Modelling of self-similar teletraffic for simulation

Recent studies of real teletraffic data in modern computer networks have shown that teletraffic exhibits self-similar (or fractal) properties over a wide range of time scales. The properties of self-similar teletraffic are very different from the traditional models of teletraffic based on Poisson, Markov-modulated Poisson, and related processes. The use of traditional models in networks characterised by self-similar processes can lead to incorrect conclusions about the performance of analysed networks. These include serious over-estimations of the performance of computer networks, insufficient allocation of communication and data processing resources, and difficulties ensuring the quality of service expected by network users. Thus, full understanding of the self-similar nature in teletraffic is an important issue. Due to the growing complexity of modern telecommunication networks, simulation has become the only feasible paradigm for their performance evaluation. In this thesis, we make some contributions to discrete-event simulation of networks with strongly-dependent, self-similar teletraffic. First, we have evaluated the most commonly used methods for estimating the self-similarity parameter H using appropriately long sequences of data. After assessing properties of available H estimators, we identified the most efficient estimators for practical studies of self-similarity. Next, the generation of arbitrarily long sequences of pseudo-random numbers possessing specific stochastic properties was considered. Various generators of pseudo-random self-similar sequences have been proposed. They differ in computational complexity and accuracy of the self-similar sequences they generate. In this thesis, we propose two new generators of self-similar teletraffic: (i) a generator based on Fractional Gaussian Noise and Daubechies Wavelets (FGN-DW), that is one of the fastest and the most accurate generators so far proposed; and (ii) a generator based on the Successive Random Addition (SRA) algorithm. Our comparative study of sequential and fixed-length self-similar pseudo-random teletraffic generators showed that the FFT, FGN-DW and SRP-FGN generators are the most efficient, both in the sense of accuracy and speed. To conduct simulation studies of telecommunication networks, self-similar processes often need to be transformed into suitable self-similar processes with arbitrary marginal distributions. Thus, the next problem addressed was how well the self-similarity and autocorrelation function of an original self-similar process are preserved when the self-similar sequences are converted into suitable self-similar processes with arbitrary marginal distributions. We also show how pseudo-random self-similar sequences can be applied to produce a model of teletraffic associated with the transmission of VBR JPEG /MPEG video. A combined gamma/Pareto model based on the application of the FGN-DW generator was used to synthesise VBR JPEG /MPEG video traffic. Finally, effects of self-similarity on the behaviour of queueing systems have been investigated. Using M/M/1/∞ as a reference queueing system with no long-range dependence, we have investigated how self-similarity and long-range dependence in arrival processes affect the length of sequential simulations being executed for obtaining steady-state results with the required level of statistical error. Our results show that the finite buffer overflow probability of a queueing system with self-similar input is much greater than the equivalent queueing system with Poisson or a short-range dependent input process, and that the overflow probability increases as the self-similarity parameter approaches one

Modelos de series temporales para simulación de procesos industriales : aplicación al dimensionamiento y control de sistemas altamente variables

[Resumen] La simulación es una reconocida metodología para la modelización de sistemas productivos. Dentro de un proyecto de simulación, el análisis de los datos de entrada al modelo es una fase crítica que condiciona la validez de los resultados. Aunque diversos autores han indicado anteriormente la importancia de modelar adecuadamente las propiedades estadísticas de las series de temporales de un proceso, pocos trabajos del área han analizado los modelos adecuados para su empleo práctico más allá de la asunción de la hipótesis de independencia e igualdad de distribución (i.i.d.). Con el fin de proporcionar una metodología flexible para la modelización de series con autocorrelación, se considera la adopción de los modelos ARTA (proceso autorregresivo a distribución general). Estos modelos son empleados para estudiar el comportamiento de líneas con autocorrelación en los tiempos de ciclo. El estudio llevado a cabo permite determinar el impacto que la presencia de autocorrelación tiene sobre el rendimiento de la línea, sobre las soluciones al problema de dimensionamiento óptimo y asignación de buffers y sobre los sistemas de control de la producción. Por otro lado, se proporciona un marco conceptual para caracterizar la presencia de variabilidad en múltiples escalas temporales y se analiza la influencia que la consideración de modelos con distintas escalas ejerce sobre los resultados. La tesis se completa con el estudio de un caso paradigmático de una línea de fabricación altamente variable. Se muestra cómo la adopción de un modelo con dos escalas temporales, junto con la consideración de los efectos de autocorrelación, fueron medios necesarios para obtener un modelo válido. Este modelo fue empleado para la valoración de mejoras bajo un enfoque de fabricación Lean