This paper focuses on helping network providers to carry out network capacity planning and sales projection by answering the question: For a given topology and capacity, whether the network can serve current flow demands with high probabilities? We name such probability as “ flow availability” and present the -flow availability estimation (FAVE) problem, which is a generalisation of network connectivity or maximum flow reliability estimations. Realistic networks are often large and dynamic, so flow availabilities cannot be evaluated analytically and simulation is often used. However, naive Monte Carlo (MC) or importance sampling (IS) techniques take an excessive amount of time. To quickly estimate flow availabilities, we utilize the correlations among link and flow failures to figure out the importance of roles played by different links in flow failures, and design three “sequential importance sampling” (SIS) methods which achieve “bounded or even vanishing relative error” with linear computational complexities. When applying to a realistic network, our method reduces the flow availability estimation cost by 900 and 130 times compared with MC and baseline IS methods, respectively. Our method can also facilitate capacity planning by providing better flow availability guarantees, compared with traditional methods.
Network connectivity reliability (NCR) : NCR is a classical reliability measure adopted by most work @cite_5 @cite_21 @cite_16 . The network ! ! is modelled as a graph where links are either failed or operational, and NCR is measured by the probability that a given set of nodes are connected when links fail with given probabilities. Authors in @cite_5 take network repair policies into consideration to model link failures, and estimate NCR with the classical MC Authors in @cite_21 combine MC with the particle swarm optimization to handle the NCR problem. To improve the efficiency of MC, authors in @cite_16 apply the IS method and use pre-computed " to approximate the optimal IS estimator.
@cite_5 @cite_21 @cite_16
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The classic all-terminal network reliability problem posits a graph, each of whose edges fails independently with some given probability. The goal is to determine the probability that the network becomes disconnected due to edge failures. This problem has obvious applications in the design of communication networks. Since the problem is @math -complete and thus believed hard to solve exactly, a great deal of research has been devoted to estimating the failure probability. In this paper, we give a fully polynomial randomized approximation scheme that, given any n-vertex graph with specified failure probabilities, computes in time polynomial in n and @math an estimate for the failure probability that is accurate to within a relative error of @math with high probability. We also give a deterministic polynomial approximation scheme for the case of small failure probabilities. Some extensions to evaluating probabilities of @math -connectivity, strong connectivity in directed Eulerian graphs and @math -way disconnection, and to evaluating the Tutte polynomial are also described. This version of the paper corrects several errata that appeared in the previous journal publication [D. R. Karger, SIAM J. Comput., 29 (1999), pp. 492--514]. We consider the network reliability problem in secure wireless sensor networks that employ a heterogeneous random key predistribution scheme. This scheme is introduced recently, as a generalization of the Eschenauer-Gligor scheme, to account for the cases when the network comprises sensors with varying level of resources or connectivity requirements; e.g., regular nodes vs. cluster heads. The scheme induces the inhomogeneous random key graph, denoted G(n;μ,K, P ), where each of the n nodes are independently assigned to one of r classes according to a probability distribution μ = (μ1, . . . , μr) and then a class-i node is assigned Ki keys uniformly at random from a pool of size P ; two nodes that share a key are then connected by an edge. We analyze the reliability of G(n;μ,K, P ) against random link failures. Namely, we consider G(n;μ,K, P, α) formed by deleting each edge of G(n;μ,K, P ) independently with probability 1 − α, and study the probability that the resulting graph i) has no isolated node; and ii) is connected. We present scaling conditions on K , P , and α such that both events take place with probability zero or one, respectively, as the number of nodes gets large. We also present numerical results to support these zero-one laws in the finite-node regime. We present a novel approach to quantify the vulnerability of a complex network, i.e., the capacity of a graph to maintain its functional performance under random damages or malicious attacks. The proposed measure represents a multiscale evaluation of vulnerability, and makes use of combined powers of the links’ betweenness. We show that the proposed approach is able to properly describe some cases for which earlier measures of vulnerability fail. The relevant applications of our method for technological network design are outlined. We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multi-layer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low failure probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.