{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T05:13:50Z","timestamp":1772774030014,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,14]],"date-time":"2021-01-14T00:00:00Z","timestamp":1610582400000},"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>Wireless charging provides continuous energy for wireless sensor networks. However, it is difficult to replenish enough energy for all sensor nodes with fixed charging alone, and even more unrealistic to charge a large number of nodes within a short time via mobile charging. In order to overcome the above weaknesses, this paper firstly puts forward a Master-Slave Charging mode for the WRSN (Wireless Rechargeable Sensor Network), where fixed charging is the master mode and mobile charging is the slave mode, respectively. However, Master-Slave Charging is a typical hybrid system involving discrete event decision and continuous energy transfer. Therefore, the Hybrid Cyber Petri net system is proposed to build a visual specification with mathematical expression of Master-Slave Charging. Moreover, wireless charging in the WRSN is modeled and evaluated from the perspective of a hybrid system for the first time. Furthermore, a greedy-genetic algorithm is proposed to obtain the deployment of fixed chargers and the path planning of a mobile charger, by maximizing the actual electric quantity of the master charging problem and minimizing the mobile charger\u2019s travelling path of the slave charging problem. Finally, the simulation results confirm and verify the Hybrid Cyber Petri net model for Master-Slave Charging. It is worth noting that the proposed model in this paper is highly adaptable to various charging modes in the WRSN.<\/jats:p>","DOI":"10.3390\/s21020551","type":"journal-article","created":{"date-parts":[[2021,1,15]],"date-time":"2021-01-15T01:33:29Z","timestamp":1610674409000},"page":"551","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Hybrid Cyber Petri net Modelling, Simulation and Analysis of Master-Slave Charging for Wireless Rechargeable Sensor Networks"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5238-2026","authenticated-orcid":false,"given":"Huaiyu","family":"Qin","sequence":"first","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212000, China"},{"name":"School of Electrical and Information Engineering, Jiangsu University of Science and Technology, Zhenjiang 212000, China"}]},{"given":"Buhui","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212000, China"}]},{"given":"Leijun","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212000, China"}]},{"given":"Xue","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Jiangsu University, Zhenjiang 212000, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1413","DOI":"10.1109\/COMST.2015.2499783","article-title":"Wireless charging technologies: Fundamentals, standards, and network applications","volume":"18","author":"Lu","year":"2016","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1109\/COMST.2014.2368999","article-title":"Wireless networks with RF energy harvesting: A contemporary survey","volume":"17","author":"Lu","year":"2015","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bai, X., Han, W.-Y., Xu, L.-J., Zhang, J.-W., and Li, Y.-X. (2020). A radio frequency and vibration energy harvesting antenna based on piezoelectric material. Int. J. Rf Microw. Comput. Aided Eng., 30.","DOI":"10.1002\/mmce.22251"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Lai, W.Y., and Hsiang, T.R. (2019). Wireless charging deployment in sensor networks. Sensors, 19.","DOI":"10.3390\/s19010201"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1016\/j.comnet.2016.01.007","article-title":"Hierarchical, collaborative wireless energy transfer in sensor networks with multiple mobile chargers","volume":"97","author":"Madhja","year":"2016","journal-title":"Comput. Netw."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.jss.2016.08.046","article-title":"GTCharge: A game theoretical collaborative charging scheme for wireless rechargeable sensor networks","volume":"121","author":"Lin","year":"2016","journal-title":"J. Syst. Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"278","DOI":"10.1109\/TVT.2015.2391119","article-title":"Optimal charging in wireless rechargeable sensor networks","volume":"65","author":"Fu","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2250","DOI":"10.1109\/TNET.2017.2684159","article-title":"Joint charging tour planning and depot positioning for wireless sensor networks using mobile chargers","volume":"25","author":"Jiang","year":"2017","journal-title":"IEEE ACM Trans. Netw."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Wang, W., Jing, H., Liao, J., Yin, F., Yuan, P., and Chen, L. (2020). A safe charging algorithm based on multiple mobile chargers. Sensors, 20.","DOI":"10.3390\/s20102937"},{"key":"ref_10","first-page":"3","article-title":"Petri-net based modelling and multi-objective optimal deployment for WRSN","volume":"22","author":"Qin","year":"2020","journal-title":"Control Eng. Appl. Inform."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1835","DOI":"10.1109\/TIE.2007.911926","article-title":"A petri net design of command filters for semiautonomous mobile sensor networks","volume":"55","author":"Lee","year":"2008","journal-title":"IEEE Trans. Ind. Electr."