Pseudo-conservation law for discrete-time multi-queue systems with priority disciplines

The authors consider a discrete-time cyclic-service system consisting of multiple stations visited by a single server. Customers from several priority classes arrive at an individual station according to independent batch Bernoulli processes. They authors assume a non-preemptive priority rule and non-zero switch-over times of the server between consecutive stations. They derive an exact expression for a weighted sum of the mean waiting times for the individual priority classes: a pseudo-conservation law. Taking the limit of our result as the length tends to zero yields previously obtained continuous-time results.