A Survivable & Reliable Network Topological Design Model

This paper is focused on the resolution of a mixed model for the design of large size networks which will be topologically robust regarding its connectivity and reliability. More precisely, we combined the Network Survivability & Network Reliability approaches. The problem of the topological design has been modeled based on the Generalized Steiner Problem with Node-Connectivity Constraints (GSP-NC), which is NP-Hard. Our aim 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. We introduce a Greedy Randomized algorithm for the construction of feasible solutions for the GSP-NC and a local search algorithm based on the Variable Neighbourhood Search (VNS) method customized for the GSP-NC. To compute the built networks reliabilities we adapted the Recursive Variance Reduction (RVR) technic as 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

Diseño topológico de redes : casos de estudio :"The generalized Steiner problem"and "The Steiner 2-edge-connected subgraph problem"

Dado un grafo G=(V,E), una matriz C de costos asociados a las aristas, un subconjunto T de nodos denominados terminales y una matriz R de requerimientos de conexión entre nodos terminales, el "Generalized Steiner Problem" (GSP)consiste en encontrar un subgrafo Gs de G de costo mínimo tal que para todo par de nodos terminales existen al menos Rij caminos de aristas-disjuntas en Gs. Un grafo se dice 2-arista-conexo si entre todo par de nodos existen al menos 2 caminos de aristas disjuntas que los unen. Dos casos particulares de GSP son: encontrar un subgrafo Gs de G 2-arista-conexo de costo mínimo que cubra el conjunto de nodos terminales T, este problema es conocido como "Steiner 2-edge-connected subgraph problem"(STECSP), - encontrar un subgrafo Gs de G de costo mínimo tal que para todo par de nodos terminales existen al menos 2 caminos de aristas disjuntas que los unen, este problema es conocido como "Steiner 2-edge survivable subgraph problem" (STESNP)

Recursive variance reduction in reliability analysis

Network reliability deals with reliability metrics of large classes of mul- ticomponent systems. Recursive Variance Reduction (RVR) is a powerful pointwise estimation method, widely applied in network reliability anal- ysis. In this paper, RVR is extended to arbitrary Stochastic Binary Sys- tems, with minor requirements. Additionally, its variance is again lower than Crude Monte Carlo (CMC), in this general context

Informe final de actividades Grupo Simuladores

Este documento presenta un informe de las actividades realizadas por el grupo Simuladores de la Actividad 6 del convenio ANTEL-FING \Análisis de la red 3G de ANTEL", en el período del proyecto

Solving the Generalized Steiner Problem in edge-survivable networks

The Generalized Steiner Problem with Edge-Connectivity constraints (GSP-EC) consists of computing the minimal cost subnetwork of a given feasible network where some pairs of nodes must satisfy edge-connectivity requirements. It can be applied in the design of communications networks where connection lines can fail and is known to be an NP-Complete problem. In this paper we introduce an algorithm based on GRASP (Greedy Randomized Adaptive Search Procedure), a combinatorial optimization metaheuristic that has proven to be very effective for such problems. Promising results are obtained when testing the algorithm over a set of heterogeneous network topologies and connectivity requirements; in all cases with known optimal cost, optimal or near-optimal solutions are found

Network reliability analysis and intractability of counting diameter crystal graphs

Consider a stochastic network, where nodes are perfect but links fail independently, ruled by failure probabilities. Additionally, we are given distinguished nodes, called terminals, and a positive integer, called diameter. The event under study is to connect terminals by paths not longer than the given diameter. The probability of this event is called diameter-constrained reliability (DCR, for short). Since the DCR subsumes connectedness probability of random graphs, its computation belongs to the class of NP-Hard problems. The computational complexity for DCR is known for fixed values of the number of terminals k n and diameter d, being n the number of nodes in the network. The contributions of this article are two-fold. First, we extend the computational complexity of the DCR when the terminal size is a function of the number of nodes, this is, when k = k(n). Second, we state counting diameter-critical graphs belongs to the class of NP-Hard problems

The capacitated m two node survivable star problem

The problem addressed in this paper attempts to efficiently solve a network design with redundant connections, often used by telephone operators and internet services. This network connects customers with one master node and sets some rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated m Two- Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated m Ring Star Problem). In this variant of CmRSP the rings are not constrained to be cycles; instead, they can be two node connected components. The contributions of this paper are (a) introduction and definition of a new problem (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work

Nash equilibrium in evolutionary competitive models of firms and workers under external regulation

The object of this paper is to study the labor market using evolutionary game theory as a framework. The entities of this competitive model are firms and workers, with and without external regulation. Firms can either innovate or not, while workers can either be skilled or not. Under the most simple model, called normal model, the economy rests in a poverty trap, where workers are not skilled and firms are not innovative. This Nash equilibria is stable even when both entities follow the optimum strategy in an on-off fashion. This fact suggests the need of an external agent that promotes the economy in order not to follow in a poverty trap. Therefore, an evolutionary competitive model is introduced, where an external regulator provides loans to encourage workers to be skilled and innovative firms. This model includes poverty traps but another Nash equilibria, where firms and workers are jointly innovative and skilled. The external regulator, in a three-phase process (loans, taxes and inactivity) achieves a common wealth, with a prosperous economy, with innovative firms and skilled workers

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