Multiple Class Symmetric G-networks with Phase Type

Abstract

We consider a queueing network of symmetric Gqueues with customers and signals. Since the seminal papers by Gelenbe in the early nineties [7, 9, 10], Generalized networks of queues have received consid- erable attention. But most papers assume to obtain product form that the service times follow exponential distributions. Here we propose a new generalisation of this model with Phase type service times. We also as- sume a new type of signal. When the signal enters a queue, it changes the phase of the customer in service when there is any. As usual after its service completion, a customer moves to another queue and may become a signal. The steady-state distribution for such a network of queues has a product form solution.