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Random walks in a queueing network environment. (English) Zbl 1344.60086

Summary: We propose a class of models of random walks in a random environment where an exact solution can be given for a stationary distribution. The environment is cast in terms of a Jackson/Gordon-Newell network although alternative interpretations are possible. The main tool are the detailed balance equations. The difference compared to earlier works is that the position of the random walk influences the transition intensities of the network environment and vice versa, creating strong correlations. The form of the stationary distribution is closely related to the well-known product formula.

MSC:

60K25 Queueing theory (aspects of probability theory)
60K37 Processes in random environments
60G50 Sums of independent random variables; random walks
60J27 Continuous-time Markov processes on discrete state spaces
60J28 Applications of continuous-time Markov processes on discrete state spaces
90B22 Queues and service in operations research
90B15 Stochastic network models in operations research
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References:

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