{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T10:51:08Z","timestamp":1783075868756,"version":"3.54.6"},"reference-count":46,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2021,7,17]],"date-time":"2021-07-17T00:00:00Z","timestamp":1626480000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A wireless sensor network (WSN) is a group of sensors connected with a wireless communications infrastructure designed to monitor and send collected data to the primary server. The WSN is the cornerstone of the Internet of Things (IoT) and Industry 4.0. Robustness is an essential characteristic of WSN that enables reliable functionalities to end customers. However, existing approaches primarily focus on component reliability and malware propagation, while the robustness and security of cascading failures between the physical domain and the information domain are usually ignored. This paper proposes a cross-domain agent-based model to analyze the connectivity robustness of a system in the malware propagation process. The agent characteristics and transition rules are also described in detail. To verify the practicality of the model, three scenarios based on different network topologies are proposed. Finally, the robustness of the scenarios and the topologies are discussed.<\/jats:p>","DOI":"10.3390\/s21144873","type":"journal-article","created":{"date-parts":[[2021,7,18]],"date-time":"2021-07-18T21:18:52Z","timestamp":1626643132000},"page":"4873","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Novel Multi-Agent Model for Robustness with Component Failure and Malware Propagation in Wireless Sensor Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3007-5110","authenticated-orcid":false,"given":"Biao","family":"Xu","sequence":"first","affiliation":[{"name":"The Key Laboratory on Reliability and Environmental Engineering Technology, Beihang University, Beijing 140191, China"},{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 140191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Minyan","family":"Lu","sequence":"additional","affiliation":[{"name":"The Key Laboratory on Reliability and Environmental Engineering Technology, Beihang University, Beijing 140191, China"},{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 140191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hong","family":"Zhang","sequence":"additional","affiliation":[{"name":"The Key Laboratory on Reliability and Environmental Engineering Technology, Beihang University, Beijing 140191, China"},{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 140191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cong","family":"Pan","sequence":"additional","affiliation":[{"name":"The Key Laboratory on Reliability and Environmental Engineering Technology, Beihang University, Beijing 140191, China"},{"name":"School of Reliability and Systems Engineering, Beihang University, Beijing 140191, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1109\/JIOT.2014.2312291","article-title":"Research directions for the internet of things","volume":"1","author":"Stankovic","year":"2014","journal-title":"IEEE Internet Things J."},{"key":"ref_2","unstructured":"Sakhnini, J., Karimipour, H., Dehghantanha, A., Parizi, R.M., and Srivastava, G. (2019). Security aspects of Internet of Things aided smart grids: A bibliometric survey. Internet Things."},{"key":"ref_3","first-page":"1","article-title":"Thoughts on reliability in the internet of things","volume":"1","author":"Kempf","year":"2011","journal-title":"Interconnecting Smart Objects Internet Work."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zin, T.T., Tin, P., and Hama, H. (2016, January 11\u201314). Reliability and availability measures for Internet of Things consumer world perspectives. Proceedings of the 2016 IEEE 5th Global Conference on Consumer Electronics, GCCE 2016, Kyoto, Japan.","DOI":"10.1109\/GCCE.2016.7800446"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Safaei, B., Monazzah, A.M.H., Bafroei, M.B., and Ejlali, A. (2017, January 20\u201322). Reliability side-effects in Internet of Things application layer protocols. Proceedings of the 2017 2nd International Conference on System Reliability and Safety, ICSRS 2017, Milan, Italy.","DOI":"10.1109\/ICSRS.2017.8272822"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Ateeq, M., Ishmanov, F., Afzal, M.K., and Naeem, M. (2019). Multi-parametric analysis of reliability and energy consumption in IoT: A deep learning approach. Sensors, 19.","DOI":"10.3390\/s19020309"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Pasricha, S. (2018, January 6\u201310). Overcoming energy and reliability challenges for IoT and mobile devices with data analytics. Proceedings of the 2018 31st International Conference on VLSI Design and 2018 17th International Conference on Embedded Systems (VLSID), Pune, India.","DOI":"10.1109\/VLSID.2018.69"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xing, L. (2019). Reliability Modeling of Wireless Sensor Networks: A Review. Recent Pat. Eng., 15.","DOI":"10.2174\/1872212113666191209091947"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, C., Xing, L., Vokkarane, V.M., and Sun, Y. (2014). Reliability and lifetime modeling of wireless sensor nodes. Microelectron. Reliab., 54.","DOI":"10.1016\/j.microrel.2013.08.001"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Deif, D., and Gadallah, Y. (2017). A comprehensive wireless sensor network reliability metric for critical Internet of Things applications. EURASIP J. Wirel. Commun. Netw., 2017.","DOI":"10.1186\/s13638-017-0930-3"},{"key":"ref_11","first-page":"419","article-title":"Fault-tolerance and reliability analysis for wireless sensor networks","volume":"5","author":"Xing","year":"2009","journal-title":"Int. J. Perform. Eng."