The on-off network traffic model under intermediate scaling. (English) Zbl 1235.60121

Dombry, Clément; Kaj, Ingemar

Queueing Syst. 69, No. 1, 29-44 (2011).

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.

Reviewer: Oleg K. Zakusilo (Kyïv)

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

Keywords:

on-off process; workload process; renewal process; intermediate scaling; fractional Poisson motion; fractional Brownian motion; Lévy motion; heavy tails; long-range dependence

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