result, the effect of relay networks decreased.
C. Number of generated blocks
The average numbers of generated blocks for the utilizing
and non-utilizing nodes were compared to investigate theeffect on individual nodes.
The results are shown in Figure 6. In our experiments, nosignificant difference was observed between utilizing nodes

and non-utilizing nodes. In fact, the values of the utilizing
nodes were larger in some cases and smaller in other cases
than those of non-utilizing nodes regardless of the utilization
rate. Additionally, the differences in the values were smaller
than 0.01 in all cases.
The main reason for this result seems to be that the propagation time differences between non-utilizing and utilizing
nodes were not sufficient. In general, hash power and time tostart mining determine a great portion of mining success. In
these experiments, we assumed that all nodes had the samehash power. Thus, it can be said that the difference in theblock propagation time produced by the relay network was
not sufficient. In fact, the differences between non-utilizing
nodes and utilizing nodes were at most 1000 ms to 2000
ms at any utilization rate, as mentioned in the previous
subsection, and it is obvious that the differences were too
small in Bitcoin’s block interval of 10 minutes. As a result,the differences were not observed at all utilization rates.
D. Orphan block rate of each node group
In the previous subsection, the focus was on the orphan
block rate to investigate the effect on the Bitcoin network.
Herein, we compare the rates of the utilizing and non-utilizing
nodes. The comparison is shown in figure 7. This result
is consistent with the previous work [8] and indicates thatutilizing nodes are significantly less likely to generate orphan
blocks than non-utilizing nodes. In fact, the values of theutilizing nodes were always below those of the non-utilizing
nodes, and the utilizing nodes generated no orphan blocks
when the utilization rate was 1%. The effect is maintained in
the realistic model.
Herein, two observations can be made. First, although
the values of the utilizing nodes were always better thanthose of the non-utilizing nodes, the non-utilizing nodes’
values consistently decreased as the utilization rate increased.
This improvement is attributable to the propagation time
improvement, as shown in Figure 4 and 5.
Second, the orphan block rate of utilizing nodes was notalways proportional to the utilization rate. One reason is asfollows. The utilizing nodes produced orphan blocks mainly
when multiple utilizing nodes produced blocks at the same

Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020

TABLE VI: A breakdown of orphan blocks (%).
Case
URa
1%
3%
6%
12%
25%
50%

case 11case 22case 33

case 44

0
3
2
10
13
24

3
3
6
14
30
24








0
0
1
0
4
4

97
94
91
76
53
48

a utilization rate.
1 the possibility that both an orphan block and the main blockare generated by utilizing nodes.
2 the possibility that an orphan block and the main block are

generated by non-utilizing and utilizing nodes, respectively.
3 the possibility that an orphan block and the main block are

Fig. 6: Average number of discovered blocks.

generated by utilizing and non-utilizing nodes, respectively.
4 the possibility that both an orphan block and the main blockare generated by non-utilizing nodes.

time. Table VI, which shows the breakdown of how orphan
blocks were produced, demonstrates that the possibilities ofcase 1 were larger than those of case 3. In other words, themajority of orphan blocks created by utilizing nodes weregenerated when an orphan block from a utilizing node wasbeaten by a block produced by another utilizing node. Whenthe utilization rate is low, the orphan block rate of utilizing
nodes is likely to be low because the number of utilizing
nodes is small and plural blocks are rarely produced by thesmall group of nodes. By contrast, it is thought that when
the utilization rate is high, the orphan block rate of utilizing
nodes is likely to be higher because the numbers of utilizing
nodes are larger and blocks are more likely to be produced at
the same time compared to cases with low utilization rates.
Therefore, it seemed that the values of utilizing nodes were
not always proportional, and the values under low utilization
rates were smaller those under high utilization rates.
Moreover, an important new discovery can be disclosed
from Table VI. The possibilities of case 2 are more than
6 times larger than those of case 3 in all utilization rates,
which indicates that the blocks provided by utilizing nodes
were quite likely to become main blocks when the nonutilizing and utilizing nodes produced blocks at the sametime. Surprisingly, the values of case 3 are 0 in some
utilization rates. Even in the worst cases, the values in case 2
are 6 times as large as those in case3. This analysis is the firstof its kind and shows an advantage of using relay networks.
Lastly, we will discuss the cause of this difference. It isconceivable that this difference stems from the characteristics
of relay networks. Utilizing nodes can send blocks to otherutilizing nodes simultaneously via a relay network, and blocks
produced by utilizing nodes are shared with other utilizing
nodes rapidly. Two outcomes result. First, the utilizing nodes
were less likely to continue hash calculation after new blocks
were discovered. Second, blocks created by utilizing nodes
were likely to win over blocks created by non-utilizing nodes.
Indeed, this can be observed from the comparison of case 2
and case 3 in Table 7. For example, the probability of case 2
was 7.5 times as large as that of case 3 at a utilization rate

