Asymptotic formula on average path length of fractal networks modeled on Sierpinski gasket

Gao, Fei; Le, Anbo; Xi, Lifeng

doi:10.1016/j.jmaa.2015.10.001

Cited by 26 publications

(5 citation statements)

References 20 publications

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“…If the components are treated as the nodes, the complex aerospace system can be regarded as a complex aerospace engineering system network. Research shows that a complex aerospace engineering system network has a larger clustering coefficient and smaller feature path length [44][45][46][47], which is consistent with the small-world complex network characteristic. So, the propagation probability can be determined by the smallworld complex network analysis method.…”

Section: Risk Feature Quantitative Analysismentioning

confidence: 72%

Reliability Assessment of Space Station Based on Multi-Layer and Multi-Type Risks

2021

Applied Sciences

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A space station is a typical phased-mission system, and assessing its reliability during its configuration is an important engineering action. Traditional methods usually require extensive data to carry out a layered reliability assessment from components to the system. These methods suffer from lack of sufficient test data, and the assessment process becomes very difficult, especially in the early stage of the configuration. This paper proposes a reliability assessment method for the space station configuration mission, using multi-layer and multi-type risks. Firstly, the risk layer and the risk type for the space station configuration are defined and identified. Then, the key configuration risks are identified comprehensively, considering their occurrence likelihood and consequence severity. High load risks are identified through risk propagation feature analysis. Finally, the configuration reliability model is built and the state probabilities are computed, based on the probabilistic risk propagation assessment (PRPA) method using the assessment probability data. Two issues are addressed in this paper: (1) how to build the configuration reliability model with three layers and four types of risks in the early stage of the configuration; (2) how to quantitatively assess the configuration mission reliability using data from the existing operational database and data describing the propagation features. The proposed method could be a useful tool for the complex aerospace system reliability assessment in the early stage.

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Section: Risk Feature Quantitative Analysismentioning

confidence: 72%

Reliability Assessment of Space Station Based on Multi-Layer and Multi-Type Risks

2021

Applied Sciences

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“…Several researchers derived analytical formulation of AP L for different type of networks. For instance, Kleinrock and Silvester [21] considered random graphs; Fronczak et al [18] and Guo et al [14] studied a large class of uncorrelated random networks with hidden variables; Zhang et al [17] examined Apollonian networks; Peng [16] dealt with Sierpinski pentagon; Gulyás et al [13] focused on the networks with given size and density; Chen et al [11] investigated Barabási-Albert scale free model; Zhi-guang et al [10] discussed belt-type networks; and Gao et al [22] analysed Sierpinski gasket in a recent article.…”

Section: Average Path Length (Apl)mentioning

confidence: 99%

Optimal Link Deployment for Minimizing Average Path Length in Chain Networks

Bilgin¹,

Güneştaş²,

Demir³

et al. 2016

Lecture Notes in Computer Science

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This study considers chain-topology networks, which has certain inherent limitations, and presents an optimization model that augments the network by the addition of a new link, with the objective of minimizing Average Path Length (APL). We built up a mathematical model for APL, and formulated our problem as Integer Programming. Then, we solved the problem experimentally by brute-force, trying all possible topologies, and found the optimal solutions that minimize APL for certain network sizes up to 1000 nodes. Later on, we derived analytical solution of the problem by applying Linear Regression method on the experimental results obtained. We showed that APL on a chain-topology network is decreased by the proposed optimization model, at a gradually increasing rate from 24.81% to asymptotic value of 41.4% as network grows. Additionally, we found that normalized length of the optimal solutions decreases logarithmically from 100 % to 58.6048 % as network size gets larger.

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“…Remark 2. For any σ ∅, as in [34], let L(σ) be the minimal number of moves for K σ to touch the boundary of K, i.e., L(σ) = d(σ, ∅) − 1. (4.1)…”

Section: Average Shortest Path Lengthmentioning

confidence: 99%

A small-world and scale-free network generated by Sierpinski Pentagon

Chen

Wang

et al. 2016

Physica A: Statistical Mechanics and its Applications

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Asymptotic formula on average path length of fractal networks modeled on Sierpinski gasket

Abstract: In this paper, we introduce a new method to construct evolving networks based on the construction of the Sierpinski gasket. Using selfsimilarity and renewal theorem, we obtain the asymptotic formula for average path length of our evolving networks.

Cited by 26 publications

References 20 publications

Reliability Assessment of Space Station Based on Multi-Layer and Multi-Type Risks

Reliability Assessment of Space Station Based on Multi-Layer and Multi-Type Risks

Optimal Link Deployment for Minimizing Average Path Length in Chain Networks

A small-world and scale-free network generated by Sierpinski Pentagon

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