A simulation Method for Network Performability Estimation using Heuristically-computed Pathsets and Cutsets

Consider a set of terminal nodes K that belong to a network whose nodes are connected by links that fail independently with known probabilities. We introduce a method for estimating any performability measure that depends on the hop distance between terminal nodes. It generalises previously introduced Monte Carlo methods for estimation of the K-reliability of networks with variance reduction compared to crude Monte Carlo. They are based on using sets of edges named d-pathsets and d-cutsets for reducing the variance of the estimator. These sets of edges, considered as a priori known in previous literature, heaviliy affect the attained performance; we hereby introduce and compare a family of heuristics for their selection. Numerical examples are presented, showing the significant efficiency improvements that can be obtained by chaining the edge set selection heuristics to the proposed Monte Carlo sampling plan

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

On the Reliability Estimation of Stochastic Binary System

A stochastic binary system is a multi-component on-off system subject to random independent failures on its components. After potential failures, the state of the subsystem is ruled by a logical function (called structure function) that determines whether the system is operational or not. Stochastic binary systems (SBS) serve as a natural generalization of network reliability analysis, where the goal is to find the probability of correct operation of the system (in terms of connectivity, network diameter or different measures of success). A particular subclass of interest is stochastic monotone binary systems (SMBS), which are characterized by non-decreasing structure. We explore the combinatorics of SBS, which provide building blocks for system reliability estimation, looking at minimal non-operational subsystems, called mincuts. One key concept to understand the underlying combinatorics of SBS is duality. As methods for exact evaluation take exponential time, we discuss the use of Monte Carlo algorithms. In particular, we discuss the F-Monte Carlo method for estimating the reliability polynomial for homogeneous SBS, the Recursive Variance Reduction (RVR) for SMBS, which builds upon the efficient determination of mincuts, and three additional methods that combine in different ways the well--known techniques of Permutation Monte Carlo and Splitting. These last three methods are based on a stochastic process called Creation Process, a temporal evolution of the SBS which is static by definition. All the methods are compared using different topologies, showing large efficiency gains over the basic Monte Carlo scheme.Agencia Nacional de Investigación e InnovaciónMath-AMSU

Topological Properties and Dynamic Programming Approach for Designing the Access Network

A wide area network (WAN) can be considered as a set of sites and a set of communication lines that interconnect the sites. Topologically a WAN is organized in two levels: the backbone network and the access network composed of a certain number of local access networks. Each local access network usually has a treelike structure, rooted at a single site of the backbone and connected users (terminal sites) either directly to this backbone site or to a hierarchy of intermediate concentrator sites which are connected to the backbone site. The backbone network has usually a meshed topology, and this purpose is to allow efficient and reliable communication between the switch sites that act as connection points for the local access networks. This work tackled the problem of designing the Access Network Design Problem (ANDP). Only the construction costs, e.g., the costs of digging trenches and placing a fiber cable into service, are considered here. Different results related to the topological structure of the ANDP solutions are studied. Given the complexity of the ANDP (the problem belongs to the NP-hard class), recurrences to solve it are proposed which are based on Dynamic Programming and Dynamic Programming with State-Space Relaxation methodology

A Survivable and Reliable Network Topological Design Model

This work is focused on the resolution of a mixed model for the design of large-sized networks. An algorithm is introduced, whose initial outcomes are promising in terms of topological robustness regarding connectivity and reliability. The algorithm combines the network survivability and the network reliability approaches. The problem of the topological design has been modeled based on the generalized Steiner problem with node-connectivity constraints (GSPNC), which is NP-hard. The aim of this study is to heuristically solve the GSP-NC model by designing low-cost highly connected topologies and to measure the reliability of such solutions with respect to a certain prefixed lower threshold. This research introduces a greedy randomized algorithm for the construction of feasible solutions for the GSP-NC and a local search algorithm based on the variable neighborhood search (VNS) method, customized for the GSP-NC. In order to compute the built network reliabilities, this work adapts the recursive variance reduction (RVR) technique, as a simulation method since the exact evaluation of this measurement is also NP-hard. The experimental tests were performed over a wide set of testing cases, which contained heterogeneous topologies, including instances of more than 200 nodes. The computational results showed highly competitive execution times, achieving minimal local optimal solutions of good quality fulfilling the imposed survivability and reliability conditions

Problema General de Steiner en Grafos :Resultados y algoritmos GRASP para la versión arista-disjunta

El Problema Generalizado de Steiner en Grafos (GSP) es un problema NP-hard de cobertura minimal de grafos con requerimientos de redundancia de conectividad, muy adecuado para modelar problemas reales de diseño topológico de redes de comunicación. La resolución determinística del problema sólo es factible para instancias de tamaño muy limitado, siendo en general para casos reales necesario recurrir a técnicas heurísticas para la generación de soluciones de bajo costo con un consumo razonable de recursos de cómputo y tiempo de ejecución. Los problemas se clasifican como de nodo-conectividad o arista-conectividad, según exijan o no los requerimientos de redundancia que no se compartan nodos intermedios entre caminos múltiples para conectar a las mismas parejas de nodos, modelándose así situaciones en las que tanto nodos como aristas pueden fallar, o solamente las aristas pueden hacerlo. En este trabajo, haciendo uso de una técnica metaheurística conocida como GRASP (Greedy Randomized Adaptive Search Procedure), extendemos las ideas planteadas en un trabajo previo para la versión de nodo-conectividad del GSP, hacia la versión de arista-conectividad. Se estudia la relación entre ambas versiones del problema, así como las complejidades introducidas por el modelo de arista-conectividad y se proponen mejoras a los algoritmos existentes. Proponemos también un mecanismo alternativo de creación voraz de soluciones y un mecanismo recursivo general para la implementación de metaheurísticas que generen soluciones para el GSP, sobre lo cual esperamos basar futuros trabajos de investigación

