# Towards Practical Applications in Modeling Blockchain System

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## Abstract

**:**

## 1. Introduction

- Network discovery. The first time a node is connected to the network, it is booted and connected to the initial boot node to get a list of neighbor’s nodes, synchronize and get the current version of the blockchain, subsequently disconnected;
- Transaction creation and verification. All nodes in the network can initiate transactions to transfer digital assets to available peers in the network. The creation of a new transaction implies that certain conditions are fulfilled by the exchange participants, so the transaction specifies the amount and the addressee and may additionally specify the terms of the transaction. Once the transaction has been created, the sender signs it with their electronic key and sends it to the network. The transaction will be rejected if it is incorrectly generated, invalid or does not contain all the information required for execution, or if the user does not have sufficient funds to complete the transaction;
- Mining. When a new transaction is received, the node initializes its addition to the block. The block is generated based on information about the past block received and the information collected. The miners try to find a solution; the block is checked, added to the registry and sent to the network to other nodes. If a solution is found by the second node, it is discarded to avoid branching;
- Checking the block for correctness. Checking the block before adding it to the register implies that the previous block exists, that the data structure is intact, that the sender has sufficient funds, that the signature is correct, that the syntax is correct, that the inputs and outputs are within acceptable values, that the transaction size is not higher than the maximum, that the transaction has not yet been processed. If confirmed, the chain is updated in the general ledger, and the transaction and user status are validated.

- We aim to create a simulation model of a communication network with a blockchain system awaiting the results of network delay simulation;
- We are dedicated to providing analysis solutions for simulation and analytical modeling;
- We include a comparison of simulation results with analytical solution results.

## 2. Related Works

## 3. Modeling Blockchain Systems on a Communication Network

_{NET}). The time interval between requests of blockchain applications, according to the solutions presented in Table 1, we refer to the Markovian (M

_{BC}). According to the properties of such flows at the router, the total flow (M

_{NET+BC}) converges to a simple flow with an intensity equal to the sum of the intensities of the original flows [44].

_{NET+BC}/Pa/v and M

_{NET+BC}/Pa/1 when considering and evaluating the performance of each device.

- M is the scale parameter;
- a is the shape parameter.

- R
^{n}(k) is the correlation function for the aggregated time series; - H is the Hurst parameter;
- k is the time shift;
- σ
^{2}is the sampling variance of the sequence.

- ρ is the system utilization factor;
- C
_{B}^{2}is the normalized variance of the service time.

- λ is the average rate of receipt of an application
- 𝜑
^{2}is the second-order momentum of a random variable.

- k—the number of nodes initiating creating the transactions needed to form the block (depends on the number of transactions in the Memory Pool), varies with the number of connected active nodes;
- t
_{proc i}—the time taken for node i to send a transaction to the network, depends on the network card and network configuration; - m—the number of network devices the packet passes through during transmission, depends on network configuration;
- t
_{delay m}—the network latency introduced by devices when transmitting a packet—a problem that can create greater potential for forks and vulnerability to hostile attacks; - t
_{MP}—dwell time of unconfirmed transactions in Memory Pool before being added to the block; - t
_{m}—time to check the block and solve the computational problem by the miners, depends on the consensus algorithm; - t
_{ver}—time taken to check the block and add it to the common chain (approximately a few milliseconds), depends on network configuration.

_{delay m}), it is proposed to use the system the simulation system AnyLogic is proposed.

_{delay m}). It can be assumed that the results obtained are correct with acceptable measurement accuracy.

## 4. Comparative Analysis of the Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 3.**Simulation results of the blockchain node system: (

**a**) Dependence of the proportion of packets on the waiting time for processing at the access node; (

**b**) dependence of the proportion of packets on the delay at the access node; (

**c**) dependence of the proportion of packets on the waiting time for processing at the aggregation node; (

**d**) dependence of the proportion of packets on the delay at the aggregation node

Research | Presented Solution | Tool/Technology | Parameters to be Considered and Characteristics to be Modeled |
---|---|---|---|

[10] | Modeling the process using multiple queues based on four phases (waiting for inclusion in the block; waiting for confirmation; waiting for service; servicing) | A state transition graph; Mass service theory; Markov processes | Simulation of block generation; State transition probabilities; Access delays |

[11] | The mining organization model is defined by M/M/n/L. The queue capacity is set as TxB, the queue policy is first-come, first-served, and the discard rule is block after service, which means that only transactions of block size TxB remain in the dynamic memory of the mining nodes, while other transactions, even if they are processed, are in the memory pool | Mass service theory | Average number of transactions per block; Total mining capacity; Number of transactions per second |

