This article proposes a new analytical model of a switching structure using a Clos network topology. The assumption is that, in the structure under consideration, it is possible to switch off temporarily a certain number of spine switches (those in the middle stage of the switching fabric) depending on the current intensity of the offered traffic to reduce power consumption. The solution presented in the article can be used in present-day multiservice switching fabrics and in networks connecting servers in data centers. The developed analytical model allows the value of blocking probabilities for different stream classes of multiservice traffic to be evaluated in switching structures (switching fabrics) with a variable number of switches in the middle stage. The results obtained on the basis of the analytical model are compared with the results obtained as a result of relevant simulation experiments for a selected structure of the switching fabric. The study confirms high accuracy of the proposed model. This model can be used in further works to evaluate the effectiveness of energy-saving switching fabrics and the networks of data centers, as well as to construct energy-saving control algorithms that would control these switching structures, that is, algorithms that would change the topology of the switching fabric depending on changes in the offered traffic.