The paper deals with a multi-server controllable queueing
system M(t)/M/K with time-dependent and, in particular, with periodic
arrival rates. The models with homogeneous and heterogeneous
servers are of interest. In latter case the fastest free server allocation
mechanism is assumed and the preemption is allowed. The control problem
consists in evaluation of the optimal number of servers during
some specified stages and is solved by finite horizon dynamic programming
approach. To calculate the transient solutions we use a forth-order
Runge-Kutta method for the system with a truncated queue length. The
results are compared with corresponding queues operating in a stationary
regime. It is shown that the optimal control policies are also time
dependent and periodic as arrival rates and heterogeneous systems are
superior in performance comparing to the homogeneous ones.