{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:25:54Z","timestamp":1761294354979,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T00:00:00Z","timestamp":1629072000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>With the rapid development and wide application of the Internet of Things (IoT), how to provide timely and fresh information for strategic analysis and decision-making has become a key issue. Recent studies have shown that preemption strategies are of great importance to the improvement of information freshness. In view of this, we focus on the multi-source preemptive queuing model and investigate how to control the generation rate of each source to achieve the optimal overall information freshness. Specifically, we consider two typical preemption strategies: self-preemption strategy and global-preemption strategy. Noting that the urgency requirements of the systems on the data of each source are different, we propose the weighted average age of information (AoI) to characterize the overall information freshness of the system. For the self-preemption strategy, we prove that the optimal generation rate allocation is a convex problem and present an efficient algorithm to find the optimal solution. Additionally, we also derive a closed-form approximate optimal solution under light load cases to meet the demands for rapid deployment. For the global-preemption strategy, we directly derive the closed-form optimal solution of the corresponding problem. By comparing the optimized weighted average AoIs, the performance achieved by the global-preemption system was better than that achieved by the self-preemption system in terms of the overall timeliness. The numerical analysis verified the correctness of the theoretical analysis and that the proposed approximate solution had high accuracy not only under light load cases but also under other cases.<\/jats:p>","DOI":"10.3390\/e23081055","type":"journal-article","created":{"date-parts":[[2021,8,16]],"date-time":"2021-08-16T21:27:45Z","timestamp":1629149265000},"page":"1055","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Internet of Things: The Optimal Generation Rates under Preemption Strategy in a Multi-Source Queuing System"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3676-7302","authenticated-orcid":false,"given":"Tianci","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5055-9756","authenticated-orcid":false,"given":"Shutong","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2289-5621","authenticated-orcid":false,"given":"Zhengchuan","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Microelectronics and Communication Engineering, Chongqing University, Chongqing 400044, China"},{"name":"National Mobile Communications Research Laboratory, Southeast University, Nanjing 210000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"4598","DOI":"10.1109\/JIOT.2019.2942271","article-title":"Toward Secure and Provable Authentication for Internet of Things: Realizing Industry 4.0","volume":"7","author":"Garg","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Pattar, S., Sandhya, C.R., Vala, D., Buyya, R., Venugopal, K.R., Iyengar, S.S., and Patnaik, L.M. (2018, January 21\u201323). Ontology based Service Discovery for Intelligent Transport Systems using Internet of Things. Proceedings of the 2018 Fourteenth International Conference on Information Processing (ICINPRO), Bangalore, India.","DOI":"10.1109\/ICINPRO43533.2018.9096694"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Barman, B.K., Yadav, S.N., Kumar, S., and Gope, S. (2018, January 1\u20132). IOT Based Smart Energy Meter for Efficient Energy Utilization in Smart Grid. Proceedings of the 2018 2nd International Conference on Power, Energy and Environment: Towards Smart Technology (ICEPE), Shillong, India.","DOI":"10.1109\/EPETSG.2018.8658501"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zualkernan, I.A., Aloul, F., Qasimi, S.A., AlShamsi, A., Marashda, M.A., and Ahli, A. (2018, January 6\u20137). DigiMesh-based Social Internet of Vehicles (SIoV) for Driver Safety. Proceedings of the 2018 International Symposium in Sensing and Instrumentation in IoT Era (ISSI), Shanghai, China.","DOI":"10.1109\/ISSI.2018.8538167"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"510","DOI":"10.1109\/JSAC.2016.2525418","article-title":"Internet of Things in the 5G Era: Enablers, Architecture, and Business Models","volume":"34","author":"Palattella","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kaul, S., Yates, R., and Gruteser, M. (2012, January 25\u201330). Real-time status: How often should one update?. Proceedings of the 2012 Proceedings INFOCOM, Orlando, FL, USA.","DOI":"10.1109\/INFCOM.2012.6195689"},{"key":"ref_7","first-page":"1365","article-title":"Age of Information: A New Metric for Information Freshness","volume":"5","author":"Sun","year":"2019","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Inoue, Y., Masuyama, H., Takine, T., and