Network reliability analysis by counting the number of spanning trees

Reliability analysis of networks using stochastic model

Circulant graphs are an extremely well-studied subclass of regular graphs, partially because they model many practical computer network topologies It has long been known that the number of spanning trees in n-node circulant graphs with constant jumps satisfies a recurrence relation in n For the non-constant-jump case, i.e., where some jump sizes can be functions of the graph size, only a few special cases such as the Mobius ladder had been studied but no general results were known. In this note we show how that the number of spanning trees for all classes of n node circulant graphs satisfies a recurrence relation in n even when the jumps are non-constant (but linear) in the graph size The technique developed is very general and can be used to show that many other structures of these circulant graphs, e.g., number of Hamiltonian Cycles, Eulerian Cycles, Eulerian Orientations, etc., also satisfy recurrence relations. The technique presented for deriving the recurrence relations is very mechanical and, for circulant graphs with small jump parameters, can easily be quickly implemented on a computer We illustrate this by deriving recurrence relations counting all of the structures listed above for various circulant graphs.

Recently, computation, communication and control are deeply and pervasively embedded into physical and engineered components of network System, to advance entire networked system performance and dependability. In such systems, the growing complexity of network structure result in need of increasing system reliability. Network reliability modeling and analysis need not only capture the complex dynamic process of network systems, but also need the facilities for applying, understanding and computing. The objective of this paper is to develop a suitable modeling and analysis framework to study the ad-hoc network reliability. Using the mutual transformations of reliability functions between the time-domain and the frequency-domain, we adopt frequency-domain analysis approach to model network reliability. The advantages of the proposed approach over the traditional time-domain approaches include capability to capture higher order moments of system characteristics, scalability to analyze reliability of complex network systems, efficiency in calculation and practicability in computer simulation, etc. Finally, numerical experiment results show the feasibility and efficacy of this approach.

: Analysis of network reliability is of major importance in computer, communication and power networks. Even the simplest models lead to computational problems which are NP-hard for general networks, although polynomial-time algorithms do exist for certain network configurations such as 'ladders' and 'wheels' and for some series-parallel structures such as the well-known 'two-terminal' series-parallel networks. In this paper, we show that a class of series-parallel networks, for which only exponentially complex algorithms were previously known, can be analyzed in polynomial time. In doing this, we introduce a new reliability-preserving graph reduction of general applicability and produce a linear-time algorithm for computing the reliability of any graph with an underlying series-parallel structure.

Let G=(V,E) be an unweighted undirected graph on n vertices. A simple argument shows that computing all distances in G with an additive one-sided error of at most 1 is as hard as Boolean matrix multiplication. Building on recent work of D. Aingworth et al. (1996), we describe an O/spl tilde/(min{n/sup 3/2/m/sup 1/2/,n/sup 7/3/}) time algorithm APASP/sub 2/ for computing all distances in G with an additive one-sided error of at most 2. The algorithm APASP/sub 2/ is simple, easy to implement, and faster than the fastest known matrix multiplication algorithm. Furthermore, for every even k>2, we describe an O/spl tilde/(min{n/sup 2-(2)/(k+2)/m/sup (2)/(k+2)/, n/sup 2+(2)/(3k-2)/}) time algorithm APASP/sub k/ for computing all distances in G with an additive one-sided error of at most k. We also give an O/spl tilde/(n/sup 2/) time algorithm APASP/sub /spl infin// for producing stretch 3 estimated distances in an unweighted and undirected graph on n vertices. No constant stretch factor was previously achieved in O/spl tilde/(n/sup 2/) time. We say that a weighted graph F=(V,E') k-emulates an unweighted graph G=(V,E) if for every u, v/spl isin/V we have /spl delta//sub G/(u,v)/spl les//spl delta//sub F/(u,v)/spl les//spl delta//sub G/(u,v)+k. We show that every unweighted graph on n vertices has a 2-emulator with O/spl tilde/(n/sup 3/2/) edges and a 4-emulator with O/spl tilde/(n/sup 4/3/) edges. These results are asymptotically tight. Finally, we show that any weighted undirected graph on n vertices has a 3-spanner with O/spl tilde/(n/sup 3/2/) edges and that such a 3-spanner can be built in O/spl tilde/(mn/sup 1/2/) time. We also describe an O/spl tilde/(n(m/sup 2/3/+n)) time algorithm for estimating all distances in a weighted undirected graph on n vertices with a stretch factor of at most 3.

