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Weak convergence of high-speed network traffic models. (English) Zbl 1028.90008
Summary: We consider a network traffic model consisting of an infinite number of sources linked to a server. Sources initiate transmissions to the server at Poisson time points. The duration of each transmission has a heavy-tailed distribution. We show that suitable scalings of the traffic process converge to a totally skewed stable Lévy motion in Skorokhod space, equipped with the Skorokhod $$M_1$$ topology. This allows us to prove a heavy-traffic theorem for a single-server fluid model.

##### MSC:
 90B15 Stochastic network models in operations research 90B18 Communication networks in operations research 90B22 Queues and service in operations research 60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
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