All-terminal Reliability Research Articles

A Method for Calculating the Reliability of 2-Separable Networks and Its Applications

This paper proposes a computational method for the reliability of 2-separable networks. Based on graph theory and probability theory, this method simplifies the calculation process by constructing a network equivalent model and designing corresponding algorithms to achieve the efficient evaluation of reliability. Considering independent random failures of edges with equal probability q, this method can accurately calculate the reliability of 2-separable networks, and its effectiveness and accuracy are verified through examples. In addition, to demonstrate the generality of our method, we have also applied it to other 2-separable networks with fractal structures and proposed linear algorithms for calculating their all-terminal reliability.

A meta-heuristic assisted method for the deployment of the multi-BWBUG cooperative system

Blended-wing-body underwater gliders (BWBUGs) are characterized by low noise and high endurance, and they are well suited for deployment in offshore missions. However, the deployment of the multi-BWBUG cooperative system faces great difficulties due to the complex ocean environment and the difficulty of accurately establishing the deployment model. Thus, a novel meta-heuristic assisted method is proposed for the deployment of the multi-BWBUG cooperative system in this study. First, the deployment optimization model of the multi-BWBUG cooperative system is established by combining the detection coverage ratio and the all-terminal reliability. In addition, Levy flight with visual expansion (LVE) is put forward to effectively enhance the search capability of the search unit. Then, an LVE-enhanced whale optimizer (LVEWO) is proposed for improving the quality of the initial population and the search strategy. The embedding of LVE and the well-designed competition mechanism can improve the convergence speed of LVEWO. Simulation experiments and statistical analysis results convincingly demonstrate the effectiveness of the proposed deployment model and the competency of LVEWO to deploy the multi-BWBUG cooperative system. The comprehensive performance of LVEWO is better than those of the FA, EABC, and WO algorithms.

A deep neural network and Bayesian method based framework for all-terminal network reliability estimation considering degradation

Most research on network reliability has considered links to have a binary state, i.e., functioning or failed, whereas nodes are considered flawless. In a more realistic scenario, both links and nodes might fail or may exhibit degradation behavior before failing. This study develops a framework to estimate the all-terminal reliability of a network that considers the degradation and probability of failure of all nodes and links in a network. Unlike previous works on network reliability that considered constant reliability for links, this paper considers the reliability of links, nodes, and the network as functions of time. In the proposed framework, the Bayesian methods (BM) are employed to estimate the reliability of links and nodes as functions of time considering degradation data. Due to the complexity of the all-terminal reliability problem, and to get fast estimations of the reliability of a network, an integration of Monte Carlo (MC) and Deep Neural Networks (DNNs) is proposed. The proposed MC algorithm can estimate the network reliability for given nodes and links reliability values. To speed up the calculation, a DNN model is integrated into the framework, thus enabling accurate and fast estimation of network reliability for given link and node reliability values. The DNN accuracy, based on the RMSE (0.01460), outperforms previous traditional artificial neural network (ANN) approaches. Moreover, the DNN model takes 0.3 ms to compute the reliability for any given links and reliability values. The proposed framework can provide not only reliability point estimates but also credible intervals. Finally, we take advantage of Bayesian methods to integrate new data into the framework as they become available. The framework uses the new data to refine and further update the degradation model parameters and the prediction of the reliability of links, nodes, and the network. The proposed methodology has been demonstrated with the real-world network topology Ion (125 nodes, 150 links) with actual degradation data.

Design and Reliability Analysis of a Novel Redundancy Topology Architecture.