The goal of a reliable network is to ensure that all transmitted messages arrive at their intended destinations uncorrupted. Most network design techniques concern themselves with channel capacity allocation and cost constraints and ignore reliability analysis. Conversely, network reliability analysis methods focus on connectivity and ignore traffic loads and channel capacities. This paper presents a design strategy to enhance the reliability of an existing network by modifying its topology. This method takes into account traffic distributions. A new reliability metric is introduced which is the probability that all transmitted messages arrive at their intended destinations under the given traffic distribution. The design strategy adds links to the network to maximize the probability that all transmitted messages arrive at their intended destinations. The network design technique uses an approximate network reliability analysis algorithm to achieve quadratic-time performance. >

An efficient Boolean algebraic algorithm for the symbolic reliability and sensitivity analysis of coherent two-terminal networks with s independent components is described. The algorithm is also applicable to a fault tree model without NOT gates. The algorithm uses the concept originally proposed by A. Grnarov, L. Kleinrock, and M. Gerla (1979). After the algorithm is presented, the errors in the original technique are illustrated by two examples. The algorithm is extended t compute the reliability importance of a given component (sensitivity of system reliability to a given component's reliability). A computer program implementing the modified algorithm is used to solve and obtain measured time complexities for a large set of network and fault tree models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

ABSTRACTIn the process of reliability analysis of computer network, there is the high probability of network failure in the application process by using the current analysis method. In this paper, a reliability analysis method of computer network based on intelligent cloud computing method is proposed. The proposed method is integrated with the theoretical idea of analytic hierarchy process. From the research angle of network reliability, the reliability model of computer network is set up by using the failure criterion of computer network, and the intelligent cloud computing method is used to calculate the reliability state parameters of the network. According to the obtained state parameters of network reliability analysis, the reliability analysis matrix of computer network is established, and then to accurately complete the reliability analysis of computer network. The simulation results show that the reliability analysis method of computer network based on intelligent cloud computing is highly accurate and robust.

We present a novel approach for assessing the reliability of error-prone systems and networks using an interpretable prototype-based classification framework. Specifically, reliability levels of consecutive k-out-of-n success systems, failure networks, and domination networks are classified using Generalized Matrix Learning Vector Quantization (GMLVQ). Beyond achieving accurate classification, the proposed method provides informative insights into the influence of input probabilities on the resulting reliability levels. To further enhance the interpretability of the learned relevance matrix in GMLVQ, we introduce two graph-based visualization strategies that reveal structural patterns and relevant feature interactions that are critical for reliability-level classification. The proposed approach is generally applicable to arbitrary coherent systems and can be further adapted to estimate the probability of a union of any finite family of events based on their individual and pairwise intersection probabilities.

Scale-free networks, as one major class of complex networks, are characterized by a specific structural feature of power-law degree distributions. Examples of scale-free real-world networks include World Wide Web (WWW), email networks, citation and co-author scientific networks, social networks (Facebook, Twitter), networks of Internet routers, and protein-protein interaction networks. In this paper we model and evaluate the reliability of scale-free complex networks using a binary decision diagram (BDD)-based method. Two-terminal reliability is considered, which is defined as the probability that a specified pair of nodes can communication through at least one fault-tree path in the network. This reliability metric can measure, for example, how reliable the information can be shared between two parties or in general how reliable the information can be disseminated within a social network. The Barabasi-Albert model is used for generating the sample scale-free networks studied in this paper. The reliability performance of scale-free networks is compared to that of random networks under the Erdos-Renyi model. Degree distributions and clustering coefficients (average fraction of pairs of neighbors of a node which are also neighbors of each other) of sample scale-free and random networks are illustrated and compared. Their effects on the performance of the BDD-based method for the reliability analysis of both scale-free and random networks are also discussed.

