Resumen

FERNANDEZ, Carina; BAVIO, José  y  MARRON, Beatriz. The significance of the Perron-Frobenius eigenvalue for the characterization of a measure of channel occupancy in data networks. Rev. Mat [online]. 2025, vol.32, n.1, pp.52-68. ISSN 1409-2433.  http://dx.doi.org/10.15517/rmta.v32i1.59733.

Telecommunications is currently one of the most important technologies, utilizing various infrastructure elements to enable communication over the Internet. When an internet connection is established, traffic packets are routed from one device to another, taking different paths through routers that process each packet. These networks present multiple challenges in processing, distributing and connecting traffic. To address these challenges it is necessary, on the one hand, to have models that describe the behavior of traffic and its evolution over time, such as the Generalized Markov Fluid Model. On the other hand, it is essential to reserve part of the available resource at each node for ongoing connections. To carry out this reservation process, the Effective Bandwidth is employed. In this paper, we describe the distribution of the buffer in equilibrium for traffic sources modeled by a Generalized Markov Fluid Model, using a system of differential equations. As the main result of this paper, we prove that it is possible for this model to characterize the effective bandwidth when the most probable duration of the buffer busy period prior to overflow becomes larger and larger. Finally, we verify this result numerically from simulated traffic traces.

Palabras clave : Effective bandwidth; Markov fluid; Eigenvalues; Perron-Frobenius method; Differential equations..

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