Topology architecture has a decisive influence on network reliability. In this paper, we design a novel redundancy topology and analyze the structural robustness, the number of redundant paths between two terminal nodes, and the reliability of the proposed topology by using natural connectivity and time-independent and time-dependent terminal pair reliability, k-terminal reliability, and all-terminal reliability comprehensively and quantitatively, and we compare these measures of the proposed topology with AFDX in three scenarios. The evaluations show that in the structural robustness analysis, when no nodes are removed, the natural connectivity of the proposed topology with 10 nodes, 16 nodes, and 20 nodes is 77.8%, 26.95%, and 81.39% higher than that of AFDX, respectively. In the time-independent reliability analysis, when the link reliability is 0.9, terminal pair reliability of the proposed topology with 10 nodes, 16 nodes, and 20 nodes is 5.78%, 17.75%, and 34.65% higher than that of AFDX, respectively; k-terminal reliability is 10.04%, 31.97%, and 53.74% higher than that of AFDX, respectively; and all-terminal reliability is 29.36%, 74.37%, and 107.91% higher than that of AFDX, respectively. In the time-dependent reliability analysis, when the operating time is 8000 h, the terminal pair reliability of the proposed topology with 10 nodes, 16 nodes, and 20 nodes is 3.53%, 10.87%, and 21.08% higher than that of AFDX, respectively; the k-terminal reliability is 6.20%, 19.65%, and 32.58% higher than that of AFDX, respectively; and the all-terminal reliability is 18.25%, 45.04%, and 63.86% higher than that of AFDX, respectively. The proposed topology increases the redundant paths of data transmission. It ensures reliable data transmission and has high robustness and reliability. It provides a new idea for improving the reliability of industrial buses.

Universal Reliability Bounds for Sparse Networks

Consider a graph with perfect nodes and edges subject to independent random failures with identical probability. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">all-terminal reliability</i> is the probability that the resulting subgraph is connected. First, we fully characterize uniformly least reliable graphs (ULRG) whose co-rank is not greater than four. Universal reliability bounds are here introduced for those graphs. It is formally proved that ULRG is invariant under bridge-contractions, and maximize the number of bridges among all connected simple graphs with a prescribed number of nodes and edges. A closed-form for the maximum number of bridges is also given, which has an intrinsic interest from a graph-theoretic point of view. Finally, the cost-reliability tradeoff is discussed, comparing the number of edges required to reduce the reliability gaps between the least and most reliable graphs. A remarkable conclusion is that the network design is critical under rare event failures, where the reliability-gap between least and most-reliable networks is monotonically increasing with the number of terminals.

Extremal graphs for the Tutte polynomial

A graph transformation called the compression of a graph G is known to decrease the number of spanning trees, the all-terminal reliability, and the magnitude of the coefficients of the chromatic polynomial of a graph G. All of these graph parameters can be derived from the Tutte polynomial of G, and in this paper we determine more generally compression's effect on the Tutte polynomial, recovering the previous results and obtaining similar results for a wide variety of other graph parameters derived from the Tutte polynomial. Since any simple connected graph can be transformed into a connected threshold graph via a series of compressions, this gives that threshold graphs are extremal simple graphs for all of the parameters considered.

All-terminal hypernetwork reliability synthesis of a kind of semi-deterministic hypergraphs

Network reliability plays an important role in analysis, synthesis and detection of real-world networks. In this paper, we first propose the concept of hypernetwork reliability, which generalizes the concept of network reliability. The model for hypernetwork reliability studies consists of a hypergraph with perfect reliable vertices and equal and independent hyperedge failure probability [Formula: see text]. The measure of reliability is defined as the probability that a hypergraph is connected. Let [Formula: see text] be an [Formula: see text]-uniform hypergraph with the number of vertices [Formula: see text] and the number of hyperedges [Formula: see text], where every hyperedge connects [Formula: see text] vertices. We confirm the possibility of the existence of a fixed hypergraph that is optimal or least for all hyperedges same survival possible [Formula: see text]. It is simple to verify that such hypergraph exists if [Formula: see text]. For a kind of 2-regular 3-uniform hypergraphs, we calculate the upper and lower bounds on the all-terminal reliability, and describe the class of hypergraphs that reach the boundary.

