{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,19]],"date-time":"2026-02-19T03:20:13Z","timestamp":1771471213761,"version":"3.50.1"},"reference-count":41,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T00:00:00Z","timestamp":1758153600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Special Research Funding from Wuxi Taihu University","award":["2025THQD059"],"award-info":[{"award-number":["2025THQD059"]}]},{"name":"Special Research Funding from Wuxi Taihu University","award":["62371119"],"award-info":[{"award-number":["62371119"]}]},{"name":"Special Research Funding from Wuxi Taihu University","award":["62301266"],"award-info":[{"award-number":["62301266"]}]},{"name":"Special Research Funding from Wuxi Taihu University","award":["2023r014"],"award-info":[{"award-number":["2023r014"]}]},{"name":"National Natural Science Foundation of China","award":["2025THQD059"],"award-info":[{"award-number":["2025THQD059"]}]},{"name":"National Natural Science Foundation of China","award":["62371119"],"award-info":[{"award-number":["62371119"]}]},{"name":"National Natural Science Foundation of China","award":["62301266"],"award-info":[{"award-number":["62301266"]}]},{"name":"National Natural Science Foundation of China","award":["2023r014"],"award-info":[{"award-number":["2023r014"]}]},{"name":"Zhi Shan Young Scholar Program of Southeast University","award":["2025THQD059"],"award-info":[{"award-number":["2025THQD059"]}]},{"name":"Zhi Shan Young Scholar Program of Southeast University","award":["62371119"],"award-info":[{"award-number":["62371119"]}]},{"name":"Zhi Shan Young Scholar Program of Southeast University","award":["62301266"],"award-info":[{"award-number":["62301266"]}]},{"name":"Zhi Shan Young Scholar Program of Southeast University","award":["2023r014"],"award-info":[{"award-number":["2023r014"]}]},{"DOI":"10.13039\/501100013156","name":"Startup Foundation for Introducing Talent of NUIST","doi-asserted-by":"publisher","award":["2025THQD059"],"award-info":[{"award-number":["2025THQD059"]}],"id":[{"id":"10.13039\/501100013156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013156","name":"Startup Foundation for Introducing Talent of NUIST","doi-asserted-by":"publisher","award":["62371119"],"award-info":[{"award-number":["62371119"]}],"id":[{"id":"10.13039\/501100013156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013156","name":"Startup Foundation for Introducing Talent of NUIST","doi-asserted-by":"publisher","award":["62301266"],"award-info":[{"award-number":["62301266"]}],"id":[{"id":"10.13039\/501100013156","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100013156","name":"Startup Foundation for Introducing Talent of NUIST","doi-asserted-by":"publisher","award":["2023r014"],"award-info":[{"award-number":["2023r014"]}],"id":[{"id":"10.13039\/501100013156","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We consider that the source sends packets to the receiver through a Ber\/Geo\/1\/2 queue modeled status updating system, where the transmitted packets are subject to potential eavesdropping. Time is discretized into identical time slots. This paper studies the tradeoffs between the information freshness and transmission security of a system, where freshness is characterized by the age of information (AoI) metric and transmission security is represented by the proportion of obtained insecure packets over a long period of time. We assume that in a time slot, the source generates a new packet with probability p, and a packet arrives at the receiver with probability \u03b3d. With probability \u03b3E, a transmitted packet is eavesdropped. At the receiver, AoI is defined as the elapsed time since the generation instant of the latest obtained packet. A packet is defined to be insecure if it is obtained by the eavesdropper earlier than the receiver. To control the proportion of insecure packets obtained in the receiver, we propose using the probabilistic deletion\/retaining scheme. More specifically, when a packet is eavesdropped before arriving at the receiver, this packet is deleted with probability \u03b4 or retained with probability 1\u2212\u03b4. Under this transmission policy, we derive the system\u2019s average AoI which we call the average \u03b4\u2212secure AoI, and investigate its relations with the insecure packet proportion, which is denoted as \u03b7(\u03b4). The obtained formulas are then calculated in three special cases, including \u03b3E=0, \u03b3E=1, and \u03b4=1. We explain that these cases correspond to the average AoI of a basic status updating system with Ber\/Geo\/1\/2 queue, packet with random geometric deadline in service process, and average age of secure information (AoSI), respectively. Numerical simulations of obtained results are provided. In particular, the tradeoffs between average \u03b4\u2212secure AoI and \u03b7(\u03b4) are analyzed in detail. We demonstrate that depending on the value of the eavesdropping probability \u03b3E, average \u03b4\u2212secure AoI varies in different trends with \u03b7(\u03b4), and in most cases the average \u03b4\u2212secure AoI and \u03b7(\u03b4) can be minimized simultaneously.