{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T16:55:52Z","timestamp":1769014552423,"version":"3.49.0"},"reference-count":44,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T00:00:00Z","timestamp":1648425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/s22072582","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T21:45:51Z","timestamp":1648590351000},"page":"2582","update-policy":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Design and Reliability Analysis of a Novel Redundancy Topology Architecture"],"prefix":"10.3390","volume":"22","author":[{"given":"Fei","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenyi","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wanjia","family":"Gao","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanfang","family":"Liu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/2.zoppoz.workers.dev:443\/https\/orcid.org\/0000-0002-2382-2870","authenticated-orcid":false,"given":"Yanjun","family":"Hu","sequence":"additional","affiliation":[{"name":"Key Laboratory of Instrumentation Science & Dynamic Measurement, Ministry of Education, North University of China, Taiyuan 030051, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,28]]},"reference":[{"key":"ref_1","first-page":"3090","article-title":"A Review of Aeronautical Electronics and Its Parallelism with Automotive Electronics","volume":"58","year":"2010","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"944","DOI":"10.1109\/JPROC.2019.2913443","article-title":"Industrial Communication Systems and Their Future Challenges: Next-Generation Ethernet, IIoT, and 5G","volume":"107","author":"Vitturi","year":"2019","journal-title":"Proc. IEEE"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.micpro.2012.04.006","article-title":"Performance analysis and comparison of 2\u00d74 network on chip topology","volume":"36","author":"Ju","year":"2012","journal-title":"Microprocess. Microsyst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1049\/iet-cdt.2016.0184","article-title":"Efficient and scalable cross-by-pass-mesh topology for networks-on-chip","volume":"11","author":"Gulzari","year":"2017","journal-title":"IET Comput. Digit. Tech."},{"key":"ref_5","unstructured":"Rushby, J. (2003). A Comparison of Bus Architectures for Safety-Critical Embedded Systems, SRI. NASA\/CR\u20132003\u2013212161."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/s11235-019-00566-8","article-title":"Reliable networking in Ethernet ring mesh networks using regular topologies","volume":"72","author":"Jahanshahi","year":"2019","journal-title":"Telecommun. Syst."},{"key":"ref_7","unstructured":"Barranco, M., Rodriguez-Navas, G., Proenza, J., and Almeida, L. (2005, January 19\u201322). CANcentrate: An active star topology for CAN networks. Proceedings of the IEEE International Workshop on Factory Communication Systems, Catania, Italy."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/TII.2006.875505","article-title":"An Active Star Topology for Improving Fault Confinement in CAN Networks","volume":"2","author":"Barranco","year":"2006","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MIC.2017.2911436","article-title":"BEEP: Balancing Energy, Redundancy, and Performance in Fat-Tree Data Center Networks","volume":"21","author":"Araujo","year":"2017","journal-title":"IEEE Internet Comput."},{"key":"ref_10","unstructured":"Ademaj, A., Sivencrona, H., Bauer, G., and Torin, J. (2003, January 22\u201325). Evaluation of fault handling of the time-triggered architecture with bus and star topology. Proceedings of the 2003 International Conference on Dependable Systems and Networks, San Francisco, CA, USA."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.comnet.2017.05.013","article-title":"Availability optimization in a ring-based network topology","volume":"124","author":"Ezran","year":"2017","journal-title":"Comput. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"802","DOI":"10.1109\/TIE.2009.2036642","article-title":"Quantitative Comparison of the Error-Containment Capabilities of a Bus and a Star Topology in CAN Networks","volume":"58","author":"Barranco","year":"2009","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1142\/S0218126611007591","article-title":"Improved Modified Fat-Tree Topology Network-On-Chip","volume":"20","author":"Bouhraoua","year":"2011","journal-title":"J. Circ. Syst. Comput."},{"key":"ref_14","unstructured":"Avizienis, A., Laprie, J.C., and Randell, B. (2000, January 24\u201326). Fundamental Concepts of Dependability. Proceedings of the 3rd IEEE Information Survivability Workshop (ISW-2000), Boston, MA, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1007\/s13198-019-00929-z","article-title":"Terminal reliability analysis of multistage interconnection networks","volume":"11","author":"Prakash","year":"2019","journal-title":"Int. J. Syst. Assur. Eng. Manag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/s10836-016-5601-5","article-title":"Reliability Analysis of Fault-Tolerant Bus-Based Interconnection Networks","volume":"32","author":"Bistouni","year":"2016","journal-title":"J. Electron. Test."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1109\/JPROC.2019.2914589","article-title":"Fault Tolerance in Highly Reliable Ethernet-Based Industrial Systems","volume":"107","author":"Vadillo","year":"2019","journal-title":"Proc. IEEE"},{"key":"ref_18","unstructured":"Wang, Y., Zhang, X., and Zhang, D. (2019, January 19\u201321). A High-reliability Network Architecture Based on Parallel Redundancy Protocol. Proceedings of the ICCSE, Toronto, ON, Canada."