Abstract
In this paper we consider a polling system with two classes of stations; high priority and low priority. High priority stations are polled more frequently than low priority stations. We derive an exact and explicit formula for computing the mean waiting times for a message when the arrival processes are batch Poisson. In general the formula requires to solve two sets of simultaneous equations By specializing them to the case of two priority classes we greatly reduce the number equations and provide a simple formula for mean waiting times. We apply the results to a data communication processing system and show that the overall mean waiting time can be reduced by using priority polling.