Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010

Peer Reviewe

Dependent Double Branching Annihilating Random Walk

Double (or parity conserving) branching annihilating random walk, introduced by Sudbury in '90, is a one-dimensional non-attractive particle system in which positive and negative particles perform nearest neighbor hopping, produce two offsprings to neighboring lattice points and annihilate when they meet. Given an odd number of initial particles, positive recurrence as seen from the leftmost particle position was first proved by Belitsky, Ferrari, Menshikov and Popov in '01 and, subsequently in a much more general setup, in the article by Sturm and Swart (Tightness of voter model interfaces) in '08. These results assume that jump rates of the various moves do not depend on the configuration of the particles not involved in these moves. The present article deals with the case when the jump rates are affected by the locations of several particles in the system. Motivation for such models comes from non-attractive interacting particle systems with particle conservation. Under suitable assumptions we establish the existence of the process, and prove that the one-particle state is positive recurrent. We achieve this by arguments similar to those appeared in the previous article by Sturm and Swart. We also extend our results to some cases of long range jumps, when branching can also occur to non-neighboring sites. We outline and discuss several particular examples of models where our results apply.Comment: 35 pages, 7 figure

Propiedades y métodos de cálculo de la confiabilidad diámetro-acotada en redes

Tribunal : Kishor S. Trivedi, Guillermo Durán, Sergio Nesmachnow, Reinaldo Vallejos, Gerardo Rubino, Bruno Tuffin.Esta tesis aborda el problema del cálculo y estimación de la confiabilidad de redes con restricción de diámetro (DCR). Este problema es una generalización del cómputo de la confiabilidad clásica de redes (CLR). Se ha dedicado un esfuerzo considerable al estudio de la confiabilidad, debido a la relevancia que dichas métricas han tomado en contexto de redes reales durante los últimos 50 años, y al hecho de que el problema tiene complejidad computacional NP-hard aún bajo fuertes simplificaciones. La restricción de diámetro ha ganado relevancia debido al surgimiento de contextos en los cuales las latencias o número de saltos de los paquetes impactan en el desempeño de la red; por ejemplo voz sobre IP, P2P e interfaces ricas dentro de aplicaciones web