Networks of Order Independent Queues with Signals

We study the steady-state distribution of networks of order independent queues with negative signals which delete customers. An Order Independent queue is defined by a service rate which is independent on the order of the customers in the queue. Such an abstract discipline may be used to model complex blocking mechanism (for instance the Multiserver Station with Concurrent Classes of Customers). Order independent queues are in general neither symmetric nor reversible. We prove that, under usual assumptions on the arrivals, the services and the routing of customers, such a network of queues with signals has a steady-state distribution with product form solution. The proof is based on the quasi-reversibility of the queues. We also present some examples of application for this new analytical result.