This paper presents a new, accurate multi-service model of a queueing system with state-dependent distribution of resources for each class of calls. The analysis of the considered queueing system was carried out at both the microstate and macrostate levels. The proposed model makes it possible to evaluate averaged parameters of queues for individual classes of calls that are offered to the system. In addition, the paper proposes a new algorithm for a determination of the occupancy distribution in the queueing system at the microstate level. The results of the calculations are compared with the results of a digital simulation for multi-service queueing systems with state-independent distribution of resources.