},{"key":"ref_12","unstructured":"Xing, L., and Shrestha, A. (2006, January 10\u201312). QoS reliability of hierarchical clustered wireless sensor networks. Proceedings of the IEEE International Performance, Computing, and Communications Conference, Phoenix, AZ, USA."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zonouz, A.E., Xing, L., Vokkarane, V.M., and Sun, Y.L. (2014). Reliability-oriented single-path routing protocols in wireless sensor networks. IEEE Sens. J., 14.","DOI":"10.1109\/JSEN.2014.2332296"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Mahmood, M.A., Seah, W.K.G., and Welch, I. (2015). Reliability in wireless sensor networks: A survey and challenges ahead. Comput. Netw., 79.","DOI":"10.1016\/j.comnet.2014.12.016"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"24735","DOI":"10.3390\/s151024735","article-title":"Resilient wireless sensor networks using topology control: A review","volume":"15","author":"Huang","year":"2015","journal-title":"Sensors"},{"key":"ref_16","unstructured":"Shrestha, A., Xing, L., and Liu, H. (October, January 29). Infrastructure communication reliability of wireless sensor networks. Proceedings of the 2nd IEEE International Symposium on Dependable, Autonomic and Secure Computing, DASC, Indianapolis, IN, USA."},{"key":"ref_17","first-page":"141","article-title":"Infrastructure communication reliability of wireless sensor networks considering common-cause failures","volume":"8","author":"Shrestha","year":"2012","journal-title":"Int. J. Perform. Eng."},{"key":"ref_18","unstructured":"Wang, C., Xing, L., Vokkarane, V.M., and Sun, Y. (2012, January 26\u201328). Manycast and anycast-based infrastructure communication reliability for wireless sensor networks. Proceedings of the 18th ISSAT International Conference on Reliability and Quality in Design, Boston, MA, USA."},{"key":"ref_19","first-page":"43","article-title":"Quantifying application communication reliability of wireless sensor networks","volume":"4","author":"Shrestha","year":"2008","journal-title":"Int. J. Perform. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zonouz, A.E., Xing, L., Vokkarane, V.M., and Sun, Y. (2013, January 20\u201323). Application communication reliability of wireless sensor networks supporting K-coverage. Proceedings of the IEEE International Conference on Distributed Computing in Sensor Systems, DCoSS, Cambridge, MA, USA.","DOI":"10.1109\/DCOSS.2013.47"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Wang, C., Xing, L., Zonouz, A.E., Vokkarane, V.M., and Sun, Y.L. (2017). Communication Reliability Analysis of Wireless Sensor Networks Using Phased-Mission Model. Qual. Reliab. Eng. Int., 33.","DOI":"10.1002\/qre.2060"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Venkatesan, L., Shanmugavel, S., and Subramaniam, C. (2013). A Survey on Modeling and Enhancing Reliability of Wireless Sensor Network. Wirel. Sens. Netw., 05.","DOI":"10.4236\/wsn.2013.53006"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Agre, J., and Clare, L. (2000). An Integrated Architecture for Cooperative Sensing Networks. Computer, 33.","DOI":"10.1109\/2.841788"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Al-Karaki, J.N., and Kamal, A.E. (2004). Routing techniques in wireless sensor networks: A survey. IEEE Wirel. Commun., 11.","DOI":"10.1109\/MWC.2004.1368893"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Anastasi, G., Conti, M., Di Francesco, M., and Passarella, A. (2009). Energy conservation in wireless sensor networks: A survey. Ad Hoc Netw., 7.","DOI":"10.1016\/j.adhoc.2008.06.003"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Koushanfar, F., Potkonjak, M., and Sangiovanni-Vincentelli, A. (2004). Fault tolerance in wireless sensor networks. Handb. Sens. Netw. Compact Wirel. Wired Sens. Syst., 812\u2013829.","DOI":"10.1201\/9780203489635.ch36"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Sudevalayam, S., and Kulkarni, P. (2011). Energy harvesting sensor nodes: Survey and implications. IEEE Commun. Surv. Tutor., 13.","DOI":"10.1109\/SURV.2011.060710.00094"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/1138127.1138128","article-title":"Vigilnet: An integrated sensor network system for energy-efficient surveillance","volume":"2","author":"He","year":"2006","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1016\/j.jnca.2011.11.016","article-title":"A