We are concerned with an M/G/1 queue in which service time distributions in each busy period may depend on the number of customers who have been served in the same busy period. This model is called an exceptional service model. Our major interest is to see a general structure of this model through the stationary waiting time distribution and some other characteristics. To this end, we take a regenerative cycle approach with respect to a busy cycle. This approach enables us to get several characteristics in tractable forms, from which we get some interesting properties of the exceptional service model. Numerical examples are presented as well.
