## 1 Introduction
The traffic overflow mechanism has also found its application in information technology (IT) systems as a strategy to increase the efficiency in data centers [18] and content delivery networks [19], among others. In the case of data centers, the two basic premises for the application of traffic overflow are equalization of load [19; 20] and reduction of energy consumption [21; 22; 23]. Load equalization can be used both within the same center and between distributed data centers that are connected with one another using appropriate network technologies. The demands that arrive at a given data center can, when they coincide with intensified and increased load, overflow to another server (virtual machine) that is part of the data center's infrastructure, or to another center within a distributed data center architecture (web-based solutions, cloud-based solutions). In the case of IT systems, the mutual overflow technique is more frequently used. This technique is appropriate for flat topologies, where network/systems are built with a certain number of primary resources without designating resources as secondary resources. In systems with mutual overflow, the request can be overflow (forwarded) bidirectionally between certain primary resources [24; 25]. Many analyses of the effectiveness of the traffic overflow mechanism show that in traditional and modern telecommunications networks alike, both access and backbone networks, the traffic overflow technique has the advantage of increasing the reliability and use of network resources, as well as optimizing traffic distribution and improving the quality of service (QoS) and the quality of experience (QoE) in multi-service traffic streams, generated by end users [26; 27; 28; 29]. To use the traffic overflow mechanism more effectively, it is necessary to develop analytical models of traffic overflow systems, in particular models of multi-service systems. The basic models of overflow systems with single-service traffic were developed in as early as the mid-20 th century. The first studies on modeling multi-service systems with traffic overflow were initiated toward the end of the 20 th century [30; 31; 32] and were soon further developed at the beginning of this century [28; 33; 34]. However, the above-mentioned studies were limited to modeling systems with PCT1 traffic streams (In traffic theory, offered traffic generated by an infinite number of sources (Poissonian call streams) is defined as PCT1 (Pure Chance Traffic of Type 1), while the model of a system that services such traffic streams--with the assumption that service time is exponential--is called the Erlang model. The term PCT2 (Pure Chance Traffic of Type 2), in turn, refers to traffic offered by a finite number of traffic sources (binomial distribution of call stream), that is, the type of traffic considered both in the Bernoulli model, in which the capacity of the system is higher than the number of traffic sources, and in the Engset model, in which the number of traffic sources of individual call classes is higher than the capacity of the system. In the literature, these terms are used interchangeably--PCT1 traffic or Erlang traffic streams, PCT2 traffic or Engset traffic streams.). The models of systems in which PCT2 traffic streams (Engest) and Pascal streams are also taken into consideration are proposed in [35]. The assumption in the latter study is that multi-service Engset and Pascal streams can be modeled by equivalent Erlang streams. The same assumption, however, leads to significant inaccuracies for Pascal streams. The present study proposes a novel model of a multi-service overflow system to which a mixture of multi-service Erlang, Engset, and Pascal traffic streams are offered. To determine the parameters of overflow traffic, offered to the primary resources as Pascal traffic, a new method has been developed. This new method makes it possible to significantly increase the accuracy of determining the average value and variance of overflow traffic. The rest of this article is divided into seven parts.