Whittle-networks with signals

We present an extension of Whittle networks with customers and signals as defined by Gelenbe in his seminal paper on negative customers. Customers are queued and served according to the balance rules defined for Whittle networks while signals are not queued but interact with the customers at their arrival. We consider various types of signals: they can delete customers, flush out a queue or change the class of a customer. We prove that all these networks have a product form steady-state distribution as soon as the signals obey a balance rule consistent with the service balance defined by Whittle.