In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate.

Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.

This paper considers a dam of infinite capacity with a discrete-valued stationary input process and a unit release whenever possible. It is shown how, by suitable manipulations of the equation governing the dam content process, the stationary distribution of the dam being empty can be obtained, as also can (with a few additional assumptions) the expected value of the dam content in the stationary case. Results obtained are applied to particular cases of input — independent and identical, Markov, Bivariate Markov and moving-average.