G-Networks With Synchronized Partial Flushing

We study generalized networks of queues with a new type of signals which deletes customers in an ordered circular list of queues. By solving the balance equations, we prove that the steady-state distribution of the queue sizes has a product form. This model could be used to analyse assembly line systems and polling mechanisms. Keywords : Queueing networks; Product form solution; Synchronised transitions. 1 Introduction We present a new type of generalized network of queues (G-networks for short) with a steadystate product form solution. G-networks have been defined by Gelenbe in [4] and have received since this seminal paper a lot of attention (see for instance [7, 2, 9, 11]). G-networks consist of queues, ordinary customers and signals. Signals interact with the queues at their arrival but they are never queued and they do not receive service. At the completion of their service, a customer may join another queue as a signal. Thus G-networks exhibit much more general synchronized tran..