On the LRD of the aggregated traffic flows in high-speed computer networks (Draft 1)

Abstract

This paper studies and analyses the behavior of the Long-Range Dependence in network traffic after classifying trafficflows in aggregated time series. Following Differentiated Services architecture principles, the generic Quality of Service applications that requirements and use the transport control protocol, a basic classification criterion of time series is established. Using the fractal theory, the resulting time series are analyzed. The Hurst exponent is estimated and used as a measure of traffic burstiness and Long- Range Dependency in each traffic class. The traffic volume per class is also measured. The study uses traffic traces collected at the core switch at the Electric Engineering Department at Universidad de Santiago de Chile in different periods of network activity.

A flow control algorithm for high-speed computer networks

“…Puesto que el modelo es discreto, el parámetro de tiempo t que representa el tiempo continuo se reemplaza por el índice de paso k, el cual representa el tiempo de ida y vuelta RTT [11]. En el nodo cuello de botella la tasa de servicio se encuentra cerca de RTT [12], por lo tanto se considera que u b (k)  u b (k  1) es una constante.…”

“…En el nodo cuello de botella la tasa de servicio se encuentra cerca de RTT [12], por lo tanto se considera que u b (k)  u b (k  1) es una constante. En el momento marcado "NOW" de la Figura 2 de [12]; al final de la kth época la totalidad de los paquetes enviados en la época k  1 han sido reconocidos [11], [12]. De forma que los únicos paquetes no reconocidos son los enviados en la misma época y esto es lo mismo que hablar del número de paquetes independientes.…”

On the generation of self-similar with long-range dependent traffic using piecewise affine chaotic one-dimensional maps (extended and renewed version)

“…These systems are of low-order because they can be described correctly by a reduced number of variables and parameters [4]. They are also dynamic systems, i.e., with the variables of interest [4], [5], which are deterministic, evolve over time, because the values of those variables at any instant of time can be determined only from their previous values given a set of dynamic laws. Finally, those dynamic laws that describe the system evolution in time are non-linear [4].…”

“…At this point it is convenient to make it clear that chaotic systems differ from conventional dynamic systems in the sense that they are intrinsically unpredictable, a fact that is evident even when its subjacent dynamic laws are of a deterministic character. But the above does not have to lead to the belief that chaos implies unpredictability, since that is only partially true because of existence of two main sources of unpredictability, namely the inaccuracy of the initial data, and its origin as a characteristic inherent to certain nonlinear relations between numerical variables [5]. Therefore, the definition of chaos as a property of a system refers to its sensitivity [6] to the initial conditions, i.e.…”

Second-order self-Similar time series and complex telecommunication systems analysis

“…OS procesos estadísticamente autosimilares representan el comportamiento estocástico invariante a cambios de escalas [1]- [4]. Estos procesos se aplican ampliamente como modelos en una amplia gama de campos de la ciencia [5]- [10]. En el área de las redes de computadoras estos procesos se usan para modelar el tráfico LAN agregado, el tráfico de vídeo VBR, el tráfico inalámbrico y el tráfico debido al WWW, entre otros.…”