Reliability of multi-dimensional network systems with nodes having stochastic connection ranges

doi:10.23919/JSEE.2025.000077

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (4): 1017-1023.doi: 10.23919/JSEE.2025.000077

• SYSTEMS ENGINEERING • Previous Articles

Reliability of multi-dimensional network systems with nodes having stochastic connection ranges

Yuqiang FU¹(), Xiaoyang MA²^,*(), Fei ZHAO³()

¹ School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China
² School of Information Management, Beijing Information Science & Technology University, Beijing 102206, China
³ School of Business Administration, Northeastern University, Shenyang 110819, China

Received:2023-09-12 Online:2025-08-18 Published:2025-09-04
Contact: Xiaoyang MA E-mail:fuyuqiang@ustb.edu.cn;maxiaoyang0218@163.com;zhaofei@neuq.edu.cn
About author:
FU Yuqiang was born in 1990. He received his Ph.D. degree in management science and engineering from University of Chinese Academy of Sciences, Beijing, China in 2019. He is a lecturer in the School of Mathematics and Physics, University of Science and Technology Beijing. His research interests include mathematical modelling, design of reliability system, optimization, reliability statistics, and importance measures. E-mail: fuyuqiang@ustb.edu.cn

MA Xiaoyang was born in 1989. She received her Ph.D. degree in management science and engineering from University of Science and Technology Beijing, China in 2018. She is a lecturer in the School of Information Management, Beijing Information Science & Technology University. Her research interests include system reliability for complex system, preventive maintenance, statistics, and optimization. E-mail: maxiaoyang0218@163.com

ZHAO Fei was born in 1984. She received her B.S. and M.S. degrees in the School of Economics and Management from Hebei University of Engineering, Handan, China, in 2008 and 2011, respectively. She received her Ph.D. degree from University of Science and Technology Beijing, China, in 2015. She is currently an associate professor with the School of Business Administration, Northeastern University. Her research interests include system reliability, maintenance, and operations research and optimization. E-mail: zhaofei@neuq.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (72101025; 72271049), the Interdisciplinary Research Project for Young Teachers of USTB (Fundamental Research Funds for the Central Universities, FRF-IDRY-24-024), the Hebei Natural Science Foundation (F2023501011), the Fundamental Research Funds for the Central Universities (FRF-TP-20-073A1), and the R&D Program of Beijing Municipal Education Commission (KM202411232015).

Abstract

Abstract:

This paper proposes a reliability evaluation model for a multi-dimensional network system, which has potential to be applied to the internet of things or other practical networks. A multi-dimensional network system with one source element and multiple sink elements is considered first. Each element can connect with other elements within a stochastic connection ranges. The system is regarded as successful as long as the source element remains connected with all sink elements. An importance measure is proposed to evaluate the performance of non-source elements. Furthermore, to calculate the system reliability and the element importance measure, a multi-valued decision diagram based approach is structured and its complexity is analyzed. Finally, a numerical example about the signal transfer station system is illustrated to analyze the system reliability and the element importance measure.

Key words: multi-dimensional network, multi-valued decision diagram, stochastic connection range, reliability analysis, importance measure

Yuqiang FU, Xiaoyang MA, Fei ZHAO. Reliability of multi-dimensional network systems with nodes having stochastic connection ranges[J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 1017-1023.

