Whittle networks with resets

We present an extension of Whittle networks which contains multiple classes of customers and some signals as defined by Gelenbe. Customers are queued and served according to the balance rules defined for Whittle networks. Signals are not queues and interact with the customers present in the queue. We consider the reset signal previously introduced for single class networks. A reset signal entering a non empty queue deletes a customer but if the queue is empty, it fills the queue with a random number of customers. The distribution of this random variable is closely related to the steady-state distribution of the queue. We prove that these networks have a product form steady-state distribution.