{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:43:49Z","timestamp":1760168629366,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T00:00:00Z","timestamp":1630972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of China","award":["62071033, 61671051 and U1834210"],"award-info":[{"award-number":["62071033, 61671051 and U1834210"]}]},{"name":"he Self-developed project of State Grid Energy Research Institute Co., Ltd","award":["SGNY202009014"],"award-info":[{"award-number":["SGNY202009014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This article investigates a relay-assisted wireless powered communication network (WPCN), where the access point (AP) inspires the auxiliary nodes to participate together in charging the sensor, and then the sensor uses its harvested energy to send status update packets to the AP. An incentive mechanism is designed to overcome the selfishness of the auxiliary node. In order to further improve the system performance, we establish a Stackelberg game to model the efficient cooperation between the AP\u2013sensor pair and auxiliary node. Specifically, we formulate two utility functions for the AP\u2013sensor pair and the auxiliary node, and then formulate two maximization problems respectively. As the former problem is non-convex, we transform it into a convex problem by introducing an extra slack variable, and then by using the Lagrangian method, we obtain the optimal solution with closed-form expressions. Numerical experiments show that the larger the transmit power of the AP, the smaller the age of information (AoI) of the AP\u2013sensor pair and the less the influence of the location of the auxiliary node on AoI. In addition, when the distance between the AP and the sensor node exceeds a certain threshold, employing the relay can achieve better AoI performance than non-relaying systems.<\/jats:p>","DOI":"10.3390\/e23091177","type":"journal-article","created":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T10:24:25Z","timestamp":1631010265000},"page":"1177","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Age-Aware Utility Maximization in Relay-Assisted Wireless Powered Communication Networks"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1033-4173","authenticated-orcid":false,"given":"Ning","family":"Luan","sequence":"first","affiliation":[{"name":"School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Beijing Key Laboratory of Traffic Data Analysis and Mining, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9364-0207","authenticated-orcid":false,"given":"Ke","family":"Xiong","sequence":"additional","affiliation":[{"name":"School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Beijing Key Laboratory of Traffic Data Analysis and Mining, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Frontiers Science Center for Smart High-Speed Railway System, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhifei","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haina","family":"Zheng","sequence":"additional","affiliation":[{"name":"School of Computer and Information Technology, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Beijing Key Laboratory of Traffic Data Analysis and Mining, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Grid Energy Research Institute Co., Ltd., Beijing 102209, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0658-6079","authenticated-orcid":false,"given":"Pingyi","family":"Fan","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering, Tsinghua University, Beijing 100084, China"},{"name":"Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gang","family":"Qu","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Maryland at College Park, College Park, MD 20742, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1109\/MWC.2019.1800020","article-title":"Narrowband IoT: A survey on downlink and uplink perspectives","volume":"26","author":"Feltrin","year":"2019","journal-title":"IEEE Wirel. 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