Multiple class G-networks with list-oriented deletions

We study a new dynamic of generalized networks (G-networks) of queues. We consider networks with multiple classes of customers and signals, and three types of service disciplines: first-in-first-out (FIFO), last-in-first-out with pre-emptive resume priority (LIFO/PR) and processor sharing (PS). Moreover, we consider a probabilistic deleting mechanism based on iterated deletions of customers according to an arbitrary list of service stations. We prove that these networks have a steady-state product-form solution and we investigate the existence of a solution to the traffic equation of such networks.