A class of cyclic queues with priority batch service (Q1903266)

The authors consider a single-server multiple-station polling system with nonzero switch-over times. At each station customers of \(k\) different types arrive according to Poisson processes with intensities depending on station and customer type. Service is given simultaneously to a batch of customers of the same type; the service time of a batch is generally distributed and may depend on station and customer type. The service discipline entails that the server, when arriving at a station, looks for the highest ranking customer type among those for which the numbers of customers present exceed certain prespecified numbers (depending on station and customer type). If the latter set is empty, the server moves to the next station, otherwise it starts serving all the customers of the highest ranking type at the same time. Several performance measures of the system such as the mean intervisit time are obtained.