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3381","DOI":"10.3390\/s110303381","article-title":"A reliable energy-efficient multi-level routing algorithm for wireless sensor networks using fuzzy petri nets","volume":"11","author":"Yu","year":"2011","journal-title":"Sensors"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ruiz, M.C., Mateo, J.A., Macia, H., Pardo, J.J., and Olivares, T. (2012, January 14\u201316). Formal modelling and performance evaluation of a novel role-based Routing Algorithm for wireless sensor networks. Proceedings of the 2012 18th Annual International Conference on Advanced Computing and Communications (ADCOM), Electronics CityHosur Main Road, Bangalore, India.","DOI":"10.1109\/ADCOM.2012.6563577"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Ruiz, M.C., Garrido-Hidalgo, C., Gruska, D.P., Olivares, T., Hortelano, D., and Roda-Sanchez, L. (2019, January 8\u20139). Modeling and evaluation of a power-aware algorithm for IoT bluetooth low energy devices. Proceedings of the 2019 IEEE International Conference on Smart Internet of Things (SmartIoT), Tianjin, China.","DOI":"10.1109\/SmartIoT.2019.00014"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mostafa, A., and Hassan, K. (2014, January 8\u201310). Robust energy harvesting aware clustering with fuzzy petri net reasoning algorithm. Proceedings of the 2014 IEEE 10th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob), Larnaca, Cyprus.","DOI":"10.1109\/WiMOB.2014.6962198"},{"key":"ref_16","unstructured":"Moreno, J.C.M., Castro, D.M., and Ramrez, J.L.V. (2015, January 14\u201316). Design of discrete event systems supported on wireless sensors and actuator networks using colored Petri Nets. Proceedings of the 2015 IEEE 2nd Colombian Conference on Automatic Control (CCAC), Manizales, Colombia."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Abrishambaf, R., Cabral, J., Monteiro, J., and Bal, M. (2015, January 17\u201319). An energy aware design flow of distributed industrial wireless sensor and actuator networks. Proceedings of the 2015 IEEE International Conference on Industrial Technology (ICIT), Seville, Spain.","DOI":"10.1109\/ICIT.2015.7125416"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1016\/j.jnca.2015.11.010","article-title":"Approaching green sensor field using queue-based optimization technique","volume":"66","author":"Jiang","year":"2016","journal-title":"J. Netw. Comput. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Berrachedi, A., and Boukala-Ioualalen, M. (2016, January 23\u201325). Evaluation of the energy consumption and the packet loss in WSNs using deterministic stochastic petri nets. Proceedings of the 2016 30th International Conference on Advanced Information Networking and Applications Workshops (WAINA), Crans-Montana, Switzerland.","DOI":"10.1109\/WAINA.2016.86"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1007\/s11276-015-0975-3","article-title":"Anycast tree-based routing in mobile wireless sensor networks with multiple sinks","volume":"22","author":"Kostin","year":"2016","journal-title":"Wirel. Netw."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Le, K., Pham, B., Tram, Q., Bui, T., and Quan, T. (2018, January 26\u201328). CODE-WSN: A formal modelling tool for congestion detection on wireless sensor networks. Proceedings of the 2018 IEEE World Symposium on Communication Engineering (WSCE), Singapore.","DOI":"10.1109\/WSCE.2018.8690537"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Riouali, Y., Benhlima, L., and Bah, S. (2017). Extended batches petri nets based system for road traffic management in WSNs. J. Sens. Actuator Netw., 6.","DOI":"10.3390\/jsan6040030"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1016\/j.future.2018.04.022","article-title":"Modeling and developing a conflict-aware scheduling in urban transportation networks","volume":"107","author":"Mahjoub","year":"2020","journal-title":"Future Gener. Comput. Syst. Int. J. Esci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.1109\/TMC.2012.161","article-title":"Energy provisioning in wireless rechargeable sensor networks","volume":"12","author":"He","year":"2013","journal-title":"IEEE Trans. Mob. Comp."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Jiang, J.R., and Liao, J.-H. (2016). Efficient wireless charger deployment for wireless rechargeable sensor networks. Energies, 9.","DOI":"10.3390\/en9090696"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Yao, K.H., Jiang, J.R., Tsai, C.H., and Wu, Z.S. (2017). Evolutionary beamforming optimization for radio frequency charging in wireless rechargeable sensor networks. Sensors, 17.","DOI":"10.3390\/s17081918"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Sun, G., Liu, Y.H., Yang, M., Wang, A.M., and Zhang, Y. (2017, January 4\u20138). Charging nodes deployment optimization in wireless rechargeable sensor network. Proceedings of the 2017 IEEE Global Communications Conference, Singapore.","DOI":"10.1109\/GLOCOM.2017.8253963"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1016\/j.compeleceng.2017.11.021","article-title":"Deploying charging nodes in wireless rechargeable sensor networks based on improved firefly algorithm","volume":"72","author":"Yang","year":"2017","journal-title":"Comput. Electr. Eng."