survey on coverage and connectivity issues in wireless sensor networks","volume":"35","author":"Zhu","year":"2012","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Zhu, L., Zhao, H., and Wang, X. (2015). Stability and bifurcation analysis in a delayed reaction-diffusion malware propagation model. Comput. Math. Appl., 69.","DOI":"10.1016\/j.camwa.2015.02.004"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Shen, S., Zhou, H., Feng, S., Liu, J., and Cao, Q. (2019). SNIRD: Disclosing Rules of Malware Spread in Heterogeneous Wireless Sensor Networks. IEEE Access, 7.","DOI":"10.1109\/ACCESS.2019.2927220"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Feng, L., Song, L., Zhao, Q., and Wang, H. (2015). Modeling and Stability Analysis of Worm Propagation in Wireless Sensor Network. Math. Probl. Eng., 2015.","DOI":"10.1155\/2015\/129598"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Liu, B., Zhou, W., Gao, L., Zhou, H., Luan, T.H., and Wen, S. (2018). Malware propagations in wireless Ad Hoc networks. IEEE Trans. Dependable Secur. Comput., 15.","DOI":"10.1109\/TDSC.2016.2642191"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Acarali, D., Rajarajan, M., Komninos, N., and Zarpel\u00e3o, B.B. (2019). Modelling the Spread of Botnet Malware in IoT-Based Wireless Sensor Networks. Secur. Commun. Netw., 2019.","DOI":"10.1155\/2019\/3745619"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Shen, S., Ma, H., Fan, E., Hu, K., Yu, S., Liu, J., and Cao, Q. (2017). A non-cooperative non-zero-sum game-based dependability assessment of heterogeneous WSNs with malware diffusion. J. Netw. Comput. Appl., 91.","DOI":"10.1016\/j.jnca.2017.05.003"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Wu, X., Cao, Q., Jin, J., Li, Y., and Zhang, H. (2019). Nodes Availability Analysis of NB-IoT Based Heterogeneous Wireless Sensor Networks under Malware Infection. Wirel. Commun. Mob. Comput., 2019.","DOI":"10.1155\/2019\/4392839"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, T., Wu, Q., Wen, S., Cai, Y., Tian, H., Chen, Y., and Wang, B. (2017). Propagation modeling and defending of a mobile sensor worm in wireless sensor and actuator networks. Sensors, 17.","DOI":"10.3390\/s17010139"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Del Rey, A.M., Guill\u00e9n, J.D.H., and S\u00e1nchez, G.R. (2016, January 15\u201316). Modeling malware propagation in wireless sensor networks with individual-based models. Proceedings of the Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Salamanca, Spain.","DOI":"10.1007\/978-3-319-44636-3_18"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Batista, F.K., Mart\u00edn del Rey, \u00c1., Quintero-Bonilla, S., and Queiruga-Dios, A. (2017, January 6\u20138). A SEIR model for computer virus spreading based on cellular automata. Proceedings of the Advances in Intelligent Systems and Computing, Leon, Spain.","DOI":"10.1007\/978-3-319-67180-2_62"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Wang, Y., Li, D., and Dong, N. (2018). Cellular automata malware propagation model for WSN based on multi-player evolutionary game. IET Netw., 7.","DOI":"10.1049\/iet-net.2017.0070"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Bose, A., and Shin, K.G. (2013). Agent-based modeling of malware dynamics in heterogeneous environments. Secur. Commun. Netw., 6.","DOI":"10.1002\/sec.298"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Hosseini, S., Abdollahi Azgomi, M., and Rahmani Torkaman, A. (2016). Agent-based simulation of the dynamics of malware propagation in scale-free networks. Simulation, 92.","DOI":"10.1177\/0037549716656060"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Bouabdallah, F., Bouabdallah, N., and Boutaba, R. (2008, January 10\u201312). Energy conservation in reliable wireless sensor networks. Proceedings of the IEEE International Conference on Communications, Hangzhou, China.","DOI":"10.1109\/ICC.2008.457"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Abar, S., Theodoropoulos, G.K., Lemarinier, P., and O\u2019Hare, G.M.P. (2017). Agent Based Modelling and Simulation tools: A review of the state-of-art software. Comput. Sci. Rev., 24.","DOI":"10.1016\/j.cosrev.2017.03.001"},{"key":"ref_45","unstructured":"Wilensky, U., and Evanston, I. (1999). NetLogo: Center for Connected Learning and Computer-Based Modeling, Northwestern University."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Li, X., Magnant, C., and Qin, Z. (2018). Random Graphs. Properly Colored Connectivity of Graphs, Springer.","DOI":"10.1007\/978-3-319-89617-5"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4873\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:31:08Z","timestamp":1760164268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/14\/4873"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,17]]},"references-count":46,"journal-issue":{"issue":"14","published-online":{"date-parts":[[2021,7]]}},"alternative-id":["s21144873"],"URL":"https:\/\/doi.org\/10.3390\/s21144873","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,17]]}}}