Pseudo-conservation law for a priority polling system with mixed service strategies

In this paper we consider a discrete-time cyclic-service system consisting of multiple stations visited by a single server. Several priority classes of customers arrive at each station according to independent batch Bernoulli processes. The head-of-the-line (HL) priority rule and non-zero switch-over times between stations are assumed. The customers are served at each station under a mixed (exhaustive, gated, and 1-limited) service strategy. We obtain an exact expression for a weighted sum of the mean waiting times for the individual priority classes, a so-called pseudo-conservation law. A continuous-time result is derived as a special case of our model.