## 7 Results of Modeling a Selected Number of Overflow System with Erlang-Engest-Pascal Traffic  
The analytical method for modeling telecommunications systems with Erlang, Engel, and Pascal traffic overflow presented in this article is an approximate method. To evaluate its accuracy, the results of the analytical modeling were compared with the data obtained in the simulation experiments. The model accuracy was verified in a simulation tool designed by us. The Microsoft.NET programming platform was chosen to build the simulator. It allows the application to be executed on all devices with Microsoft operating systems. For the development of the simulator the C# language was chosen because of its efficiency and rich library resources. The program interface was designed in the WPF (Windows Presentation Foundation) structure in the XAML language, and its code was separated from the functional code according to the MVVM (model-view-view-model) architectural pattern. Building our own simulator allows us to examine the operation of the models as accurately as possible and allows for high flexibility of system construction. The results of the simulation studies for three example overflow systems, whose parameters are given in Table 1 (Systems 1 and 2) and Table 2 (System 3), are shown in Figures 7-9. According to the general scheme of traffic overflow (Section 3), requests, the parameters of which are given in Tables 1 and 2, are first directed to the primary resources, where an attempt is made to handle them. If there are not enough free resources to handle a given request, it is redirected to the secondary resources. If the current state of the secondary resources also does not support the request, it is lost. In Tables 1 and 2, the amount of resources requested by the calls of individual classes is marked as \(t_{\text{X,No}}\), where X stands for the type of traffic (X = Pa\(|\)En\(|\)Er) and No. is the number of the traffic class. For Engset and Pascal traffic classes, the tables provide information on the number of sources generating traffic streams of a given class (parameters \(S_{\text{En,No}}\), and \(S_{\text{Pa,No}}\), respectively). For Erlang traffic classes, the information about the number of traffic sources is not provided because these sources are assumed to be unlimited (infinite). System 1 services exclusively Pascal traffic classes, while Systems 2 and 3 service Erlang-Engset-Pascal traffic classes. System 1 is composed of two primary resources with a capacity of \(V_{1}=120\) AUs and \(V_{2}=90\) AUs, and a secondary resource with a capacity of \(V_{0}=50\) AUs. Only traffic from Pascal-type classes is offered to System 1. In System 2, the primary resource with a capacity of \(V_{1}=70\) AUs supports all three types of traffic, that is, Erlang. Engset, and Pascal, while the other primary resource with a capacity of \(V_{2}=100\) AUs supports only Pascal traffic flows. The secondary resource of System 2 has a capacity of \(V_{0}=60\) AUs. In System 3, the first primary resource with a capacity of \(V_{1}=90\) AUs handles Erlang, Engset, and Pascal streams, while the second primary resource with a capacity of \(V_{2}=110\) AUs handles Erlang and Pascal classes. The requests that cannot be handled by the primary resources are overflown to the secondary resource with a capacity of \(V_{0}=40\) AUs. The parameters of the tested systems were selected so as to be able to verify the accuracy of the method in the worst cases, that is, for a large share of the Pascal stream in the total traffic offered to the system. At the same time, using Erlang, Engset, and Pascal traffic streams allows taking into account the diverse nature of traffic sources at the level of reports. Erlang traffic can be used to characterize the traffic generated by a very large population of traffic sources associated with a given traffic class (constant traffic intensity).