Diameter-constrained reliability : theory and applications

A classical requirement in the design of communication networks is that all entities must be connected. In a network where links may fail, the connectedness probability is called all-terminal reliability. The model is suitable for FTTH services, where link failures are unpredictable. In real scenarios, terminals must be connected by a limited number of hops. Therefore, we study the Diameter- Constrained Reliability (DCR). We are given a simple graph G = (V,E), a subset K V of terminals, a diameter d and independent failure probabilities q = 1 − p for each link. The goal is to find the probability Rd K,G that all terminals remain connected by paths composed by d hops or less. The general DCR computation is NP-Hard, and the target probability is a polynomial in p. In this chapter we study the DCR metric. It connects reliability with quality, and should be considered in the design of the physical layer in FTTH services together with connectivity requirements. We include a full discussion of the computational complexity of the DCR as a function of the number of terminals k = |K| and diameter d. Then, we find efficient DCR computation for Monma graphs, an outstanding family of topologies from robust network design. The computation suggests corollaries that enrich the subset of instances that accept efficient DCR computation. Given its NP-Hardness, several Monte Carlo-based algorithms algorithms are designed in order to find the DCR in general, inspired in two approaches: counting and interpolation. The results suggest that counting techniques outperform interpolation, and show scalability properties as well. Open problems and trends for future work are included in the conclusions

Pulso mínimo de agua para la emergencia de plántulas de tres especies de gramíneas perennes nativas del Monte Central (Argentina), influenciado por el efecto de la sombra y la estación del año

In deserts, seedling emergence occurs only after precipitation threshold has been exceeded, however, the presence of trees modifies microenvironmental conditions that might affect the effectiveness of a water pulse. In the Monte desert, Prosopis flexuosa trees generate different micro-environmental conditions that might influence grass seedlings establishment. The objective of this work was: a) to know the effective minimum water input event that triggers the emergence of native perennial grass seedlings; b) to relate this fact with the effect of the shade of P. flexuosa canopy and the seasonal temperatures. Three important forage species of the Monte were studied: Pappophorum caespitosum and Trichloris crinita, with C4, and Jarava ichu, with C3 metabolism. Each season, seeds of these species were sown in pots placed at two light conditions: shade (similar to P. flexuosa cover) and open area, and with seven irrigation treatments (0, 10, 20, 30, 40, 2*10 and 3*10 mm). J. ichu did not emerge in any of the treatments. Significant seedling emergence was registered for P. caespitosum and T. crinita in shade conditions with 40 mm irrigation treatment in summer. Since 40 mm precipitation events are infrequent in the Monte, seedling emergence for these species would be restricted to exceptional rainy years. The facilitating effect of P. flexuosa shade would be important during the hot season.En los desiertos, la emergencia de las plántulas se produce cuando un evento de precipitación excede un valor umbral. La presencia de árboles modifica las condiciones micro ambientales y en consecuencia, la efectividad de los eventos de lluvia. En el Monte, las condiciones generadas por Prosopis flexuosa (algarrobo) afectarían el establecimiento de las gramíneas. El objetivo del trabajo fue: a) conocer el evento mínimo de agua necesario para desencadenar la emergencia de gramíneas perennes; b) relacionarlo con la influencia de la sombra del algarrobo y las temperaturas estacionales. Se trabajó con tres especies nativas de gramíneas forrajeras perennes: Pappophorum caespitosum, Trichloris crinita, (C4), y Jarava ichu (C3). En cada estación del año, semillas de las tres especies fueron sembradas en macetas bajo dos condiciones lumínicas: sombra (similar a la sombra de P. flexuosa) y área abierta y con siete niveles de riego (0, 10, 20, 30, 40, 2*10 y 3*10 mm). Jarava ichu no emergió en ningún tratamiento. En el verano se obtuvo emergencia significativa de T. crinita y P. caespitosum solo en los tratamientos de 40 mm y a la sombra. Debido a que en el Monte los eventos de precipitación de 40 mm son infrecuentes, la emergencia de estas especies ocurriría en los años excepcionalmente lluviosos. El efecto facilitador de la sombra del algarrobo sería de importancia en la estación cálida.Fil: Greco, Silvina A.. Universidad Nacional de Cuyo. Facultad de Ciencias AgrariasFil: Sartor, Carmen E.. Universidad Nacional de Cuyo. Facultad de Ciencias AgrariasFil: Villagra, Pablo E.. Universidad Nacional de Cuyo. Facultad de Ciencias Agraria