## 1 Introduction  
Traffic overflow is one of the oldest techniques for the optimization of traffic stream distributions in telecommunications and computer networks. The overflow mechanism is initiated in time intervals that correspond to the states of total occupancies of resources termed _primary resources_, historically _primary group_ or _direct group_ (Defining the resources of a network by the term \"link group\" originated from the construction of the first telecommunications networks, in which the basic resource was the link, with the link corresponding to a physical pair of cables linking, for example, telephone exchanges with one another. In this study, to describe the resources of present-day telecommunications networks, the term \"network resources\" is used, expressed in allocation units, for example, links, channels or basic bandwidth units [1]). In such states, new calls that cannot be serviced by the primary resources will be directed (will overflow) to other available resources that can service a given call at the time. The resources to which traffic overflows are called _secondary resources_ or _alternative resources_, historically _secondary groups_ or _alternative groups_. Initially, traffic overflow was primarily used in single-service hierarchical telecommunications networks with traffic redirection through alternative routes [2; 3; 4; 5]. An application of two or more levels of hierarchy in networks with traffic redirectioroutes largely led to the effective use of network resources satisfying at the same time the requirements of demanded service quality. The use of alternative resources also guaranteed easy adaptability of a network to changeable load conditions resulting from both changes in the intensity and structure of offered traffic and from damages to certain elements of the network (link groups, exchanges), without the costly necessity to develop and expand switching exchanges [6]. Today, the traffic overflow mechanism in telecommunications networks, defined as the so-called _vertical call handover_[7; 8], is mainly used to optimize the use of resources that are offered by a number of different technologies that operate within the same area, as is the case with overlay networks [8; 9]. As a result, a decision as to whether connections are to be redirected (overflow traffic) is frequently related not so much to the mobility of users but rather to the pursuit of operators to obtain required load (e.g., balanced/sustainable) for individual networks operating with different technologies or redirecting connections to resources that are optimal from a point of view of a service that is being executed (traffic class). It follows from the practice of many mobile network operators that for overlay networks, composed of picocells, microcells, and macrocells, one of the most frequently executed call admission policies is to treat cells with a larger range (macrocells) as cells that service traffic that could not be serviced in cells with a lower range (picocells, microcells) [7; 9; 10; 11; 12]. When this is the case, traffic redirected to a macrocell is then overflow traffic with different characteristics from traffic offered directly to the network by users [10; 11]. In today's circumstances, the traffic overflow mechanism is considered to be one of the most effective methods to balance (equalize) load in self-organizing (self-optimizing, self-configuring) networks [13; 14]). The recent research studies show that the traffic overflow technique is often considered in 5G networks. The authors of [15] consider a system consisting of base stations encompassing both 5G millimeter-wave New Radio (NR) technology and Wireless Gigabit Alliance (WiGiG) technologies occupying a spectrum at 60 GHz. The authors assumed that NR users' requests can be overflown to WiGiG technology. This overflow (off-loading) technique could also be used in 5G systems with network slicing [16; 17].