<\/jats:p>","DOI":"10.3390\/e27090972","type":"journal-article","created":{"date-parts":[[2025,9,18]],"date-time":"2025-09-18T12:54:26Z","timestamp":1758200066000},"page":"972","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Timely Updating on Ber\/Geo\/1\/2 Queue Modeled Status Updating System with Eavesdropper"],"prefix":"10.3390","volume":"27","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0962-2063","authenticated-orcid":false,"given":"Jixiang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of IoT Engineering, Wuxi Taihu University, Wuxi 214063, China"},{"name":"Provincial Key Laboratory of Intelligent Internet of Things Technology and Applications, Wuxi Taihu University, Wuxi 214063, China"},{"name":"School of Information Science and Engineering, Southeast University, Nanjing 210096, China"}]},{"given":"Han","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Southeast University, Nanjing 210096, China"}]},{"given":"Anqi","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of IoT Engineering, Wuxi Taihu University, Wuxi 214063, China"},{"name":"Provincial Key Laboratory of Intelligent Internet of Things Technology and Applications, Wuxi Taihu University, Wuxi 214063, China"}]},{"given":"Daming","family":"Cao","sequence":"additional","affiliation":[{"name":"School of Electrical and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3191-6903","authenticated-orcid":false,"given":"Yinfei","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Southeast University, Nanjing 210096, China"}]},{"given":"Chengyu","family":"Lin","sequence":"additional","affiliation":[{"name":"School of IoT Engineering, Wuxi Taihu University, Wuxi 214063, China"},{"name":"Provincial Key Laboratory of Intelligent Internet of Things Technology and Applications, Wuxi Taihu University, Wuxi 214063, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kaul, S., Gruteser, M., Rai, V., and Kenney, J. (2011, January 27\u201330). Minimizing age of information in vehicular networks. Proceedings of the 8th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECOM), Salt Lake City, UT, USA.","DOI":"10.1109\/SAHCN.2011.5984917"},{"key":"ref_2","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 IEEE International Conference on Computer Communications (INFOCOM), Orlando, FL, USA.","DOI":"10.1109\/INFCOM.2012.6195689"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kaul, S.K., Yates, R.D., and Gruteser, M. (2012, January 21\u201323). Status updates through queues. Proceedings of the 46th Annual Conference on Information Sciences and Systems, Princeton, NJ, USA.","DOI":"10.1109\/CISS.2012.6310931"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sun, Y., Uysal-Biyikoglu, E., Yates, R., Koksal, C.E., and Shroff, N.B. (2016, January 10\u201314). Update or wait: How to keep your data fresh. Proceedings of the 35th Annual IEEE International Conference on Computer Communications, San Francisco, CA, USA.","DOI":"10.1109\/INFOCOM.2016.7524524"},{"key":"ref_5","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_6","doi-asserted-by":"crossref","first-page":"6419","DOI":"10.1109\/TIT.2018.2818739","article-title":"On the Age of Information with Packet Deadlines","volume":"64","author":"Kam","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Inoue, Y. (2018, January 17\u201322). Analysis of the Age of Information with Packet Deadline and Infinite Buffer Capacity. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Vail, CO, USA.","DOI":"10.1109\/ISIT.2018.8437853"},{"key":"ref_8","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_9","doi-asserted-by":"crossref","first-page":"1807","DOI":"10.1109\/TIT.2018.2871079","article-title":"The Age of Information: Real-Time Status Updating by Multiple Sources","volume":"65","author":"Yates","year":"2019","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Pappas, N., Gunnarsson, J., Kratz, L., Kountouris, M., and Angelakis, V. (2015, January 8\u201312). Age of information of multiple sources with queue management. Proceedings of the IEEE International Conference on Communications (ICC), London, UK.","DOI":"10.1109\/ICC.2015.7249268"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1109\/JCN.2019.000039","article-title":"Age of information performance of multiaccess strategies with packet management","volume":"21","author":"Kosta","year":"2019","journal-title":"J. Commun. Netw."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"7297","DOI":"10.1109\/TCOMM.2021.3106347","article-title":"The Multi-Source Probabilistically Preemptive M\/PH\/1\/1 Queue with Packet Errors","volume":"69","author":"Dogan","year":"2021","journal-title":"IEEE Trans. Commun."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1109\/TIT.2015.2511791","article-title":"Effect of Message Transmission Path Diversity on Status Age","volume":"62","author":"Kam","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1109\/TNET.2024.3474052","article-title":"Age of Information for Multiple-Source Multiple-Server Networks","volume":"33","author":"Javani","year":"2025","journal-title":"IEEE Trans. Netw."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1109\/TCOMM.2024.3424223","article-title":"Improving Information Freshness via Multi-Sensor Parallel Status Updating","volume":"73","author":"Chen","year":"2025","journal-title":"IEEE Trans. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1109\/TMC.2024.3471391","article-title":"Monitoring Correlated Sources: AoI-Based Scheduling is Nearly Optimal","volume":"24","author":"Ramakanth","year":"2025","journal-title":"IEEE. Trans. Mob. Comput."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2639","DOI":"10.1109\/TCOMM.2024.3351362","article-title":"Age-Aware Dynamic Frame Slotted ALOHA for Machine-Type Communications","volume":"72","author":"Moradian","year":"2024","journal-title":"IEEE Trans. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1109\/JSAC.2023.3280986","article-title":"Age of Information in Downlink Systems: Broadcast or Unicast Transmission?","volume":"41","author":"Tang","year":"2023","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4707","DOI":"10.1109\/TCOMM.2023.3281486","article-title":"Age of Information in Reservation Multi-Access Networks with Stochastic Arrivals: Analysis and Optimization","volume":"71","author":"Wang","year":"2023","journal-title":"IEEE Trans. Commun."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3905","DOI":"10.1109\/TCOMM.2023.3274143","article-title":"Scheduling Policies for AoI Minimization with Timely Throughput Constraints","volume":"71","author":"Fountoulakis","year":"2023","journal-title":"IEEE Trans. Commun."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1109\/JSAC.2021.3065038","article-title":"Age of Information-Based Wireless Powered Communication Networks with Selfish Charging Nodes","volume":"39","author":"Zheng","year":"2021","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"5185","DOI":"10.1109\/TIT.2022.3167618","article-title":"Precoding and Scheduling for AoI Minimization in MIMO Broadcast Channels","volume":"68","author":"Feng","year":"2022","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","unstructured":"Tripathi, V., Talak, R., and Modiano, E. (2019). Age of Information for Discrete Time Queues. arXiv."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kosta, A., Pappas, N., Ephremides, A., and Angelakis, V. (2020, January 7\u201311). Non-linear Age of Information in a Discrete Time Queue: Stationary Distribution and Average Performance Analysis. Proceedings of the IEEE International Conference on Communications (ICC), Dublin, Ireland.","DOI":"10.1109\/ICC40277.2020.9148775"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1352","DOI":"10.1109\/JSAC.2021.3065045","article-title":"The Age of Information in a Discrete Time Queue: Stationary Distribution and Non-Linear Age Mean Analysis","volume":"39","author":"Kosta","year":"2021","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"14531","DOI":"10.1109\/JIOT.2021.3053768","article-title":"Discrete-Time Queueing Model of Age of Information with Multiple Information Sources","volume":"8","author":"Akar","year":"2021","journal-title":"IEEE Internet Things J."