The article presents an overview of the resource queuing systems used for modeling of a wide class of real systems with admittedly limited resources. Despite the objective importance of studying of such systems, there have been very few works devoted to their analysis until recently, which was due to the complexity of constructing a random process to describe their functioning and, accordingly, of obtaining the numerical results. However, in recent years, there has been a significant shift in the study of the resource systems - new methods for their analysis have been proposed, which made it possible to construct recursive algorithms suitable for the numerical calculations. In this regard, the current review reflects only a part of the previously obtained results, namely, it considers the resource systems without waiting space with exponentially distributed service time. The authors consider the models of wireless communication systems based on resource queuing systems, expressions for estimating the main probabilistic, and temporal characteristics and algorithms for their calculation.