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1109\/TNET.2018.2793949","article-title":"SCAPE: Safe charging with adjustable power","volume":"26","author":"Dai","year":"2018","journal-title":"IEEE ACM Trans. Netw."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1109\/TNET.2017.2786463","article-title":"Radiation constrained scheduling of wireless charging tasks","volume":"26","author":"Dai","year":"2018","journal-title":"IEEE ACM Trans. Netw."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1145\/3289182","article-title":"Radiation constrained fair charging for wireless power transfer","volume":"15","author":"Li","year":"2019","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Wan, P., Cheng, W., Wu, B., and Wang, G. (2019). An algorithm to optimize deployment of charging base stations for WRSN. Eur. J. Wirel. Commun. Netw., 63.","DOI":"10.1186\/s13638-019-1393-5"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2411","DOI":"10.1109\/TC.2015.2490060","article-title":"A mobile data gathering framework for wireless rechargeable sensor networks with vehicle movement costs and capacity constraints","volume":"65","author":"Wang","year":"2016","journal-title":"IEEE Trans. Comput."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"560","DOI":"10.1109\/TMC.2017.2732979","article-title":"Combining solar energy harvesting with wireless charging for hybrid wireless sensor networks","volume":"17","author":"Wang","year":"2018","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7415","DOI":"10.1109\/TVT.2015.2481920","article-title":"ESync: Energy synchronized mobile charging in rechargeable wireless sensor networks","volume":"65","author":"Fu","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1109\/TII.2016.2586028","article-title":"Joint energy replenishment and operation scheduling in wireless rechargeable sensor networks","volume":"13","author":"Shu","year":"2017","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1699","DOI":"10.1109\/TMC.2015.2473163","article-title":"Near-optimal velocity control for mobile charging in wireless rechargeable sensor networks","volume":"15","author":"Shu","year":"2016","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1016\/j.jss.2018.09.002","article-title":"Hybrid charging scheduling schemes for three-dimensional underwater wireless rechargeable sensor networks","volume":"146","author":"Lin","year":"2018","journal-title":"J. Syst. Softw."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"5100","DOI":"10.1109\/TVT.2019.2906234","article-title":"An active mobile charging and data collection scheme for clustered sensor networks","volume":"68","author":"Liu","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3531","DOI":"10.1007\/s11276-019-01948-1","article-title":"Energy provisioning in wireless rechargeable sensor networks with limited knowledge","volume":"25","author":"Sheikhi","year":"2019","journal-title":"Wirel. Netw."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"28668","DOI":"10.1109\/ACCESS.2018.2818790","article-title":"A smart collaborative charging algorithm for mobile power distribution in 5G networks","volume":"6","author":"Ai","year":"2018","journal-title":"IEEE Access"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"8202","DOI":"10.1109\/JIOT.2019.2918837","article-title":"Energy-aware multiple mobile chargers coordination for wireless rechargeable sensor networks","volume":"6","author":"Mo","year":"2019","journal-title":"IEEE Internet Things J."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3518","DOI":"10.1109\/JSYST.2020.2977984","article-title":"A periodic multinode charging and data collection scheme with optimal traveling path in WRSNs","volume":"14","author":"Lyu","year":"2020","journal-title":"IEEE Syst. J."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"73096","DOI":"10.1109\/ACCESS.2020.2987920","article-title":"The charging strategy of mobile charging vehicles in wireless rechargeable sensor networks with heterogeneous sensors","volume":"8","author":"Tian","year":"2020","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1109\/TNET.2014.2303979","article-title":"Multi-node wireless energy charging in sensor networks","volume":"23","author":"Xie","year":"2015","journal-title":"IEEE ACM Trans. Netw."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1380","DOI":"10.1109\/TASE.2014.2336874","article-title":"Stochastic petri net modeling, simulation and analysis of public bicycle sharing systems","volume":"12","author":"Labadi","year":"2015","journal-title":"IEEE Trans. Autom. Sci. Eng."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/551\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:11:05Z","timestamp":1760159465000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/2\/551"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,14]]},"references-count":46,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["s21020551"],"URL":"https:\/\/doi.org\/10.3390\/s21020551","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,14]]}}}