We consider a discrete-time cyc}ic-service system consisting of multiple stations visited by a single server. Custemers from severa} priorit,y classes arrive at an individual station according to independent batcli Bernoulli processes. We assume a non-preemptive priority rule and non-zero switch-over times of the server between consecutive stations. "la derive an exact expressien for a weighted sum of the mean waiting times for the individual priority classes: a pseudo-conservation law. Taking

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... he limit of our result as the length tends to zero yields previeusly obtained continuous-time results. The Opeiations Reseaich Society of Japan Rs'eudo-a)nservettion Lnw for Discrcte-Timc ,S}fsten?s 451 batch Bernoulli process input system, In Section 4, by letting the slot length tend to zero, we obtain the continuous-time results foi' Poisson input systems (2, 8, 171 as special cases. Model description and preliminary results Time is divided into slots which are equa,1 to time unity (one) in Iength. This unit-time slot, is assumed for Sections 2 and 3. We consider a multi-queue, single-server system with College of Engineering 3-9-11 Midori-cho, Musashino-shi