Stability of batch processing networks under batch First-In First-Out service

Based on the steady state of the standard queuing network, a batch FIFO service discipline is defined. By bringing in a random vector of the batch size, the authors have adapted the batch processing queuing network model into the corresponding standard queuing network model, demonstrating that the two queuing network models have the same fluid model. Furthermore, they have obtained a sufficient condition of the rate stability of the batch processing queuing network under the batch FIFO service disciplines.