Fig. 7: Orphan block rates of utilizing nodes and non-utilizing
nodes.

of 12%. These two factors were considered to contribute to
the low orphan block rates of utilizing nodes.
V. R ELATED W ORK
Prior work has investigated relay network effects. For
example, Gervais et al. [7] reported that the orphan block rate
decreased when all nodes utilized the relay network. However,this study did not consider the effects on individual nodes, andtheir simulation was performed only at utilization rates of 0%
and 100%. Our prior study [8] reported that the relay network
had good effects not only on the Bitcoin network but also on
the utilizing nodes. However, the relay network model wasquite simple and rough. Moreover, the hash power of eachnode was set uniformly in the simulation, which might haveinfluenced the results. Thus, there is a need to confirm that thebenefits that they found were maintained. In addition, someof the results were not thoroughly examined. For example,
the factors responsible for the smaller orphan block rateof utilizing nodes compared with non-utilizing nodes were
not sufficiently discussed. In addition, these previous studies[7], [8] performed simulations under the network state fromapproximately 2016, and the network state at that time,

Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020

including the latency and bandwidth, was quite different fromthe current one. In this study, we used a more realistic relay
network model and performed exact and in-depth analyses ofeach relay network effect in the latest network.

ACKNOWLEDGMENT
This work was supported by SECOM Science and Technology Foundation.
R EFERENCES

VI. C ONCLUSION
In this study, we used a realistic relay network modeland performed exact and in-depth analyses of the relay
network effects in the latest network. The investigation ofrelay network effects under the most current network stateis one of the major contributions of this study. In terms of
the effects on the Bitcoin network, we observed a decreasein the orphan block rate and in the 50th percentile of blockpropagation time, as indicated in previous studies. However,a new finding is that the improvement of the orphan block
rate by the relay network became smaller as the Internet speed
increased. We also found that the relay network improved the90th percentile of block propagation time, and this paper isthe first to investigate the relay network effect on the 90th percentile of block propagation time. Moreover, the comparisonof the 90th and 50th percentiles of block propagation time
revealed that relay networks have a larger influence on the50th percentile. Furthermore, the degree of block propagation
time improvements were approximately the same for utilizing
and non-utilizing nodes. However, the propagation times ofutilizing nodes were always better.
Regarding the effects on individual nodes, we confirmedthat blocks of utilizing nodes were quite unlikely to becomeorphan blocks even in the current fast network. Moreover,
we investigated the outcome when non-utilizing and utilizing
nodes produced blocks simultaneously. The result confirmedthat blocks of utilizing nodes are far more likely to become
main blocks than those of non-utilizing nodes, which seems
to be a significant benefit of the use of relay networks byutilizing nodes. This finding is also a major contribution ofthis study. As this study and other studies have indicated,when more nodes utilize a relay network, the effects of
the relay network are greater. Hence, it seems desirable toencourage more nodes to utilize the relay network, and our
results may provide a motive for these nodes to do so. In
terms of the mining success rate, we observed that the relay
network did not exert a significant influence: the differences
between utilizing and non-utilizing nodes were below 0.1 atany utilization rate.
Some limitations are worth noting. Although our results
found effects of relay networks when they worked ideally,
their effects when they are not working ideally, for example,
because of heavy load, are not clear. Therefore, future work
should include a follow-up investigation of the effects whenrelay networks do not work well. In addition, the effects
on other blockchain networks, such as Ethereum, should be
examined.

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Proc. 3rd IEEE Int'l Conf. on Blockchain(IEEE Blockchain 2020), pp.214-220, November 2020