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Heavy traffic approximation for the stationary distribution of stochastic fluid networks. (English) Zbl 1242.60092
Summary: It has recently been shown that in the heavy traffic limit, the stationary distribution of the scaled queue length process of a Generalized Jackson Network converges to the stationary distribution of its corresponding Reflected Brownian Motion limit. In this paper, we show that this “interchange of limits” is valid for Stochastic Fluid Networks with Lévy inputs. Furthermore, under additional assumptions, we extend the result to show that the interchange is valid for moments of the stationary distribution and for state-dependent routing. The results are obtained using monotonicity and sample-path arguments.
MSC:
60K25 Queueing theory (aspects of probability theory)
60G17 Sample path properties
90B15 Stochastic network models in operations research
90B18 Communication networks in operations research
60J25 Continuous-time Markov processes on general state spaces
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