| Article ID: | iaor20127449 |
| Volume: | 34 |
| Issue: | 4 |
| Start Page Number: | 427 |
| End Page Number: | 448 |
| Publication Date: | Oct 2000 |
| Journal: | RAIRO - Operations Research |
| Authors: | Fourneau Jean-Michel, Verchre Dominique |
| Keywords: | queues: theory |
We study networks with positive and negative customers (or Generalized networks of queues and signals) in a random environment. This environment may change the arrival rates, the routing probabilities, the service rates and also 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 general result on multidimensional Markov chains.