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Barranco, M., Proenza, J., and Almeida, L. (2010, January 18\u201321). Reliability improvement achievable in CAN-based systems by means of the ReCANcentrate replicated star topology. Proceedings of the 2010 IEEE International Workshop on Factory Communication Systems Proceedings, Nancy, France.","DOI":"10.1109\/WFCS.2010.5548633"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1109\/TII.2012.2198663","article-title":"Design and Verification of a Media Redundancy Management Driver for a CAN Star Topology","volume":"9","author":"Gessner","year":"2012","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Amari, A., and Mifdaoui, A. (2018). Specification and Performance Indicators of AeroRing-A Multiple-Ring Ethernet Network for Avionics Embedded Systems. Sensors, 18.","DOI":"10.3390\/s18113871"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.csi.2011.10.004","article-title":"Modeling the reliability of a group membership protocol for dual-scheduled time division multiple access networks","volume":"34","author":"Rosset","year":"2012","journal-title":"Comput. Stand. Interfaces"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Lange, R., Vasques, F., Portugal, P., and de Oliveira, R.S. (2012, January 21\u201324). Guaranteeing real-time message deadlines in the FlexRay static segment using a on-line scheduling approach. Proceedings of the 2012 9th IEEE International Workshop on Factory Communication Systems, Lemgo\/Detmold, Germany.","DOI":"10.1109\/WFCS.2012.6242578"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Zheng, Z., He, F., Li, H., and Lu, J. (2019, January 8\u201312). Design Optimization of Time-Triggered Ethernet based on Routing and Scheduling Strategy. Proceedings of the 2019 IEEE\/AIAA 38th Digital Avionics Systems Conference (DASC), San Diego, CA, USA.","DOI":"10.1109\/DASC43569.2019.9081772"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"23720","DOI":"10.1109\/ACCESS.2020.2970266","article-title":"Enhancing Real-Time and Determinacy for Network-Level Schedule in Distributed Mixed-Critical System","volume":"8","author":"Lu","year":"2020","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1007\/s11241-016-9265-0","article-title":"Timing analysis of rate-constrained traffic in TTEthernet using network calculus","volume":"53","author":"Zhao","year":"2017","journal-title":"Real-Time Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/j.jocs.2017.12.007","article-title":"Research on the scheduling method of AFDX terminal system based on time triggered and event triggered","volume":"27","author":"Xu","year":"2018","journal-title":"J. Comput. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1109\/TII.2019.2895046","article-title":"A Fault-Tolerant Ethernet for Hard Real-Time Adaptive Systems","volume":"15","author":"Gessner","year":"2019","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"142564","DOI":"10.1109\/ACCESS.2019.2943543","article-title":"A Revised Trajectory Approach for the Worst-Case Delay Analysis of an AFDX Network","volume":"7","author":"Tang","year":"2019","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1109\/MC.2019.2944337","article-title":"An Architecture for Highly Reliable Fault-Tolerant Adaptive Distributed Embedded Systems","volume":"53","author":"Barranco","year":"2020","journal-title":"Computer"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"\u00c1lvarez, I., Furi\u00f3, I., Proenza, J., and Barranco, M. (2021). Design and Experimental Evaluation of the Proactive Transmission of Replicated Frames Mechanism over Time-Sensitive Networking. Sensors, 21.","DOI":"10.3390\/s21030756"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1515\/freq-2012-0034","article-title":"Multi-Objective Topology Design of Industrial Ethernet Networks","volume":"66","author":"Zhang","year":"2012","journal-title":"Frequenz"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kong, F., Huang, Y., and Zhang, M. (2019, January 15\u201318). Fast Non-dominated Sorting Genetic Algorithm with Three Crossover Individuals for Network Topology Optimization in Industrial Internet of Things. Proceedings of the 2019 19th International Conference on Control, Automation and Systems (ICCAS), Jeju, Korea.","DOI":"10.23919\/ICCAS47443.2019.8971663"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/0012-365X(73)90138-6","article-title":"Tough graphs and hamiltonian circuits","volume":"5","year":"1973","journal-title":"Discret. Math."},{"key":"ref_35","first-page":"13","article-title":"Vulnerability in graphs\u2014A comparative survey","volume":"1","author":"Barefoot","year":"1987","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"ref_36","unstructured":"Alavi, Y., and Schwenk, A. (1995). The Tenacity of a Graph. Graph Theory. Combinatorics, and Algorithms, Wiley."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"078902","DOI":"10.1088\/0256-307X\/27\/7\/078902","article-title":"Natural Connectivity of Complex Networks","volume":"27","author":"Wu","year":"2010","journal-title":"Chin. Phys. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1016\/S0166-218X(96)00133-3","article-title":"Measuring the vulnerability for classes of intersection graphs","volume":"77","author":"Kratsch","year":"1997","journal-title":"Discret. Appl. Math."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Bauer, E. (2010). Design for Reliability: Information and Computerbased Systems, Wiley.","DOI":"10.1002\/9781118075104"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1504\/IJRS.2013.057092","article-title":"Reliability prediction of distributed systems using Monte Carlo method","volume":"7","author":"Gunawan","year":"2013","journal-title":"Int. J. Reliab. Saf."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1109\/12.42134","article-title":"Multistage interconnection network reliability","volume":"38","author":"Blake","year":"1989","journal-title":"IEEE Trans. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"468","DOI":"10.1007\/s11227-014-1175-0","article-title":"Design of 4-disjoint gamma interconnection network layouts and reliability analysis of gamma interconnection Networks","volume":"69","author":"Rajkumar","year":"2014","journal-title":"J. Supercomput."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1142\/S0218539302000809","article-title":"An Efficient Multi-Variable Inversion Algorithm for Reliability Evaluation of Complex Systems Using Path Sets","volume":"9","author":"Chaturvedi","year":"2002","journal-title":"Int. J. Reliab. Qual. Saf. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1002\/qre.2715","article-title":"Reliability of safety-critical systems: A state-of-the-art review","volume":"36","author":"Maurya","year":"2020","journal-title":"Qual. Reliab. Eng. Int."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/22\/7\/2582\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:44:48Z","timestamp":1760136288000},"score":1,"resource":{"primary":{"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/www.mdpi.com\/1424-8220\/22\/7\/2582"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,28]]},"references-count":44,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["s22072582"],"URL":"https:\/\/2.zoppoz.workers.dev:443\/https\/doi.org\/10.3390\/s22072582","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,28]]}}}