###### Abstract
In real-world systems, in addition to the devices and the wait locations, customers may require various resources (both discrete and continuous) to be occupied while waiting for a service to start, or during a service, or while the requirement is in the system. In this case, the terms \"resource QS\" or \"QS with a random volume of requirements\" are used. The random volume of the resource occupied by the customer for the entire duration of their stay in the system can be either discrete or continuous. Resources are related to the most commonly used amount of memory. At the same time, in wireless networks, such as long-term evolution (4G LTE) networks or New Radio (5G NR), network bandwidth is understood as a resource, which is notoriously limited and must be distributed when the user receives a call and released at the end of the session by the device or a separate system. [PERSON] and [PERSON] first formulated a generalization of the Erlang problem, in which each arriving customer has some information quality, which the authors call the amount of the requirement [5]. Later, [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] made a significant contribution to the development of research methods on resource QSs [6; 7; 8; 9; 10; 11; 12]. In their works, the authors considered a QS with a random volume of requirements, as a class of systems with some capacity, which is dependent upon or independent of the volume of requirements and the time of service. Resource QSs with limited resources have been used in some works as models of the next generation of wireless communication networks [13; 14; 15]. Despite the large list of applied problems that can be solved using queuing models with an arrival process involving a random amount of requirements, to date, accurate analytical results regarding the study of the total volume of requirements in the system exist only for the case of the Poisson arrival process and classical QSs. However, the results of studies of real flows indicate the presence of a correlation and a large variance between the moments of receipt of requests, which has led to the use of models of correlated flows. Therefore, the queueing theory with correlated flows developed by [PERSON], [PERSON], [PERSON] [16; 17] has found wide application in the study of telecommunication systems. However, it should be noted that for resource systems with non-Poisson arrival processes (non-Markov systems), there is currently no universal approach to the study and most of the results are obtained by means of simulations, and analytical results have been obtained only for some special cases. Therefore, in this article we propose to use asymptotic methods for the study of a QS developed at the Tomsk scientific school of applied probabilistic analysis under the guidance of [PERSON] [18]. Such methods make it possible to obtain asymptotic expressions acceptable for practice regarding the desired characteristics of the system in cases where their analytical analysis is impossible. The first results for a QS with an infinite number of servers were obtained in the middle of the last century in [19; 20; 21; 22]. The main distinguishing feature of systems with an unlimited number of servers is the lack of queues and the dropping of service applications. Markovian QSs with an unlimited number of servicing devices were investigated in the first half of the 20 th century, when the most of the problems of queueing theory were solved for models with the stationary Poisson arrival process and an exponential time for servicing applications. It was shown that the number of occupied devices in the M/M/\(\infty\) system is distributed according to Poisson's law. For systems with an arbitrary function of the distribution of the service time, [PERSON] solved the Erlang problem for M/G/N systems in 1958 and showed that as \(N\to\infty\) the distribution converges to the Poisson distribution.