The paper deals with polling systems consisting of $N$ queues, where Poisson streams of jobs arrive from outside (transient jobs). A single server serves the queues in a cyclic manner and reside in each queue according to some service discipline. All queues will be served by the same discipline which may be gated, exhaustive or globally-gated. When moving from station $i$ to $i+1$, the server incurs a random switch-over time. In addition there are $M$ permanent jobs in the system, each one randomly routed from one queue to another every time it completes a service. For this system the multidimensional generating functions of the number of jobs at the various queues at polling instants and at arbitrary points in time are derived. For each regime the interaction between the two populations of jobs are investigated and formulae for the means, as well as expressions for calculating the second moments, of the number of jobs at the various queues are derived. Waiting times and throughput rates are calculated and the systems are compared with each other.
Reviewer: A.Brandt (Berlin)