An alternative model for queueing systems with single arrivals, batch services and customer coalescence
In this paper we consider a queueing system with single arrivals, batch services and customer coalescence and we use it as a building block for constructing queueing networks that incorporate such characteristics. Chao et al. (1996) considered a similar model and they proved that it possesses a geometric product form stationary distribution, under the assumption that if the number of units present at a service completion epoch is less than the required number of units, then all the units coalesce into an incomplete (defective) batch which leaves the system. We drop this assumption and we study a model without incomplete batches. We prove that the stationary distribution of such a queue has a nearly geometric form. Using quasi-reversibility arguments we construct a network model with such queues which provides relevant bounds and approximations for the behaviour of assembly processes. Several issues about the validity of these bounds and approximations are also discussed.
batch service customer coalescence queueing network product form quasi-reversibility geometric distribution