The article gives an overview of resource queuing systems with the concentration on the methods of their investigation. A valuable part of the article is devoted to the method, which leads to a significant simplification of the system analysis while maintaininghigh accuracy of the estimate, and in some cases without any loss of accuracy. Simplification is to consider a system with random resource amount release at the instant of a customer departure instead of a system with the exact resource amount release equal to the occupied by the customer at the beginning of service. Subsequently, for the case of a Poisson flow of arrivals and exponential service time, the equivalence of the results for the initial and the simplified models was rigorously proved. In addition, a significant part of the paper is devoted to the overview of publications on the recurrent service discipline.