## 2 Related Work  
Analytical modeling of overflow networks (overflow systems) is a complex problem. The division of resources into primary and secondary resources leads to a significant change in the characteristics of traffic streams that overflow from the primary resources and are offered to the secondary resources, thus preventing the PCT1 (Erlang) model or the PCT2 model from being applied. Unlike PCT1 traffic, which can be fully described by the average value of traffic intensity, overflow traffic requires many more parameters. The analytical models of overflow systems published in the literature involve both single-service and multi-service systems. Single-service traffic overflow systems have been addressed in many analyses presented in the literature, for example in [3; 4; 5; 36; 37; 38]. The basic mathematical models for overflow systems with single-service traffic were developed as early as the mid-20 th century. These models were further expanded into three groups of methods for analyzing overflow systems, that is, methods based on the analysis of state equations resulting from the service process in the system [39; 40; 41], methods based on the analysis of the state space of the service process [3; 5; 37] and methods based on the analysis of the call admission process [36; 42]. The methods modeling overflow systems that are commonly and widely used in engineering applications typically belong to the group of methods based on the analysis of the state space on account of their high accuracy and accompanying low complexity resulting from a description of the overflow traffic stream that is reduced to just its first two moments. In the three best known methods in this group, presented in [3; 5; 37], the following two parameters are used to describe the traffic stream offered to the secondary resources--the average value and the variance. Methods of this group are still used in modeling modern telecommunications systems. For example, in [15; 43], the traffic overflow phenomenon is considered in the context of fifth-generation (5G) millimeter-wave networks. In [43], the authors analyzed the performance metrics of mobile traffic overflow from one base station to another. As the main metric, they used the blocking probability, which was defined as the proportion of user requests that cannot be served by any of the neighboring base stations due to either physical-layer blocking or capacity-limited blocking. To determine physical-layer blocking the authors applied line-of-sight model [44], while in order to determine capacity-limited blocking they applied the Erlang B formula [45]. The request blocked in the base station of the first choice form the overflow traffic offered to subsequent neighboring base stations. The parameters of the overflow traffic are determined according to the Erlang fixed-point approximation method. The model elaborated in [43] does not offer the possibility of calculating blocking probabilities individually for different traffic streams, with different requirements. The authors of [15] consider a system consisting of base stations encompassing both 5G millimeter-wave New Radio (NR) technology and WiGiG technologies occupying spectrum at a 60 GHz, known as NR-U (New Radio Unlicensed). They assumed that user requests that cannot be serviced with a given bitrate at the NR part of the NR-U base station can be overflow to the WiGiG technology (depending on the technology implemented in user equipment). Using an M/G/K/K model to service processes of NR-U sessions at the NR part of NR-U base station, the authors were able to determine the fraction of load that NR-U cannot handle in the licensed spectrum using the NR part of the NR-U base station [15]. However, the model proposed in [15] does not take into account the difference in the volume of required resources by different traffic streams--only the minimum bitrate is considered. The problem of multi-service traffic overflow in telecommunications networks has been addressed in many studies.