Figures/Tables 6

Fig 1

Fig 2

Fig 3

Table 1

Fig 4

Table 2

References 30

1	MA X Y, ZHANG X D, PENG R Reliability of intelligent management of research infrastructure based on internet of things. Control and Decision, 2019, 34 (5): 1116- 1120.
2	SALEHI F, OZGER M, CAVDAR C Reliability and delay analysis of 3-Dimensional networks with multi-connectivity: satellite, HAPs, and cellular communications. IEEE Trans. on Network and Service Management, 2024, 21 (1): 437- 450. doi: 10.1109/TNSM.2023.3307909
3	WANG X Y, NING R, ZHAO X, et al Reliability evaluations for a multi-state k-out-of-n: F system with m subsystems supported by multiple protective devices. Computers & Industrial Engineering, 2022, 171 (1): 108409.
4	GAO K Y, PENG R, QU L, et al. Linear system design with application in wireless sensor networks. Journal of Industrial Information Integration, 2022, 27(12): 100279.
5	FAN H H, SUN X H A multi-state reliability evaluation model for p2p networks. Reliability Engineering & System Safety, 2010, 95 (4): 402- 411.
6	YANG K W, LI J C, LIU M D, et al Complex systems and network science: a survey. Journal of systems engineering and electronics, 2023, 34 (3): 543- 573. doi: 10.23919/JSEE.2023.000080
7	MEENA K S, VASANTHI T Reliability analysis of mobile ad hoc networks using universal generating function. Quality & Reliability Engineering International, 2016, 32 (1): 111- 122.
8	JANE C C, LAIH Y W A dynamic bounding algorithm for approximating multi-state two-terminal reliability. European Journal of Operational Research, 2010, 205 (3): 625- 637. doi: 10.1016/j.ejor.2010.01.033
9	JANE C C, LAIH Y W Distribution and reliability evaluation of max-flow in dynamic multi-state flow networks. European Journal of Operational Research, 2017, 259 (3): 1045- 1053. doi: 10.1016/j.ejor.2016.12.030
10	YEH W C New method in searching for all minimal paths for the directed acyclic network reliability problem. IEEE Trans. on Reliability, 2016, 65 (3): 1263- 1270. doi: 10.1109/TR.2016.2570552
11	CHANG P C MC-based simulation approach for two-terminal multi-state network reliability evaluation without knowing d-MCs. Reliability Engineering & System Safety, 2022, 220, 108289.
12	HE R W, LIANG H Y, WU J, et al Reliability assessment of cyber-physical distribution system using multi-dimensional information network model. IEEE Trans. on Smart Grid, 2023, 14 (6): 4683- 4692. doi: 10.1109/TSG.2023.3246955
13	JIA H P, PENG R, DING Y, et al Reliability analysis of distributed storage systems considering data loss and theft. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2020, 234 (2): 303- 321. doi: 10.1177/1748006X19885508
14	JIA H P, PENG R, YANG L, et al Reliability evaluation of demand-based warm standby systems with capacity storage. Reliability Engineering & System Safety, 2022, 218, 108132.
15	ZHANG T, GUO B. Capacitated stochastic coloured Petri net-based approach for computing two-terminal reliability of multi-state network. Journal of Systems Engineering and Electronics, 2012, 23(2): 304–313.
16	CHEN Z W, ZHOU Z M, ZHANG L G, et al Mission reliability modeling and evaluation for reconfigurable unmanned weapon system-of-systems based on effective operation loop. Journal of Systems Engineering and Electronics, 2023, 34 (3): 588- 597. doi: 10.23919/JSEE.2023.000082
17	LIU T, BAI G H, TAO J Y, et al Modeling and evaluation method for resilience analysis of multi-state networks. Reliability Engineering & System Safety, 2022, 226, 108663.
18	HUANG C L, YEH W C, WU H S, et al. A novel 3D binary-state angle network and its reliability evaluate. Proc. of the 12th World Congress on Intelligent Control and Automation, 2016: 1876−1880.
19	HSIEH C C, LIN M H. Reliability-oriented multi-resource allocation in a stochastic-flow network. Reliability Engineering & System Safety, 2003, 81(2): 155–161.
20	LIN Y K, HUANG C F Reliability evaluation of a multi-state network with multiple sinks under individual accuracy rate constraint. Communications in Statistics-Theory and Methods, 2014, 43 (21): 4519- 4533. doi: 10.1080/03610926.2012.716137
21	FORGHANI-ELAHABAD M, MAHDAVI-AMIRI N. Reliability assessment of a multi-source multi-sink stochastic-flow network in terms of minimal paths. Proc. of the 9th International Iranian Operation Research Conference, 2016: 1065–1069.
22	HASSAN M R. Maximizing reliability of the capacity vector for multi-source multi-sink stochastic-flow networks subject to an assignment budget. Journal of Industrial and Management Optimization, 2021, 17(3): 1253–1267.
23	SI S B, ZHAO J B, CAI Z Q, et al Recent advances in system reliability optimization driven by importance measures. Frontiers of Engineering Management, 2020, 7 (3): 335- 358. doi: 10.1007/s42524-020-0112-6
24	QIU S Q, MING X G, SALLAK M, et al A Birnbaum importance-based two-stage approach for two-type component assignment problems. Reliability Engineering & System Safety, 2022, 218, 108051.
25	LI Y, NIU J Q, XING M X, et al Reliability modeling of weighted-k-out-of-n: G system under multiple failure modes with dependent components. Communications in Statistics-Theory and Methods, 2024, 53 (13): 4880- 4897. doi: 10.1080/03610926.2023.2196594
26	DUI H Y, LI S M, XING L D, et al System performance-based joint importance analysis guided maintenance for repairable systems. Reliability Engineering & System Safety, 2019, 186, 162- 175.
27	ZHANG P, ZHOU Z J, HU C H, et al Performance evaluation of non-repairable cyclic phased-mission systems using evidential reasoning rule and multi-valued decision diagrams. Applied Mathematical Modelling, 2023, 124 (2): 24- 63.
28	LI X Y, XIONG X, GUO J, et al Reliability assessment of non-repairable multi-state phased mission systems with backup missions. Reliability Engineering & System Safety, 2022, 223, 108462.
29	ZAITSEVA E, LEVASHENKO V, RABCAN J A new method for analysis of multi-State systems based on multi-valued decision diagram under epistemic uncertainty. Reliability Engineering & System Safety, 2023, 229, 108868.
30	KARANKI D R. Frontiers of performability engineering. Singapore: Springer, 2024.

