Triggered Concurrent Batch Arrivals and Batch Departures in Queueing Networks

We consider a queueing network with concurrent batch arrivals and batch services. In addition to the batch movement assumptions made in the regular queueing literature, in this paper we assume that the batch movement can also be triggered by arrivals and/or departures. Specifically, an arriving or departing batch may induce another event to occur before they are routed. This triggered event may either be the addition of a batch of customers to the network, or the removal of a batch of customers from the network. This special feature makes it useful in the study of discrete event dynamic systems with concurrent or simultaneous sequential activities. By assuming that there is an additional arrival process to the network, we show that its stationary distribution has a product form, which depends on a set of non-standard nonlinear traffic equations. Furthermore, this simple product form solution is a stochastic upper bound for the network without the additionally introduced arrivals. Besides, we show that the network satisfies a class of non-standard local balance equations.