Due to the low cost of easy-to-use components of open-source hardware and software, the Internet of Things may be pervading through everything everywhere. The dependability of the Internet of Things is critical because the services will be concerned with real life. However, the inexpensive hardware provides limited resources for communication. In this paper, we present exact all-terminal reliability of the wireless networks of which the number of links of each node is bounded. First, we analyze the all-terminal reliability of the regular wireless network, where any two nodes are connected by a wireless link consisting of a pair of radio modules. The reliability polynomial is derived from the Tutte polynomial that is the seminal work of the algebraic graph theory. Second, we analyze the all-terminal reliability of the wireless network including the random mesh network under the assumption that if the module fails, all radio links connected through a radio module are cut off. We consider both the fault of the communication module and the fading of the wireless channel in the indoor channel condition. For improving the reliability, we also propose a fault-tolerant method giving redundant radio modules into each node. We also analyze cost-effectiveness. We also calculate the mean-time-to-failure (MTTF) for wireless networks. We show that the random mesh network of which each node includes three or more the radio-broadcast modules is more dependable than any other regular network of which each node comprises four point-to-point modules if it is the connected graph in the static environment.

In a probabilistic network, source-to-multiple-terminal reliability (SMT reliability) is the probability that a specified vertex can reach every other vertex. This paper derives a new topological formula for the SMT reliability of probabilistic networks. The formula generates only non-cancelling terms. The non-cancelling terms in the reliability expression correspond one-to-one with the acyclic t-subgraphs of the network. An acyclic t-subgraph is an acyclic graph in which every link is in at least one spanning rooted tree of the graph. The sign to be associated with each term is easily computed by counting the vertices and links in the corresponding subgraph. Overall reliability is the probability that every vertex can reach every other vertex in the network. For an undirected network, it is shown the SMT reliability is equal to the overall reliability. The formula is general and applies to networks containing directed or undirected links. Furthermore link failures in the network can be s-dependent. An algorithm is presented for generating all acyclic t-subgraphs and computing the reliability of the network. The reliability expression is obtained in symbolic factored form.

This paper presents a model to calculate the reliability of communication networks with multimode components. Previous research on network reliability has focused on models in which each component may be in one of two modes, namely, operative or failed. In reality, a component may undergo degradations in performance before a complete outage, and will therefore operate in more than two modes. Traditional network reliability measures, such as the probability that a pair of nodes is connected, are not meaningful in a multimode model. Therefore, the mean message delay of the network is defined as the performance measure. An exact calculation of this reliability measure is not feasible due to the large number of network states, corresponding to network components being in different modes. We have developed an approximation method to calculate this reliability measure. This method requires us to work with the states of the network in order of decreasing probability. An algorithm ORDER- M is developed to generate these states in the proper order.

Generating electricity from wind resources has many environmental and economic advantages over traditional fossil-fueled generation. As a result, there is little doubt that energy from wind will be a significant contribution to the electricity portfolio of the future. Due to the sensitivity of the network and the volatility of the wind resource, analysis of power system operations using expected wind generation is not representative of actual system operations. In order to account for this fundamental uncertainty in wind generation, a Monte Carlo simulation model is developed based on an Optimal Power Flow model, and tested on the IEEE 39-bus test system. The results of these simulations indicate that while the average cost of serving load decreases with increasing wind penetration, the reliability of the system is highly sensitive to the ability of other generators on the system to ramp production either up or down on very short timescales.

A proper vertex coloring of a graph G is achromatic (respectively harmonious) if every two colors appear together on at least one (resp. at most one) edge. The largest (resp. the smallest) number of colors in an achromatic (resp. a harmonious) coloring of G is called the achromatic (resp. harmonious chromatic) number of G and denoted by (resp. ). For a finite set of positive integers and a positive integer n, a circulant graph, denoted by , is an undirected graph on the set of vertices that has an edge if and only if either or is a member of (where substraction is computed modulo n). For any fixed set , we show that is asymptotically equal to , with the error term . We also prove that is asymptotically equal to , with the error term . As corollaries, we get results that improve, for a fixed k, the previously best estimations on the lengths of a shortest k‐radius sequence over an n‐ary alphabet (i.e., a sequence in which any two distinct elements of the alphabet occur within distance k of each other) and a longest packing k‐radius sequence over an n‐ary alphabet (which is a dual counterpart of a k‐radius sequence).