Abstract
The paper deals with queueing systems in which N- and D-policies are
combined into one. This means that an idle or vacationing server will resume his
service if the queueing or workload process crosses some specified fixed level N or
D, respectively. For the proposed (N,D)-policy we study the queueing processes in
models with and without server vacations, with compound Poisson input, and
with generally distributed service and vacation periods. The analysis of the
models is essentially based on fluctuation techniques for two-dimensional marked
counting processes newly developed by the author. The results enable us to arrive
at stationary distributions for the embedded and continuous time parameter
queueing processes in closed analytic forms, enhancing the well-known Kendall
formulas and their modifications.
This article is dedicated to the memory of Roland L. Dobrushin.