Analysis of the Departure Process of a Batch Service Queueing System

We investigate a queueing system with batch service or bulk service Batch servers are common in many areas of manufacturing for example in the manufacturing of semiconductors In particular we study a batch server operated under the minimum batch size rule Under this rule a service will be initiated as soon as the number of lots waiting for service reaches a certain threshold This threshold can be arbitrarily chosen Using discrete time analysis we derive the interdeparture time distribution for batches and for single lots It is shown that the interdeparture time distribution of a batch service system has characteristic properties that can not be approximated with su cient accuracy by other commonly used distributions We further study the distribution of the number of lots in the departing batches and the correlation between interdeparture times and batch sizes