Anisotropic scaling of the random grain model with application to network traffic. (English) Zbl 1351.60064

Pilipauskaitė, Vytautė; Surgailis, Donatas

J. Appl. Probab. 53, No. 3, 857-879 (2016).

Summary: We obtain a complete description of anisotropic scaling limits of the random grain model on the plane with heavy-tailed grain area distribution. The scaling limits have either independent or completely dependent increments along one or both coordinate axes and include stable, Gaussian, and ‘intermediate’ infinitely divisible random fields. The asymptotic form of the covariance function of the random grain model is obtained. Application to superimposed network traffic is included.

MSC:

60G60	Random fields
60G22	Fractional processes, including fractional Brownian motion
60G51	Processes with independent increments; Lévy processes
60K25	Queueing theory (aspects of probability theory)

Keywords:

random grain model; anisotropic scaling; long-range dependence; Lévy sheet; fractional Brownian sheet; workload process