Estimating Network Reliability Research Articles

Network reliability of a stochastic flow network by wrapping linear programming models into a Monte-Carlo simulation

A stochastic flow network (SFN) serves as a fundamental framework for real-life network-structured systems and various applications. Network reliability NRd is defined as the probability that an SFN can successfully send at least d units of demand from a source to a terminal. Current analytical algorithms for the network reliability evaluation are classified into an NP-hard problem. This limitation hinders the ability of decision-makers to monitor and manage decisions for an SFN flexibly and immediately. Therefore, this paper develops an algorithm to estimate network reliability by wrapping developed linear programming (LP) models based on minimal paths (MPs) into a Monte-Carlo simulation. The developed LP models present satisfaction of the demand d in the SFN in terms of minimal paths. The effectiveness and efficiency of the proposed algorithm are verified using a series of numerical investigations. Contributions are manifold: (1) an integrated model with the simulation and LP models is provided to estimate network reliability in terms of the MPs, thereby filling a crucial gap in existing research; (2) the scalability and efficiency of the proposed method are shown for the complex SFNs; (3) decision-making capabilities can be provided under real-time reliability predictions.

Network reliability analysis through survival signature and machine learning techniques

As complex networks become ubiquitous in modern society, ensuring their reliability is crucial due to the potential consequences of network failures. However, the analysis and assessment of network reliability become computationally challenging as networks grow in size and complexity. This research proposes a novel graph-based neural network framework for accurately and efficiently estimating the survival signature and network reliability. The method incorporates a novel strategy to aggregate feature information from neighboring nodes, effectively capturing the response flow characteristics of networks. Additionally, the framework utilizes the higher-order graph neural networks to further aggregate feature information from neighboring nodes and the node itself, enhancing the understanding of network topology structure. An adaptive framework along with several efficient algorithms is further proposed to improve prediction accuracy. Compared to traditional machine learning-based approaches, the proposed graph-based neural network framework integrates response flow characteristics and network topology structure information, resulting in highly accurate network reliability estimates. Moreover, once the graph-based neural network is properly constructed based on the original network, it can be directly used to estimate network reliability of different network variants, i.e., sub-networks, which is not feasible with traditional non-machine learning methods. Several applications demonstrate the effectiveness of the proposed method in addressing network reliability analysis problems.

Road networks reliability estimations and optimizations: A Bi-directional bottom-up, top-down approach

In this paper, we present a novel three-stage reduction-based estimation and optimization heuristics to evaluate and improve large-scale road networks’ reliability efficiently. Some necessary rules and tools are developed, in the 1st stage, to translate a large-scale physical road network into a mathematical graph. Then, in the 2nd stage, a bottom-up reduction algorithm is formulated to estimate network reliability. Finally, in the 3rd stage, a top-down method is proposed to improve the road network reliability by employing mathematical optimization models. Hence, this is a bidirectional bottom-up top-down (BUTD) method that (1) is genuinely based on the mathematical theory of reliability, (2) is computationally efficient by avoiding NP-hardness, and (3) by relaxing the need to employ pseudo metrics of reliability, e.g., vulnerability, resilience, etc. from the complex network theory in analyzing the large-scale road networks. The approach is explained using an illustrative example and a case study.

Wang–Landau sampling for estimation of the reliability of physical networks

Modern physical networks, for example in communication and transportation, can be interpreted as directed graphs. Network models are used to identify the probability that given nodes are connected, and therefore the effect of a failure at a given link. This is essential for network design, optimization, and reliability. In this study, we investigated three alternative ensembles for estimating network reliability using the Wang–Landau algorithm. The first performed random walks on a structure function having two possible states: connected and disconnected. The second used random walks on a reliability polynomial. The third combined random walks with the average of connecting probabilities. The accuracy and limitations of the three ensembles were compared by estimating the reliability of three network models: a bridge network, a ladder-type network, and a dodecahedron network. The simulation results showed that the use of a random walk on a structure function failed to produce estimates when applied to highly reliable networks in any of the three network types. The other two approaches performed efficiently for bridge or ladder-type networks at any level of network reliability. The random walk on a probability space using the 1∕t algorithm was the only ensemble that was able to yield accurate estimates for a dodecahedron network, though even this failed at the highest level of network reliability. The other two methods failed to converge within 108 Monte Carlo trials. The use of the average of connecting probabilities required a shorter computation time when applied to a large network. Methods that can reduce variance for large, highly reliable networks require further investigation.

Research on reliability of complex network for estimating network reliability

Network reliability is an important index in measuring the reliability of large-sized network, but network reliability calculation is a NP-hard problem, and simulation is a feasible approach to estimating network reliability. Aiming at the problem of reliability evaluation in a complex network, dev elop a general scheme that combines Crude Monte Carlo and event-driven, and a novel reliability assessment method based on event-driven is put forward. The unbiased and the accurate estimation of the proposed method are analyzed from a theoretical point of view. Experimental results demonstrate that the proposed method is more efficient than other algorithms, such as high simulation efficiency, fine estimation accuracy and greatly reducing the algorithm complexity.

