Poisson's equation for the recurrent M/G/1 queue
- 1 December 1994
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 26 (4) , 1044-1062
- https://doi.org/10.2307/1427904
Abstract
This paper shows how to calculate solutions to Poisson's equation for the waiting time sequence of the recurrent M/G/l queue. The solutions are used to construct martingales that permit us to study additive functionals 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 addition, we show how to explicitly calculate the scaling constants that appear in the central limit theorems for additive functionals of the waiting time sequence.Keywords
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