Tanaka, T. (2017, January 25\u201330). The stationary distribution of the age of information in FCFS single-server queues. Proceedings of the 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany.","DOI":"10.1109\/ISIT.2017.8006592"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"8305","DOI":"10.1109\/TIT.2019.2938171","article-title":"A General Formula for the Stationary Distribution of the Age of Information and Its Application to Single-Server Queues","volume":"65","author":"Inoue","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Yates, R.D., and Kaul, S. (2012, January 1\u20136). Real-time status updating: Multiple sources. Proceedings of the 2012 IEEE International Symposium on Information Theory Proceedings, Cambridge, MA, USA.","DOI":"10.1109\/ISIT.2012.6284003"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Moltafet, M., Leinonen, M., and Codreanu, M. (2019, January 25\u201328). Closed-Form Expression for the Average Age of Information in a Multi-Source M\/G\/1 Queueing Model. Proceedings of the 2019 IEEE Information Theory Workshop (ITW), Visby, Sweden.","DOI":"10.1109\/ITW44776.2019.8989346"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1897","DOI":"10.1109\/TIT.2016.2533395","article-title":"On the Age of Information in Status Update Systems With Packet Management","volume":"62","author":"Costa","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Huang, L., and Modiano, E. (2015, January 14\u201319). Optimizing age-of-information in a multi-class queueing system. Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT), Hong Kong, China.","DOI":"10.1109\/ISIT.2015.7282742"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Najm, E., and Nasser, R. (2016, January 10\u201315). Age of information: The gamma awakening. Proceedings of the 2016 IEEE International Symposium on Information Theory (ISIT), Barcelona, Spain.","DOI":"10.1109\/ISIT.2016.7541764"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Najm, E., Yates, R., and Soljanin, E. (2017, January 25\u201330). Status updates through M\/G\/1\/1 queues with HARQ. Proceedings of the 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany.","DOI":"10.1109\/ISIT.2017.8006504"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Najm, E., and Telatar, E. (2018, January 5\u201319). Status updates in a multi-stream M\/G\/1\/1 preemptive queue. Proceedings of the IEEE INFOCOM 2018\u2014IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), Honolulu, HI, USA.","DOI":"10.1109\/INFCOMW.2018.8406928"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Farazi, S., Klein, A.G., and Richard Brown, D. (2019, January 3\u20136). Average Age of Information in Multi-Source Self-Preemptive Status Update Systems with Packet Delivery Errors. Proceedings of the 2019 53rd Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/IEEECONF44664.2019.9048914"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1109\/JIOT.2020.3012835","article-title":"AoI-Minimal Trajectory Planning and Data Collection in UAV-Assisted Wireless Powered IoT Networks","volume":"8","author":"Hu","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Sert, E., Sonmez, C., Baghaee, S., and Uysal-Biyikoglu, E. (2018, January 2\u20135). Optimizing age of information on real-life TCP\/IP connections through reinforcement learning. Proceedings of the 2018 26th Signal Processing and Communications Applications Conference (SIU).","DOI":"10.1109\/SIU.2018.8404794"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2293","DOI":"10.1109\/TCAD.2019.2948905","article-title":"Energy-Constrained Data Freshness Optimization in Self-Powered Networked Embedded Systems","volume":"39","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1109\/TCOMM.2020.3027877","article-title":"Statistical Guarantee Optimization for AoI in Single-Hop and Two-Hop FCFS Systems with Periodic Arrivals","volume":"69","author":"Champati","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Wang, Y., and Chen, W. (2020, January 7\u201310). An AoI-Optimal Scheduling Method for Wireless Transmissions with Truncated Channel Inversion. Proceedings of the ICC 2020\u20142020 IEEE International Conference on Communications (ICC), Virtual.","DOI":"10.1109\/ICC40277.2020.9149436"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"11329","DOI":"10.1109\/JIOT.2021.3051722","article-title":"Status Update in IoT Networks: Age-of-Information Violation Probability and Optimal Update Rate","volume":"8","author":"Hu","year":"2021","journal-title":"IEEE Internet Things J."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1055\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:47:10Z","timestamp":1760165230000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1055"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,16]]},"references-count":23,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23081055"],"URL":"https:\/\/doi.org\/10.3390\/e23081055","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,8,16]]}}}