Estimation of all-terminal network reliability using press forward GA with stochastic selection method

Network reliability is an important measure of how well the network meets its design aim and mathematically is the probability that a network will perform communication efficiently for at least a given period of time. The reliability analysis is used for determining the probability of correct functioning of a system in terrain conditions. Estimating the all-terminal network reliability is an NP-hard problem, the press forward Genetic Algorithm is also an alternative to solve the problem of all-terminal network reliability. This paper presents a reliability evaluation method by using a feed-forward genetic algorithm with a random selection of nodes and links i.e., estimate the network reliability such that the flow is not less than a given threshold. To verify the efficiency of an algorithm, various sets of runs are applied to identify the most reliable network and the algorithm is tested on the network size of 2,4,6,8, --------256 nodes with link N(N-1)/2. The results of the algorithm are obtained for all-terminal reliability problem based on close analysis of the complexity of the network. Our assumption for reliability evaluation of node 1 to node N, with link reliability of 50%. Another result of the proposed GA approach is the significant reduction in computational time.

Graph vulnerability parameters, compression, and threshold graphs

Given a simple graph G and vertices u,v∈V(G), let NG(u) and NG(v) denote the neighborhoods in G of u and v respectively. The compression of G from u to v produces a new graph Gu→v by, for each x∈NG(u)−NG(v)−{v}, removing edges from G of the form ux and replacing them with corresponding edges of the form vx. Kelmans, and independently Satyanarayana, Schoppmann, and Suffel, showed that for any graph G and any u,v∈V(G), compression from u to v could not increase, and typically decreased, both the number of spanning trees and the all-terminal reliability of G. Both the number of spanning trees and all-terminal reliability are vulnerability parameters, i.e., measures of the strength of a network. We show that a number of other prominent vulnerability parameters—including vertex connectivity, toughness, scattering number, edge connectivity, edge toughness, and binding number—are affected by compression in the same way as number of spanning trees and all-terminal reliability. As a consequence, as with the number of spanning trees and the all-terminal reliability, threshold graphs are extremal graphs for all of the vulnerability parameters considered.

Analysis and reliability of separable systems

The operation of a system, such as a vehicle, communication network or automatic process, heavily depends on the correct operation of its components. A Stochastic Binary System (SBS) mathematically models the behavior of on-off systems, where the components are subject to probabilistic failures. Our goal is to understand the reliability of the global system.The reliability evaluation of an SBS belongs to the class of NP-Hard problems, and the combinatorics of SBS imposes several challenges. In a previous work by the same authors, a special sub-class of SBSs called separable systems was introduced. These systems accept an efficient representation by a linear inequality on the binary states of the components. However, the reliability evaluation of separable systems is still hard.A theoretical contribution in the understanding of separable systems is given. We fully characterize separable systems under the all-terminal reliability model, finding that they admit efficient reliability evaluation in this relevant context.

Optimization of multiple autonomous underwater vehicle cooperative system communication network topology based on total energy consumption

Given the importance of the communication energy consumption of multiple autonomous underwater vehicle cooperative systems in practical work, this work optimizes the network topology to reduce total energy consumption. In accordance with the characteristics of underwater communication, the energy consumption of communication links is obtained, thereby obtaining the total communication energy consumption of multiple autonomous underwater vehicle cooperative systems. Taking the all-terminal reliability of the communication network as a constraint and the total energy consumption of network communication as the optimization goal, this work puts forward an optimization model for the communication network topology of multiple autonomous underwater vehicle cooperative systems. Furthermore, this work creatively describes the network topology optimization problem as a special path optimization problem suitable for the ant colony optimization algorithm presented to solve the optimization problem and shown to be effective and efficiency on this problem.

All-terminal reliability of multi-AUV cooperative systems in horizontally stratified SOFAR channel

ABSTRACT This work develops a calculation method of all-terminal reliability for multi-AUV cooperative systems in horizontally stratified sound fixing and raging channel (SOFAR channel), considering the sound speed profile in SOFAR channel. The working environment of multi-AUV (autonomous underwater vehicle) cooperative systems is complex and the reliability under different environmental conditions is different. This work adopts the Kraken normal mode method to get the transmission loss, and calculates the reliability of the communication link based on the relationship between the transmission loss and signal-to-noise ratio. All-terminal reliability of multi-AUV cooperative systems can be obtained.

