This paper proposes a new analytical model of a multiservice switching network with overflow links in the first stage and resource reservation for selected call classes in output directions. The proposed model assumes that both the overflow mechanism and the resource reservation mechanism can be used in a number of selected, or all, classes of calls. A particular attention is given to the way the effective availability parameter for networks with overflow links in the point-to-point selection mode is determined. The proposed model makes it possible to determine dependencies between the internal blocking probability, capacity of overflow links, and the number of reserved resources for call classes to be analysed. Simulation experiments confirm high accuracy of the proposed method and potential applications of the model in engineering issues.