Аннотация:The controllable multiple queuing system (QS) with a switching number of service channels is considered. Such switches are possible at special periodical moments of time (control points) equidistant in time. The intensity of simple input flow at control points randomly changes and these changes ate governed by Markov chain process. It is assumed that during one step (an interval between neighbor control points) QS is in time for a stationary mode. The switching strategy is constructed to maximize a mean one-step profit. Threshold feature of optimal strategy is proved and algorithms for threshold values calculating are derived.