Stability of Discrete-Time Jackson Networks with Batch Movements

Abstract

We introduce a discrete-time Jackson network with batch movements. Not more than one node simultaneously completes service, but arbitrary sizes of batch arrivals, departures and transfers are allowed under a Markovian routing of batches including changes of their sizes. This model corresponds with the continuous-time network work with batch movements studied by Miyazawa and Taylor [11], but needs a care for the discrete-time setting. It is shown that the stationary joint distribution of queue length vector is stochastically bounded by a product of geometric distributions under the stability condition. Its improvements and tightness are discussed. We also provide an algorithm to calculate the decay rates of the geometric distributions, which answers the stability of the network as well.KeywordsTime SlotBatch SizeGeometric DistributionQueueing SystemBatch ArrivalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.