The paper is concerned with a controllable multiple queuing system (QS) where control with a constant time step reduces to connecting spare service devices or to disconnection of main service devices. The maximal average profit from serving the demands in a multi-step planning period is taken to be the criterion of the QS operation optimality. Two models are considered. In first one the QS is assumed to have a simple demands arrival flow at a random rate that varies with homogeneous Markov chain. It is assumed that it takes one step for a stationary mode to set in QS. The second model does not assume a stationary mode but the simple input flow rate is assumed to vary with the specified time function. For both models algorithms are obtained that determine the optimal switching strategies.
