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Prognosis and optimization of homogeneous Markov message handling networks. (English) Zbl 1265.60140
Summary: Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchical networks, we find a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of system design and management are discussed, as well as the program 5P (program for prognosis of performance parameters and problems) based on the presented theoretical conclusions. The theoretic achievements as well as the practical applicability of the program are illustrated on a hypermarket network with 34 servers at different locations of the Czech Republic.
##### MSC:
 60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) 90B15 Stochastic network models in operations research
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