###### Abstract
A similar result was obtained in 1969 by [PERSON] [23], who showed that in stationary mode, the number of customers in the M/G/\(\infty\) system has a Poisson distribution, which depends on the average speed of receipt of applications and the average time of call service. In the work of [PERSON] [24], a diffusion approximation of the number of occupied devices for the M/M/\(\infty\) model with identical independent servers was obtained under the condition of a high incoming flow intensity (\(\lambda\to\infty\)) and fixed service time characteristics \(\mu\), and it was shown that in stationary mode, it is distributed according to the normal law with parameter \(\frac{\lambda}{\mu}\). Similar results were first obtained for non-exponential service time by [PERSON], and later in the papers of other scientists [25; 26; 27]. As a rule, when studying multi-server systems, it is usually assumed that the servers are identical and that arriving requests can occupy an arbitrary server to be serviced. QSs with heterogeneous servers are much less frequently studied, which makes them a more interesting object of research [28; 29; 30; 31; 32; 33; 34]. Nontrivial optimization problems often arise related to the assignment of servers to arriving orders depending on the ratio of the service rates of the facilities and the costs of their use. Non-trivial optimization problems also often arise related to the assignment of servers to incoming calls depending on the ratio of the service rates of the funds and the costs of their use. For example, in the theory of teletraffic, the concepts of \"fast\" and \"slow\" communication channels are used. In this case, a situation is possible when a copy is created for the incoming request, which is transmitted via another communication channel. In this case, as a mathematical model, one can use a QS with parallel service [35]. In this paper, we propose models that significantly expand the scope of practical applications, namely, a QS with various nodes for processing heterogeneous data (information) that require arbitrary resource capacities for their service. When a customer arrives in the system, its customer type is randomly selected according to the set of probabilities \(p_{i}\). Then the customer goes to a server of the corresponding device type, where its service is performed during a random time interval with a distribution function depending on the type of customer. Moreover, each customer requires a random amount of resources, of which the distribution function also depends on its type, but is independent of its service time. In practice, the total amount of resources is limited, which leads to additional losses of customers. In this study, we make the assumption that resources are unlimited. In contrast to the previously known models, the models under consideration will make it possible to estimate the required volumes of reserved resources, for example, for Internet of Things traffic, and to develop a resource allocation strategy with competing traffic. The object of our study is heterogeneous queueing resource systems with an unlimited number of servers and an arrival process in the form of a Markov-modulated Poisson process or a stationary renewal process, and requests for a random amount of heterogeneous resources. Our research goal was to obtain a random process that describes the total volumes of occupied resource capacities. To study a random process that describes the total volumes of occupied resource capacities, dynamic probabilities are introduced, the aim of which is to consider only those requests with their own volumes that have not completed their service. Analysis is performed under the condition of the growing intensity of the arrival process. We formulate theorems stating that under high-load conditions the total resource amount has a multidimensional Gaussian distribution. This paper is a continuation and generalization of previously obtained results [32; 33; 34].