The distributions and the first two moments of the busy and idle periods in classical controllable M / G/1 queueing models operating under the N -policy, the T-policy and the D-policy are derived. We also consider controllable M/G/1 queueing systems operating under six dyadic policies. Each of these policies is a different combination of the three aforementioned simple policies. For the distributions of the busy and idle periods the desired results are obtained in terms of the respective distributions for the ordinary M/G/1 queueing system. In all instances, we prove that the probability that the server is busy in the steady state is equal to the traffic intensity. The special case of the M/M/1 system is studied