Element	${\boldsymbol{X}_i}$	P
1	(5, 3, 1)	(0.8, 0.15, 0.05)
2	(3, 2)	(0.95, 0.05)
3	(4, 1)	(0.95, 0.05)
4	(6, 4, 2)	(0.9, 0.08, 0.02)
5	(5, 2)	(0.95, 0.05)
6	(7, 5, 3)	(0.85, 0.1, 0.05)
7	(10, 2)	(0.7, 0.3)
8	(16, 9)	(0.9, 0.1)
9	(9, 3)	(0.8, 0.2)
10	(18, 12, 6)	(0.9, 0.05, 0.05)

Element i	$ {I_i} $	Element i	$ {I_i} $
2	0.0092	7	0.1614
3	0.0092	8	0
4	0.0016	9	0.2421
5	0	10	0
6	0.8925	−	−

[1]	Changxiao ZHAO, Hao LI, Wei ZHANG, Jun DAI, Lei DONG. Risk identification and safety assessment of human-computer interaction in integrated avionics based on STAMP [J]. Journal of Systems Engineering and Electronics, 2024, 35(3): 689-706.
[2]	Xing PAN, Huixiong WANG, Yanjing YANG, Guozhong ZHANG. Resilience based importance measure analysis for SoS [J]. Journal of Systems Engineering and Electronics, 2019, 30(5): 920-930.
[3]	Binghua Song, Zhongbao Zhou, Chaoqun Ma, Jinglun Zhou, and Shaofeng Geng. Reliability analysis of monotone coherent multi-state systems based on Bayesian networks [J]. Journal of Systems Engineering and Electronics, 2016, 27(6): 1326-1335.
[4]	Xibin Zhao, Shubin Si, Hongyan Dui, Zhiqiang Cai, and Shudong Sun. Integrated importance measure for multi-state coherent systems of k level [J]. Journal of Systems Engineering and Electronics, 2013, 24(6): 1029-1037.
[5]	He Liping & Qu Fuzheng. Possibilistic entropy-based measure of importance in fault tree analysis [J]. Journal of Systems Engineering and Electronics, 2009, 20(2): 434-444.

Reliability of multi-dimensional network systems with nodes having stochastic connection ranges

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 6

References 30

Related Articles 5

Recommended Articles

Metrics

Comments