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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.

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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