<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332025000100052</article-id>
<article-id pub-id-type="doi">10.15517/rmta.v32i1.59733</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[The significance of the Perron-Frobenius eigenvalue for the characterization of a measure of channel occupancy in data networks]]></article-title>
<article-title xml:lang="es"><![CDATA[Importancia del autovalor de Perron-Frobenius para la caracterización de una medida de ocupación del canal en redes de datos]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Fernández]]></surname>
<given-names><![CDATA[Carina]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bavio]]></surname>
<given-names><![CDATA[José]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Marrón]]></surname>
<given-names><![CDATA[Beatriz]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad Nacional del Sur Departamento de matemática ]]></institution>
<addr-line><![CDATA[Bahía Blanca Buenos Aires]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad Nacional del Sur Departamento de matemática ]]></institution>
<addr-line><![CDATA[Bahía Blanca Buenos Aires]]></addr-line>
<country>Argentina</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad Nacional del Sur Departamento de matemática ]]></institution>
<addr-line><![CDATA[Bahía Blanca Buenos Aires]]></addr-line>
<country>Argentina</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>03</month>
<year>2025</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>03</month>
<year>2025</year>
</pub-date>
<volume>32</volume>
<numero>1</numero>
<fpage>52</fpage>
<lpage>68</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332025000100052&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332025000100052&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332025000100052&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract 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.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen En la actualidad, una de las tecnologías más importantes son las telecomunicaciones, las cual despliega diversos elementos de infraestructura para permitir la comunicación a través de internet. Cuando se establece una conexión a internet, los paquetes de tráfico se dirigen de un dispositivo a otro, recorriendo diversas rutas a través de routers que procesan cada paquete. Estas redes presentan múltiples desafíos a la hora de procesar, distribuir y conectar el tráfico. Para abordar estos retos es necesario, por un lado, disponer de modelos que describan el comportamiento del tráfico y su evolución en el tiempo, como el Modelo de Flujo Markoviano Generalizado. Por otro lado, reservar en cada nodo parte del recurso disponible para las conexiones en proceso y para llevar a cabo este proceso de reserva se utiliza el Ancho de Banda Efectivo. En este trabajo describimos, a partir de un sistema de ecuaciones diferenciales, la distribución del buffer en equilibrio en fuentes de tráfico modeladas por un Modelo de Flujo Markoviano Generalizado. Como resultado principal de este trabajo, demostramos para este modelo, que es posible caracterizar el ancho de banda efectivo cuando la duración más probable del periodo ocupado del buffer antes del desbordamiento se hace cada vez mayor. Finalmente, verificamos numéricamente este resultado a partir de trazas de tráfico simuladas.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Effective bandwidth]]></kwd>
<kwd lng="en"><![CDATA[Markov fluid]]></kwd>
<kwd lng="en"><![CDATA[Eigenvalues]]></kwd>
<kwd lng="en"><![CDATA[Perron-Frobenius method]]></kwd>
<kwd lng="en"><![CDATA[Differential equations.]]></kwd>
<kwd lng="es"><![CDATA[Ancho de banda efectivo]]></kwd>
<kwd lng="es"><![CDATA[Flujo markoviano]]></kwd>
<kwd lng="es"><![CDATA[Autovalores]]></kwd>
<kwd lng="es"><![CDATA[Método de Perron-Frobenius]]></kwd>
<kwd lng="es"><![CDATA[Ecuaciones diferenciales.]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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