POISSONS-EQUATION FOR THE RECURRENT M G/1 QUEUE/

This paper shows how to calculate solutions to Poisson's equation for the waiting time sequence of the recurrent M/G/1 queue. The solutions are used to construct martingales that permit us to study additive fun ctionals associated with the waiting time sequence. These martingales provide asymptotic expressions, for the mean of additive functionals, that reflect dependence on the initial state of the process. In additi on, we show how to explicitly calculate the scaling constants that app ear in the central limit theorems for additive functionals of the wait ing time sequence.