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The on-off network traffic model under intermediate scaling. (English) Zbl 1235.60121
The paper establishes an invariance principle for the normalized cumulative workload of a network with \(m\) on-off sources and time rescaled by a factor \(a\). When both the number of sources \(m\) and the time scale \(a\) tend to infinity with a relative growth given by the so-called “intermediate connection rate” condition, the limit process is the fractional Poisson motion.

MSC:
60K10 Applications of renewal theory (reliability, demand theory, etc.)
60G22 Fractional processes, including fractional Brownian motion
60F05 Central limit and other weak theorems
60K05 Renewal theory
90B15 Stochastic network models in operations research
90B20 Traffic problems in operations research
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