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By Marc Schleyer

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Meng and Heragu (2004) achieve the same results with a somewhat different approach. They introduce the concept of a relative batch size which puts the batch size of an operation relative to the batch size of the succeeding operation. In our work we will derive different queueing models which include batch processes. In contrast to the above named authors who develop models for queueing networks with batch processing in the continuous time domain, we do our analysis in the discrete time 27 3. Queueing Analysis of Batch Processes domain.

We know that there is limited capacity in information and communication systems. The memory, the processor performance, and the capacity of the communication network have all their physical limitations. Thus, it is common in such systems to collect packages of data before it is sent or processed. Finally, the daily life is abound in examples of batch processes. For example, people arrive in groups for visiting a museum and the museum guide waits until a quota of persons to arrive before he starts his guiding tour.

Neuts (1965) studies the busy period of the M/G[1,K] /1-queue. 2. Literature Review of the distribution of the busy period by means of an embedded Markov chain. Additionally, he shows that the busy period is equal to the time elapsed between successive visits to the state “zero customers in the system” in a semi-Markov process. It is again Neuts (1967) who introduces a batch server system controlled by a control strategy called the minimum batch size rule. This strategy is driven by the number of customers in the queue.

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