  We consider a model describing the waiting time of a server alternating
between two service points. This model is described by a Lindley-type equation.
We are interested in the time-dependent behaviour of this system and derive
explicit expressions for its time-dependent waiting-time distribution, the
correlation between waiting times, and the distribution of the cycle length.
Since our model is closely related to Lindley's recursion, we compare our
results to those derived for Lindley's recursion.