Reliable communication network design: The hybridisation of metaheuristics with the branch and bound method

Reliable communication network design (RCND) is a well-known optimisation problem to produce a network with maximum reliability. This paper addresses the minimum cost communication network design problem under the all-terminal reliability constraint. Due to the NP-hard nature of RCND, several different metaheuristic algorithms have been widely applied to solve this problem. The aim of this paper is to propose two new hybrid metaheuristic algorithms, namely, GABB and SABB, by integrating either a Genetic Algorithm (GA) with the Branch and Bound method (B&B) or Simulated Annealing (SA) with B&B. The GABB and SABB algorithms have the advantages of finding higher performance solutions produced from the GA or SA, along with the ability to repair infeasible solutions or improve solution quality by integrating the B&B method. To investigate the effectiveness of the proposed algorithms, extensive comparisons with individual application of the GA and SA (the basic forms of GABB and SABB), two different hybrid algorithms (GABB and SABB) and other two approaches (ACO_SA and STH) that give the best results in the literature for the design problems are carried out in a three-stage experimental study (ie, small-, medium-, and large-sized networks). The computational results show that hybridisation of metaheuristics with the B&B method is an effective approach to designing reliable networks and finding better solutions for existing problems in the literature.

Classes of uniformly most reliable graphs for all-terminal reliability

The all-terminal reliability polynomial of a graph G is the probability that G remains connected if each edge is independently included with fixed probability p. Among all graphs with a fixed number of n vertices and m edges, a graph is uniformly most reliable if its reliability polynomial is greater than or equal to all other graphs on the same number of vertices and edges for every value of p∈[0,1]. We find a new class of graphs that are uniformly most reliable. Specifically, we show that when n≥5 is odd and m is either n2−n+12 or n2−n+32, there exists a unique uniformly most reliable graph, and we give its construction.

On the reliability roots of simplicial complexes and matroids

Assume that the vertices of a graph G are always operational, but the edges of G fail independently with probability q∈[0,1]. The all-terminal reliability of G is the probability that the resulting subgraph is connected. The all-terminal reliability can be formulated into a polynomial in q, and it was conjectured that all the roots of (nonzero) reliability polynomials fall inside the closed unit disk. It has since been shown that there exist some connected graphs which have their reliability roots outside the closed unit disk, but these examples seem to be few and far between, and the roots are only barely outside the disk. In this paper we generalize the notion of reliability to simplicial complexes and matroids and investigate when the roots fall inside the closed unit disk. We show that such is the case for matroids of rank 3 and paving matroids of rank 4. We also prove that the reliability roots of shellable complexes are dense in the complex plane, and that the real reliability roots of any matroid lie in [−1,0)∪{1}. Finally, we also show that the reliability roots of thickenings of the Fano matroid can lie outside the unit disk.

Graph vulnerability parameters, compression, and quasi-threshold graphs

Kelmans, and later independently Bogdanowicz and Satyanarayana, Schoppmann, and Suffel, showed that a graph operation which has come to be known as the compression of G from vertex u to vertex v could not increase, and typically decreased, both the number of spanning trees and the all-terminal reliability of a graph. Both these quantities are well-known vulnerability parameters, i.e., measures of the strength of a network, and subsequently a number of other prominent vulnerability parameters — including vertex connectivity, toughness, scattering number, edge connectivity, edge toughness, and binding number — have been shown to be affected by compression in a similar way. As a consequence threshold graphs are extremal for all of the parameters mentioned. In this paper we show that for the graph vulnerability parameters integrity, tenacity, and k-component order connectivity, if u,v are adjacent then compression cannot increase, and typically decreases them. As a consequence, these parameters have quasi-threshold graphs as extremal graphs. We also show, however, that there are graphs with non-adjacent u,v where compression increases these parameters. To the best of our knowledge, these parameters are the first identified that behave differently under compression depending upon which pairs of vertices are used in the compression.