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Xu, Y. (2021, January 17\u201321). On Age of Information for Discrete Time Status Updating System with Ber\/G\/1\/1 Queues. Proceedings of the IEEE Information Theory Workshop (ITW), Kanazawa, Japan.","DOI":"10.1109\/ITW48936.2021.9611393"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Xu, Y. (2022, January 1\u20139). On Age of Information for Discrete Time Status Updating System with Infinite Size. Proceedings of the IEEE Information Theory Workshop (ITW), Mumbai, India.","DOI":"10.1109\/ITW54588.2022.9965796"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Xu, Y. (2022). Age Analysis of Status Updating System with Probabilistic Packet Preemption. Entropy, 24.","DOI":"10.20944\/preprints202205.0010.v1"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"20099","DOI":"10.1109\/JIOT.2024.3368625","article-title":"Discrete Age of Information for Bufferless System with Multiple Prioritized Sources","volume":"11","author":"Zhang","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"11357","DOI":"10.1109\/TMC.2024.3396993","article-title":"Can We Realize Data Freshness Optimization for Privacy Preserving-Mobile Crowdsensing with Artificial Noise?","volume":"23","author":"Yang","year":"2024","journal-title":"IEEE. Trans. Mob. Comput."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3276","DOI":"10.1109\/LWC.2024.3406913","article-title":"Reinforcement Learning-Based Sensing Decision for Data Freshness in Blockchain-Empowered Wireless Networks","volume":"13","author":"Kim","year":"2024","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Costa, M., and Sagduyu, Y.E. (2024, January 9\u201313). Timely NextG Communications with Decoy Assistance against Deep Learning-based Jamming. Proceedings of the IEEE International Conference on Communications Workshops (ICC Workshops), Denver, CO, USA.","DOI":"10.1109\/ICCWorkshops59551.2024.10615460"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"17341","DOI":"10.1109\/JIOT.2024.3357123","article-title":"Timeliness and Secrecy-Aware Uplink Data Aggregation for Large-Scale UAV-IoT Networks","volume":"11","author":"Ma","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"11024","DOI":"10.1109\/JIOT.2023.3243038","article-title":"Permutation-Based Short-Packet Transmissions Improve Secure URLLCs in the Internet of Things","volume":"10","author":"Yang","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Yang, Y. (2023, January 10\u201313). Secure and Timely Status Updates in the IoT using Short-Packet Permutation-Based Transmissions. Proceedings of the IEEE 98th Vehicular Technology Conference (VTC2023-Fall), Hong Kong, China.","DOI":"10.1109\/VTC2023-Fall60731.2023.10333568"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, Q., Chen, H., Mohapatra, P., and Pappas, N. (2024, January 20). Secure Status Updates under Eavesdropping: Age of Information-based Secrecy Metrics. Proceedings of the IEEE Conference on Computer Communications Workshops (INFOCOM WKSHPS), Vancouver, BC, Canada.","DOI":"10.1109\/INFOCOMWKSHPS61880.2024.10620867"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.1002\/j.1538-7305.1975.tb02040.x","article-title":"The wiretap channel","volume":"54","author":"Wyner","year":"1975","journal-title":"Bell Syst. Tech. J."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"3232","DOI":"10.1109\/LWC.2024.3462717","article-title":"Achieving Secure and Fresh Information Updates via Short-Packet Communications","volume":"13","author":"Xu","year":"2024","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"5455","DOI":"10.1109\/JIOT.2023.3307351","article-title":"AoI-Based Transmission Scheduling for Cyber Physical Systems Over Fading Channel Against Eavesdropping","volume":"11","author":"Yuan","year":"2024","journal-title":"IEEE Internet Things J."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Zhang, J., Xu, H., Zheng, A., Cao, D., Xu, Y., and Lin, C. (2025). Transmitting Status Updates on Infinite Capacity Systems with Eavesdropper: Freshness Advantage of Legitimate Receiver. Entropy, 27.","DOI":"10.3390\/e27060571"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/9\/972\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:48:07Z","timestamp":1760035687000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/9\/972"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,18]]},"references-count":41,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["e27090972"],"URL":"https:\/\/doi.org\/10.3390\/e27090972","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,18]]}}}