{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T03:04:45Z","timestamp":1769310285791,"version":"3.49.0"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T00:00:00Z","timestamp":1739923200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T00:00:00Z","timestamp":1739923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"High level cultivation projects of Minnan Normal University","award":["No.MSGJB2021007"],"award-info":[{"award-number":["No.MSGJB2021007"]}]},{"name":"Fujian Province Undergraduate Education and Teaching Research Project","award":["No.FBJY20230170"],"award-info":[{"award-number":["No.FBJY20230170"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["No.62372488"],"award-info":[{"award-number":["No.62372488"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Peer-to-Peer Netw. Appl."],"published-print":{"date-parts":[[2025,5]]},"DOI":"10.1007\/s12083-025-01926-9","type":"journal-article","created":{"date-parts":[[2025,2,19]],"date-time":"2025-02-19T10:14:12Z","timestamp":1739960052000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Computation offloading and pricing strategy for heterogeneous multicell network with mobile edge computing"],"prefix":"10.1007","volume":"18","author":[{"given":"Minli","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yifeng","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingmin","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liwei","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wenjie","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,19]]},"reference":[{"issue":"5","key":"1926_CR1","doi-asserted-by":"publisher","first-page":"637","DOI":"10.1109\/JIOT.2016.2579198","volume":"3","author":"W Shi","year":"2016","unstructured":"Shi W, Cao J, Zhang Q, Li Y, Xu L (2016) Edge computing: vision and challenges. IEEE Internet of Things J 3(5):637\u2013646","journal-title":"IEEE Internet of Things J"},{"key":"1926_CR2","doi-asserted-by":"crossref","unstructured":"Pang S, He X, Yu S, Wang M, Qiao S, Gui H, Qi Y (2023) A stackelberg game scheme for pricing and task offloading based on idle node-assisted edge computational model. Simul Model Pract Theory 124:102725","DOI":"10.1016\/j.simpat.2023.102725"},{"issue":"5","key":"1926_CR3","doi-asserted-by":"publisher","first-page":"2500","DOI":"10.1109\/TII.2018.2874693","volume":"15","author":"A Rahman","year":"2018","unstructured":"Rahman A, Jin J, Cricenti AL, Rahman A, Kulkarni A (2018) Communication-aware cloud robotic task offloading with on-demand mobility for smart factory maintenance. IEEE Trans Indust Inf 15(5):2500\u20132511","journal-title":"IEEE Trans Indust Inf"},{"issue":"3","key":"1926_CR4","doi-asserted-by":"publisher","first-page":"1628","DOI":"10.1109\/COMST.2017.2682318","volume":"19","author":"P Mach","year":"2017","unstructured":"Mach P, Becvar Z (2017) Mobile edge computing: a survey on architecture and computation offloading. IEEE Commun Survey Tutor 19(3):1628\u20131656","journal-title":"IEEE Commun Survey Tutor"},{"issue":"2","key":"1926_CR5","first-page":"1","volume":"53","author":"P Cong","year":"2020","unstructured":"Cong P, Zhou J, Li L, Cao K, Wei T, Li K (2020) A survey of hierarchical energy optimization for mobile edge computing: a perspective from end devices to the cloud. ACM Comput Survey 53(2):1\u201344","journal-title":"ACM Comput Survey"},{"key":"1926_CR6","doi-asserted-by":"crossref","unstructured":"Wang T, Mei Y, Liu X, Wang J, Dai H-N, Wang Z (2021) Edge-based auditing method for data security in resource-constrained internet of things. J Syst Arch 114:101971","DOI":"10.1016\/j.sysarc.2020.101971"},{"key":"1926_CR7","doi-asserted-by":"crossref","unstructured":"Feng C, Han P, Zhang X, Yang B, Liu Y, Guo L (2022) Computation offloading in mobile edge computing networks: a survey. J Netw Comput Appl 202:103366","DOI":"10.1016\/j.jnca.2022.103366"},{"issue":"7","key":"1926_CR8","doi-asserted-by":"publisher","first-page":"5298","DOI":"10.1109\/JIOT.2020.3033298","volume":"8","author":"Z Liao","year":"2020","unstructured":"Liao Z, Peng J, Huang J, Wang J, Wang J, Sharma PK, Ghosh U (2020) Distributed probabilistic offloading in edge computing for 6g-enabled massive internet of things. IEEE Internet of Things J 8(7):5298\u20135308","journal-title":"IEEE Internet of Things J"},{"key":"1926_CR9","doi-asserted-by":"crossref","unstructured":"Song S, Ma S, Zhu X, Li Y, Yang F, Zhai L (2023) Joint bandwidth allocation and task