Splitting sequential Monte Carlo for efficient unreliability estimation of highly reliable networks

Assessing the reliability of complex technological systems such as communication networks, transportation grids, and bridge networks is a difficult task. From a mathematical point of view, the problem of estimating network reliability belongs to the #P complexity class. As a consequence, no analytical solution for solving this problem in a reasonable time is known to exist and one has to rely on approximation techniques. In this paper we focus on a well-known sequential Monte Carlo algorithm — Lomonosov’s turnip method. Despite the fact that this method was shown to be efficient under some mild conditions, it is known to be inadequate for a stable estimation of the network reliability in a rare-event setting. To overcome this obstacle, we suggest a quite general combination of sequential Monte Carlo and multilevel splitting. The proposed method is shown to bring a significant variance reduction as compared to the turnip algorithm, is easy to implement and parallelize, and has a proven performance guarantee for certain network topologies.

Energy‐efficient network design via modelling: optimal designing point for energy, reliability, coverage and end‐to‐end delay

Considering that practical wireless sensor networks are mostly built upon energy-constrained sensor nodes, network lifetime becomes a key deployment factor for sustainability of such networks initiating an attempt for prolonging the lifetime. Adopting a new multi-mode switching protocol for sensor nodes between active and sleep states, in this study, the authors propose a new mathematical method using an embedded simulation-based computing of an energy-efficient strategy performance metric to maintain resiliency of the network against side effects appearing in duty-cycling protocols. Here, the authors use a Monte Carlo simulation to estimate network reliability. Then the proposed mathematical model enables us to build a decision for optimised performance upon trade-offs between consumed energy, reliability, coverage intensity and end-to-end delays by locating a network's operational points. The authors show the trade-off operational significance of the model against the percentage of sleeping probability via some design factors including figure of merit.

Reliability Prediction of Wireless Sensor Network Based on Neural Network

Reliability is one of key indexes of communication network system performance assessment, which is also main basis for network optimal design, network management and control. Based on definition of network node reliability and link reliability, the paper given description on Wireless Sensor Network (WSN) reliability assessment and presented a kind of WSN reliability prediction model and its learning algorithm of WSN based on RBF neural network. The method can accurately estimate network reliability according to reliability of network node and link under any topology of WSN. Simulation results show that the method is effective in the prediction of reliability of WSN.

Performance analysis of cellular automata Monte Carlo Simulation for estimating network reliability

Network reliability is very important for the decision support information. Monte Carlo Simulation (MCS) is one of the optimal algorithms to estimate the network reliability for different kinds of network configuration. The traditional reliability estimation requires the information of all Minimal Paths (MPs) or Minimal Cuts (MCs). However, finding all MPs/MCs is extremely computationally expensive. This paper has compared and analyzed three Monte Carlo Simulation (MCS) methods for estimating the two-terminal network reliability of a binary-state network: (1) MCS1 simulates the network reliability in terms of known MPs, (2) MCS2 estimates the network reliability in terms of known MCs; and (3) CAMCS (based on cellular automata, CA) estimates the network reliability directly without knowing any information of MPs or MCs. Our simulation results show that the direct estimation without knowing any information of MPs or MCs can speedup about 185 times when compared with other traditional approaches which require MPs or MCs information.

Estimation of all-terminal network reliability using an artificial neural network

The exact calculation of all-terminal network reliability is an NP-hard problem, with computational effort growing exponentially with the number of nodes and links in the network. During optimal network design, a huge number of candidate topologies are typically examined with each requiring a network reliability calculation. Because of the impracticality of calculating all-terminal network reliability for networks of moderate to large size, Monte Carlo simulation methods to estimate network reliability and upper and lower bounds to bound reliability have been used as alternatives. This paper puts forth another alternative to the estimation of all-terminal network reliability — that of artificial neural network (ANN) predictive models. Neural networks are constructed, trained and validated using the network topologies, the link reliabilities, and a network reliability upperbound as inputs and the exact network reliability as the target. A hierarchical approach is used: a general neural network screens all network topologies for reliability followed by a specialized neural network for highly reliable network designs. Both networks with identical link reliability and networks with varying link reliability are studied. Results, using a grouped cross-validation approach, show that the ANN approach yields more precise estimates than the upperbound, especially in the worst cases. Using the reliability estimation methods of the ANN, the upperbound and backtracking, optimal network design by simulated annealing is considered. Results show that the ANN regularly produces superior network designs at a reasonable computational cost. Scope and purpose An important application area of operations research is the design of structures, products or systems where both technical and business aspects must be considered. One expanding design domain is the design of computer or communications networks. While cost is a prime consideration, reliability is equally important. A common reliability measure is all-terminal reliability, the probability that all nodes (computers or terminals) on the network can communicate with all others. Exact calculation of all-terminal reliability is an NP-hard problem, precluding its use during optimal network topology design, where this calculation must be made thousands or millions of times. This paper presents a novel computationally practical method for estimating all-terminal network reliability. Is shown how a neural network can be used to estimate all-terminal network reliability by using the network topology, the link reliabilities and an upperbound on all-terminal network reliability as inputs. The neural network is trained and validated on a very minute fraction of possible network topologies, and once trained, it can be used without restriction during network design for a topology of a fixed number of nodes. The trained neural network is extremely fast computationally and can accommodate a variety of network design problems. The neural network approach, an upper bound approach and an exact backtracking calculation are compared for network design using simulated annealing for optimization and show that the neural network approach yields superior designs at manageable computational cost.

Polynomial algorithms for estimating network reliability

AbstractWe consider the problem of calculating the best possible bounds on the reliability of a system given limited information about the joint density function of its components. We show that a polynomial algorithm for this problem exists iff such an algorithm exists for a certain related problem of minimizing a linear objective function over a clutter. We give numerous examples of network as well as other problems for which the algorithm runs in polynomial time. We also use our construction to prove NP‐hardness for others.