G-networks in a random environment

We study networks with positive and negative customers (or Generalized netw orks of queues and signals) in a random environment. This environment may c hange the arrival rates, the routing probabilities, the service rates and a lso the effect of signals. We prove that the steady-state distribution has a product form. This property is obtained as a corollary of a much more gen eral result on multidimensional Markov chains.