In this paper, the authors present an exact analysis of a queueing system with Poisson arrivals and batch service. The system has a finite number S of waiting places and a batch service capacity b. A service period is initialized when a service starting threshold a of waiting customers has been reached. The model is denoted accordingly by M/G’[a’,b’]/1-S. The motivation for this model arises from manufacturing environments with batch service work stations, e.g. in machines for computer components and chip productions. The method of embedded Markov chain is used for the analysis, whereby a representation of the general service time is obtained via a moment matching approach. Numerical results are shown in order to illustrate the dependency of performance measures on special sets of system parameters. Furthermore, attention is devoted to the issues of starting rules, where performance objectives like short waiting time, small blocking probability and minimal amount of work in progress are taken into account.
