On conditions for a product-form stationary probability distribution of states of a multimode service network

We consider open and closed queueing networks with Markovian routing and symmetric service policies. Single-server nodes may operate in several modes. In each node, the amount of work required for servicing an arrival or for switching the mode is distributed arbitrarily. The performance rate for each of these operations depends on the residual amount of work. For open networks, the arrival flow is Poissonian. We establish conditions for a productform stationary distribution of states of the piecewise continuous process that describes the network behavior.