MODELING AND ANALYSIS OF THE CHARACTERISTICS OF MULTICHANNEL AND MULTI-NODE COMPUTER NETWORKS WITH PRIORITY SERVICE

. The subject of the research is modeling and analysis of the characteristics of multichannel and multi-node computer networks with priority services. The work is devoted to the study of the qualitative indicators of the functioning of computer networks with priority service. In this work, mathematical models are developed that make it possible to assess the quality of functioning of modern computer networks, taking into account the number of channels, waiting places in network nodes and the number of network nodes. The proposed methods for calculating the probability of failures and the probability of timely delivery of a stream of requests make it possible to determine the real values of the qualitative indicators of the functioning of computer networks and are suitable for both designed and operating computer networks. The proposed technique makes it possible to determine the number of packets in the queue and the optimal amount of buffer memory in computer network nodes.


Introductıon
The article shows a mathematical model of a multi-channel, multi-node computer network with a limited queue and absolute priority, depending on the number of network nodes, waiting places in individual nodes and the probability of failure of requests of individual priorities. It is shown that in multichannel, multinode computer networks, to ensure the required quality of functioning, it is necessary to choose the optimal number of channels (s), waiting places (k) in the network nodes and the load of individual priorities ( 1 ,  2 ). It was revealed that with an increase in the number of network nodes (N), it becomes necessary to increase the number of channels (s) and waiting places (k) in the network nodes. The resulting tables and functional dependencies make it possible to design a computer network that functions with the required quality indicators. In [8] and [9] article, the calculation is performed in singlechannel multi-node families, the probability of failure for requests of the first and second priorities with a limited service queue. In contrast to [8] and [9], the proposed calculation methods make it possible to determine the delivery time, the number of packets in the queue, the probability of request flow failures in multi-channel multi-node computer networks with a limited queue and absolute priority.
The operation of an analytical model of a computer corporate network is studied, the probabilities of loss and timely delivery of requests are determined. The work of the computer corporate network "SEÇKİLƏR" of the Republic of Azerbaijan has been studied [7].

Materials and methods
In computer networks based on modern technologies, voice and text information are exchanged digitally in the form of packets. Due to the limited network resources, there is a delay and loss of packets, which leads to an increase in the quality of service. In practice, computer networks with different architectural structures are used [1]. As shown in figure 1, there are cases when a network consists of dozens of nodes and one or more parallel communication channels connecting these nodes to each other in a certain order.
Computer networks and various types of information's are divided into packets and transported from one address to another for exchange between network operators. As a rule, at the first node of the network, the information is processed by dividing it into packets. The processed individual packets are transported from these nodes to the required address in different ways, depending on the addresses written on them. In the process of transportation, packets may be forced to pass through several nodes of the network, which is due to the limited and busy communication channels between nodes. When packets are processed at nodes, they may be delayed due to delays, and new routes and high priority may be established to service them. Let's consider the activity of a computer network with an arbitrary structure when prioritizing packages [3]. In this paper, the characteristics of such a network are optimized in terms of QoS.
Let us consider a multichannel queuing system (QS) with waiting places. The system receives two streams of requirements with intensities and respectively [4] The distribution functions of the service time for the first and second priority requirements are exponential with the parameter. In this case, the intensity of the incoming load of the first and second priorities will be respectively equal to and. The first thread has absolute priority over the second thread.
In multichannel single-node computer networks with a limited queue and absolute priority, the probability of failure for the first priority request flow due to the limited queue in service is determined by the following dependence [5]: where: Sis the number of channels; knumber of waiting places; 1load of the first priority.
With S = 1, it is possible to obtain a dependency for a singlechannel network with a limited queue and absolute priority.
The probability of denial of service for requests of the second priority is equal to the probability that there are already requests of the first and / or second priority in the queue: where: 1is the load of the first priority; 2load of the second priority.
An algorithm for solving the problem was developed for the calculation. In Fig. 2. an algorithm for calculating the probability of denial of service for requests of the first and/or second priorities in a multichannel single-node network is presented. The calculation according to this algorithm was performed using the Excel 2019 program.
Let's move on to obtaining a mathematical model for a multichannel multi-node network. To obtain a mathematical model, you can use the position of probability theory and mathematical statistics. According to which, a sequence of random events is called monotonically increasing (non-decreasing) or monotonically decreasing (non-increasing), if for each The union of all events of such a sequence will be written as [2]: Since in multi-channel multi-node computer networks with a limited queue and absolute priority, the probability of failure increases with an increase in the number of switching nodes used, taking into account (3) from expressions (1) and (2) for singlepriority and two-priority services, the following mathematical models can be obtained to calculate the probability failures in multichannel multi-node computer networks.
If we consider the probabilities of node failures to be the same, then the mathematical model for determining the probability of failure in multi-channel multi-node computer networks for firstpriority requests due to a limited service queue has the following form: where: Nis the number of network nodes; the load of the first priority,the number of channels,the number of waiting places;the th network node.
If we consider the probabilities of node failures to be the same, the mathematical model of the probability of failures in multi-channel multi-node computer networks for secondpriority requests due to a limited-service queue will have the following form: where:  i2is the load of the second priority i-the network node.

Results and discussions
When designing a specific communication network, it is necessary to take into account the real probability of failures of the designed network nodes [6]. The calculation was performed according to the algorithm shown in Fig. 2.      Table 1 shows the results of calculating the probability of denial of service for requests of the second priority (P2m) with a different number of waiting places ( ). Number of nodes -N = 1. − 2 = 0.8 second priority load, − = 2 number of parallel channels. Table 1 shows the results of calculating the probability of denial of service for the requirements of the second priority ( 2 ) with a different number of switching nodes (N) and waiting places ( ). - 2 = 0.8 is the load of the second priority, -S = 4 is the number of parallel channels.
In Fig. 3. the results of calculations of the probability of denial of service for requests of the second priority ( 2 ) with a different number of waiting places ( ) are given. The number of nodes -N = 3, - 2 = 0.8 the load of the second priority and -S = 4 the number of parallel channels. Table 2 shows the results of calculating the probability of denial of service for requests of the first and second priorities with a different number of switching nodes (N), parallel channels (s) and waiting places (k). Second priority load - 2 = 0.8. The results of calculating the probability of denial of service for requests of the second priority (- 2 = 0.8) in a multi-channel multi-node computer network with a different number of waiting places and different load of the first priority (= 0.1-2).

Conclusion
An algorithm has been developed for determining the probability of failure in multichannel and multinode networks for requests of the first and second priority due to a limited queue in service. Numerical calculations of the probability of denial of service for requests of the first and second priorities are given. It can be seen from the obtained characteristics and tables that in order to ensure the required QoS value, it is necessary to provide the required number of parallel serving channels between specific network nodes, as well as to determine the optimal number of waiting places (accumulator capacity) in its corresponding switching nodes.