offloading in multi-access edge computing. Exp Syst Appl 217:119563","DOI":"10.1016\/j.eswa.2023.119563"},{"issue":"2","key":"1926_CR10","doi-asserted-by":"publisher","first-page":"668","DOI":"10.1109\/COMST.2021.3059896","volume":"23","author":"Y Xu","year":"2021","unstructured":"Xu Y, Gui G, Gacanin H, Adachi F (2021) A survey on resource allocation for 5g heterogeneous networks: current research, future trends, and challenges. IEEE Commun Survey Tutor 23(2):668\u2013695","journal-title":"IEEE Commun Survey Tutor"},{"key":"1926_CR11","doi-asserted-by":"crossref","unstructured":"Kan T-Y, Chiang Y, Wei H-Y (2018) Task offloading and resource allocation in mobile-edge computing system. In: 2018 27th Wireless and Optical Communication Conference, pp 1\u20134. IEEE","DOI":"10.1109\/WOCC.2018.8372737"},{"issue":"1","key":"1926_CR12","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1109\/MVT.2018.2882873","volume":"14","author":"Z Ning","year":"2018","unstructured":"Ning Z, Wang X, Huang J (2018) Mobile edge computing-enabled 5g vehicular networks: toward the integration of communication and computing. IEEE Veh Technol Magaz 14(1):54\u201361","journal-title":"IEEE Veh Technol Magaz"},{"key":"1926_CR13","doi-asserted-by":"crossref","unstructured":"Peng Q, Xia Y, Feng Z, Lee J, Wu C, Luo X, Zheng W, Pang S, Liu H, Qin Y (2019) Mobility-aware and migration-enabled online edge user allocation in mobile edge computing. In: 2019 IEEE International Conference on Web Services, pp 91\u201398. IEEE","DOI":"10.1109\/ICWS.2019.00026"},{"issue":"1","key":"1926_CR14","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1049\/iet-com.2014.0329","volume":"9","author":"Z Liu","year":"2015","unstructured":"Liu Z, Hao L, Xia Y, Guan X (2015) Price bargaining based on the stackelberg game in two-tier orthogonal frequency division multiple access femtocell networks. IET Commun 9(1):133\u2013145","journal-title":"IET Commun"},{"issue":"1","key":"1926_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13638-016-0791-1","volume":"2017","author":"Y Qi","year":"2017","unstructured":"Qi Y, Wang H, Li B, Chen F (2017) A refunding strategy: opportunistic user association with congestion-based pricing in macro-femto hybrid network. EURASIP J Wireless Commun Netw 2017(1):1\u201312","journal-title":"EURASIP J Wireless Commun Netw"},{"issue":"6","key":"1926_CR16","doi-asserted-by":"publisher","first-page":"6699","DOI":"10.1109\/TVT.2020.2986236","volume":"69","author":"Z Liu","year":"2020","unstructured":"Liu Z, Wang W, Chan KY, Ma K, Guan X (2020) Rate maximization for hybrid access femtocell networks with outage constraints based on pricing incentive mechanism. IEEE Trans Veh Technol 69(6):6699\u20136708","journal-title":"IEEE Trans Veh Technol"},{"key":"1926_CR17","doi-asserted-by":"crossref","unstructured":"Pourkabirian A, Dehghan Takht\u00a0Fooladi M, Zeinali\u00a0Khosraghi E, Rahmani AM (2019) An evolutionary game-theoretic approach for base station allocation in wireless femtocell networks. Wireless Person Commun 107(1):217\u2013242","DOI":"10.1007\/s11277-019-06251-y"},{"key":"1926_CR18","doi-asserted-by":"crossref","unstructured":"Pourkabirian A, Dehghan Takht\u00a0Fooladi M, Zeinali E, Rahmani AM (2018) Dynamic resource allocation for ofdma femtocell networks: a game-theoretic approach. Telecommun Syst 69(1):51\u201359","DOI":"10.1007\/s11235-018-0420-x"},{"key":"1926_CR19","doi-asserted-by":"crossref","unstructured":"Guo J, Zhang H, Yang L, Ji H, Li X (2017) Decentralized computation offloading in mobile edge computing empowered small-cell networks. In: 2017 IEEE Globecom Workshops, pp 1\u20136 . IEEE","DOI":"10.1109\/GLOCOMW.2017.8269049"},{"issue":"2","key":"1926_CR20","first-page":"89","volume":"1","author":"S Sardellitti","year":"2015","unstructured":"Sardellitti S, Scutari G, Barbarossa S (2015) Joint optimization of radio and computational resources for multicell mobile-edge computing. IEEE Trans Signal and Inf Process over Netw 1(2):89\u2013103","journal-title":"IEEE Trans Signal and Inf Process over Netw"},{"issue":"2","key":"1926_CR21","doi-asserted-by":"publisher","first-page":"200","DOI":"10.23919\/JCC.2021.02.013","volume":"18","author":"C Liu","year":"2021","unstructured":"Liu C, Zhang H, Ji H, Li X (2021) Mec-assisted flexible transcoding strategy for adaptive bitrate video streaming in small cell networks. China Commun 18(2):200\u2013214","journal-title":"China