[12] | The M/M/1 model is used to model the blockchain memory pool, and the mining pool is modeled by the M/M/n model. There can only be one block in a mining pool at any one time. However, within a mining pool, processes can be divided into multiple tasks or threads for parallel processing by multiple mining nodes in the network. | Mass service theory | Average number of transactions per block; The speed at which transactions arrive; Average mining time per block; system/transaction throughput; waiting time in memory pool; The number of unconfirmed transactions in the entire system; Total number of transactions |

[13] | The mining process is modeled using a queuing system, analyzing transaction confirmation times. The authors consider the M/G/1 model with batch service, in which a newly arrived transaction cannot reach the service facility even if the number of transactions in the service facility does not reach the maximum batch size. In this model, the dwell time of a transaction corresponds to its confirmation time. | Mass service theory | Average block generation time; Average number of transactions in the system |

[14] | The system is considered using the M/G/1 model as an example. Data arrivals to nodes are modeled as a heterogeneous Poisson process, where the distribution of arrival rate to nodes is derived from an analytical model of the data delivery protocol. | Mass service theory | Block and transaction allocation time probabilities; Node response time; The likelihood of a branching chain; Duration of the period of the inconsistency of the register |

[15] | Stochastic network models are proposed to capture the evolution and dynamics of the blockchain. A combination of analytical calculations and simulation experiments is used to investigate both steady-state and transient performance characteristics | Stochastic models | The effect of a block’s propagation delay; Hashing power of nodes |

[16] | Game theories are proposed for modeling to address common problems in the blockchain network, such as security, problems related to mining management, and issues related to the economics of the blockchain. | Game theory | Economic aspects |

[17] | The system is examined using the M/G/∞ model as an example. Equivalence between two specific service disciplines is used to obtain the stationary distribution of the model. | Mass service theory | Distribution of busy periods; service delays |

[18] | The theory of mass service in blockchain systems is developed, and system performance is evaluated. For this purpose, a Markov queuing system of packet service is developed with two different stages, which are suitable for explicitly expressing the process of mining in a pool of miners and constructing a new blockchain. | Mass service theory; Markov processes | Average number of transactions per queue, Average number of transactions per block; Average transaction confirmation time. |

The Solution | Description | Software Packages |
---|---|---|

Test networks | A test network of a particular system is used to test the performance or relevance of an application. Coin analyses that have no real value are used | Bitcoin Testnet Explorer [19]; Blockcypher [20]; Bitcoin Testnet Faucet [21]; Rinkeby network [22]; Ganachecli [23]; Ethereum Tester [24]; Truffle framework [25]; Remix ide [26]; IBM Blockchain platform [27]; Remme [28]; Cryptospaniards [29] |

Demonstration of how the technology works | These solutions show how basic blockchain operations work, such as hashing, mining and distribution. It also provides information about the result of the procedure when certain parameters are changed | Blockchain demo [30]; |

Simulators for event management | With these solutions, users can explore the underlying characteristics and performance of the network, investigate interactions between nodes and compare different simulation scenarios. They serve as a fair comparison across platforms and provide a deeper understanding of different system design options. Applied to pretest to evaluate overall performance and with workloads to evaluate individual tier performance | Vibes [31]; Simblock [32]; Blocksim [33]; BlockLite [34]; Bitcoin simulator [35]; Blockbench [36]; Hyperledger Caliper [37] |

Network section simulator | The solutions combine mathematical and logical aspects and reproduce the real behavior of the system using computer software | AnyLogic [38]; MATLAB [39]; NS3 [40]; GPSS World [41] |

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**MDPI and ACS Style**

Vladyko, A.; Spirkina, A.; Elagin, V.
Towards Practical Applications in Modeling Blockchain System. *Future Internet* **2021**, *13*, 125.
https://doi.org/10.3390/fi13050125

**AMA Style**

Vladyko A, Spirkina A, Elagin V.
Towards Practical Applications in Modeling Blockchain System. *Future Internet*. 2021; 13(5):125.
https://doi.org/10.3390/fi13050125

**Chicago/Turabian Style**

Vladyko, Andrei, Anastasia Spirkina, and Vasiliy Elagin.
2021. "Towards Practical Applications in Modeling Blockchain System" *Future Internet* 13, no. 5: 125.
https://doi.org/10.3390/fi13050125