A diffusion approximation for batch queues of type GX/G(b,b)/1

Queues with bulk arrivals and batch service arise in a variety of application areas, in particular in the performance analysis of manufacturing lines, like semiconductor fabrications. In the course of this paper, a diffusion approximation for queueing systems with bulk arrivals and batch service for general and independent interarrival time distributions, as well as general service time distributions, is presented. The approximation uses a modified absorbing barrier and instantaneous return approach. The accuracy of the gained approximation is shown by a subsequent comparison with the corresponding discrete event simulation results.