Invulnerability of planar two-tree networks

Let us model the network by an undirected graph G, in which each edge fails independently with probability q∈[0,1], the all-terminal reliability of the network is the probability that the graph G remains connected and it is one of the important measure for the invulnerability of the network. Clearly, the all-terminal reliability can be written as a polynomial in either q. Theoretically, it has been proved that calculating all-terminal reliability for planar networks is #P-complete. Up now we cannot find any results for some special classes of the planar networks. This paper studies the all-terminal reliability of the two-tree networks and its generalizations. A linear algorithm for calculating the reliability of a planar two-tree networks is proposed, with algorithmic complexity O(n), where n is the number of steps. Then both the uniformly-most reliable network model and the uniformly-worst reliable network model are determined by using the algorithm. Finally, a polynomial algorithm for planar two-connected networks is proposed based on an expended algorithm and the corresponding uniformly-most reliable network model and uniformly-worst reliable network model are also presented, with computational complexity O(n), where n is the number of steps.

A Fast and Accurate Failure Frequency Approximation for $k$ -Terminal Reliability Systems

This paper considers the problem of approximating the failure frequency of large-scale composite $\boldsymbol{k}$ -terminal reliability systems. In such systems, the nodes ( $\boldsymbol{k}$ of which are terminals) are connected through components, which are subject to random failure and repair processes. At any time, a system failure occurs if the surviving system fails to connect all the $\boldsymbol{k}$ terminals together. We assume that each component's up times and down times follow statistically independent stationary random processes, and these processes are statistically independent across the components. In this setting, the exact computation of failure frequency is known to be computationally intractable (NP-hard). In this paper, we present an algorithm to approximate the failure frequency for any given multiplicative error factor that runs in polynomial time in the number of (minimal) cutsets. Moreover, for the special case of all-terminal reliability systems, i.e., where all the nodes are terminals, we propose an algorithm for approximating the failure frequency within an arbitrary multiplicative error that runs in polynomial time in the number of nodes (which can be much smaller than the number of cutsets). Our simulation results confirm that the proposed method is much faster and more accurate than the standard Monte Carlo simulation technique for approximating the failure frequency.

Evaluating Reliability/Survivability of Capacitated Wireless Networks

In telecommunication network design problems, survivability and reliability are often used to evaluate quality of service while usually ignoring link capacity. In this paper, a new metric that combines network reliability with network resilience is presented to measure reliability/survivability effectively for capacitated networks. Capacitated resilience is compared with well-known network reliability/survivability metrics ( $k$ -terminal reliability, all-terminal reliability, traffic efficiency, and $k$ -connectivity), and its benefits and computational efficiency are discussed. An application is shown using heterogeneous wireless networks (HetNets). With the growing use of new telecommunication technologies such as 4G and wireless hotspots, HetNets are gaining more attention. The source of heterogeneity of a HetNet can either be the differences in nodes (such as transmission ranges, failure rates, and energy levels) or the differences in services offered in the network (such as GSM and WiFi).

A self-healing evaluation model for dedicated protection optical fiber sensor networks using All-terminal reliability function

Abstract With the increase of the number of sensors and nodes, the existing self-healing evaluation models for large-scale optical fiber sensor networks (OFSNs) have become insufficient to evaluate their self-healing capability. Here, we propose a self-healing evaluation model using the All-terminal reliability function for OFSNs. On the basis of this model, we establish equations for loop topology using the state enumeration method, and for more complicated star–ring and double-loop topologies, using both state enumeration method and Monte-Carlo method. In our self-healing evaluation model, the self-healing capability is a function of the number of the sensors (N) and the working probability of link fibers (p). We have conducted a comparative study on the effects of these two factors on the self-healing capability among these network topologies. The results show that with the increase of N or the decrease of p, the self-healing capability of the all topologies declines, and the star-ring topology displays the best self-healing capability.