# Towards Practical Applications in Modeling Blockchain System
## 3 Modeling Blockchain Systems on a Communication Network
Most existing applications adhere to the nature of unicast, whereby traffic is directed from a single source to a single destination. Broadcasting is used to send a single stream of control commands and other service information to all subscribers on the network. However, due to the nature of the blockchain algorithm, there is a significant increase in multicast traffic when updating data in the registry, which duplicates information for different blockchain nodes. When transmitted over a network, traffic is affected by network devices, processing policies in these network devices, quality of service mechanisms, congestion at nodes,operation of transport layer protocols, dynamic routing, load balancing, etc. Thus, flow characteristics can be significantly modified by network influences [47]. In data transmission networks, there are many queues to transmit, which interact with each other, merging with parts of other streams occurs, which affects and complicates the nature of the processes [47; 48]. The result of aggregating random processes will also be a random process with modified characteristics. In this regard, the interaction model--G/G/1 and G/G/n--can be arranged at the edge router. However, one way to estimate the probability-time characteristics of telecommunication nodes of an infocommunication network as a WAN under weak correlation is to solve the Lindley integral equations. Let us pay special attention to the final formula obtained in the derivation of the equation [46]. The expression of the integral waiting time function for any values of the argument will be:  
\[W(y)=\int_{-\infty}^{y}W(y-u)c(u)du \tag{5}\]  
Thus, the proposed model as a mass service network consists of coupled models characterized at the access level by M/M/1, at the primary hub level by M/G/1, and at the edge router level by G/G/1. Due to the complexity of self-similar processes, simulation methods are usually applied to calculate their analytical models [49]. The time for adding a transaction to the block and confirming it in general terms:  
\[t_{BL}=\underset{i=k}{\text{max}}_{\text{{prec}}\ i}+\sum_{m}t_{delay\ m}+t_{ MP}+t_{m}+t_{ver} \tag{6}\]  
where:  
\(k\)--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;  
\(t_{\text{{prec}}\ i}\)--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. For the model presented, the transaction confirmation time will be represented as follows:  
\[t_{BL}=\underset{i=k}{\text{max}}t_{\text{{prec}}\ i}+\sum_{m}\left[\rho_{m}+ \rho_{m}\frac{1+C_{BL}^{2}}{2(1-\rho_{m})}\right]+t_{MP}+t_{m}+t_{ver} \tag{7}\]  
Analytical modeling of a blockchain network faces many challenges. For example, the variability in the number of connections between nodes affects the data distribution algorithm and introduces variability in the transmission rates of data arriving at the nodes [16]. To simulate the network delay (\(t_{delay\ m}\)), it is proposed to use the system the simulation system AnyLogic is proposed.