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Zbl 0991.90038
Fourneau, Jean-Michel; Verchère, Dominique
Generalized networks in a random environment. ($G$-réseaux dans un environment aléatoire.)
(French)
[J] RAIRO, Oper. Res. 34, No.4, 427-448 (2000). ISSN 0399-0559; ISSN 1290-3868/e

Summary: 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.
MSC 2000:
*90B22 Queues and service
90C40 Markov decision processes, etc.
90B10 Flows in networks

Keywords: queues; product form; random environment; generalized network

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