Commun"},{"key":"1926_CR22","doi-asserted-by":"publisher","first-page":"396","DOI":"10.1109\/JSAC.2020.3020680","volume":"39","author":"Z Zhou","year":"2021","unstructured":"Zhou Z, Wang Z, Yu H, Liao H, Mumtaz S, Oliveira L, Frascolla V (2021) Learning-based urllc-aware task offloading for internet of health things. IEEE J Select Areas in Commun 39:396\u2013410","journal-title":"IEEE J Select Areas in Commun"},{"issue":"8","key":"1926_CR23","doi-asserted-by":"publisher","first-page":"4924","DOI":"10.1109\/TWC.2017.2703901","volume":"16","author":"C Wang","year":"2017","unstructured":"Wang C, Liang C, Yu FR, Chen Q, Tang L (2017) Computation offloading and resource allocation in wireless cellular networks with mobile edge computing. IEEE Trans Wireless Commun 16(8):4924\u20134938","journal-title":"IEEE Trans Wireless Commun"},{"issue":"2","key":"1926_CR24","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1109\/TMC.2019.2945956","volume":"20","author":"L Chen","year":"2021","unstructured":"Chen L, Shen C, Zhou P, Xu J (2021) Collaborative service placement for edge computing in dense small cell networks. IEEE Trans Mobile Comput 20(2):377\u2013390","journal-title":"IEEE Trans Mobile Comput"},{"key":"1926_CR25","doi-asserted-by":"publisher","first-page":"16444","DOI":"10.1109\/ACCESS.2018.2883692","volume":"7","author":"Q-V Pham","year":"2019","unstructured":"Pham Q-V, Le LB, Chung S-H, Hwang W-J (2019) Mobile edge computing with wireless backhaul: joint task offloading and resource allocation. IEEE Access 7:16444\u201316459","journal-title":"IEEE Access"},{"key":"1926_CR26","doi-asserted-by":"publisher","first-page":"5896","DOI":"10.1109\/ACCESS.2016.2597169","volume":"4","author":"K Zhang","year":"2016","unstructured":"Zhang K, Mao Y, Leng S, Zhao Q, Li L, Peng X, Pan L, Maharjan S, Zhang Y (2016) Energy-efficient offloading for mobile edge computing in 5g heterogeneous networks. IEEE Access 4:5896\u20135907","journal-title":"IEEE Access"},{"issue":"1","key":"1926_CR27","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/j.dcan.2018.10.003","volume":"5","author":"L Huang","year":"2019","unstructured":"Huang L, Feng X, Zhang C, Qian L, Wu Y (2019) Deep reinforcement learning-based joint task offloading and bandwidth allocation for multi-user mobile edge computing. Digital Commun Netw 5(1):10\u201317","journal-title":"Digital Commun Netw"},{"issue":"4","key":"1926_CR28","doi-asserted-by":"publisher","first-page":"2483","DOI":"10.1109\/JIOT.2020.3033285","volume":"8","author":"G Yang","year":"2020","unstructured":"Yang G, Hou L, He X, He D, Chan S, Guizani M (2020) Offloading time optimization via markov decision process in mobile-edge computing. IEEE Internet of Things J 8(4):2483\u20132493","journal-title":"IEEE Internet of Things J"},{"issue":"1","key":"1926_CR29","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1109\/TII.2022.3158974","volume":"19","author":"X Dai","year":"2022","unstructured":"Dai X, Xiao Z, Jiang H, Alazab M, Lui JC, Dustdar S, Liu J (2022) Task co-offloading for d2d-assisted mobile edge computing in industrial internet of things. IEEE Trans Indust Inf 19(1):480\u2013490","journal-title":"IEEE Trans Indust Inf"},{"issue":"7","key":"1926_CR30","doi-asserted-by":"publisher","first-page":"1728","DOI":"10.1109\/LCOMM.2024.3399407","volume":"28","author":"Y Zuo","year":"2024","unstructured":"Zuo Y, Guo J, Sheng B, Dai C, Xiao F, Jin S (2024) Fluid antenna for mobile edge computing. IEEE Commun Lett 28(7):1728\u20131732","journal-title":"IEEE Commun Lett"},{"issue":"12","key":"1926_CR31","doi-asserted-by":"publisher","first-page":"12176","DOI":"10.1109\/TMC.2024.3407792","volume":"23","author":"Y Zuo","year":"2024","unstructured":"Zuo Y, Gui L, Cui K, Guo J, Xiao F, Jin S (2024) Mobile blockchain-enabled secure and efficient information management for indoor positioning with federated learning. IEEE Trans Mobile Comput 23(12):12176\u201312194","journal-title":"IEEE Trans Mobile Comput"},{"key":"1926_CR32","doi-asserted-by":"crossref","unstructured":"Fragkos G, Kemp N, Tsiropoulou EE, Papavassiliou S (2020) Artificial intelligence empowered uavs data offloading in mobile edge computing. In: 2020 IEEE International Conference on Communications (ICC), pp 1\u20137","DOI":"10.1109\/ICC40277.2020.9149115"},{"issue":"4","key":"1926_CR33","doi-asserted-by":"publisher","first-page":"700","DOI":"10.1109\/LWC.2020.3039863","volume":"10","author":"S Chen","year":"2020","unstructured":"Chen S, Li L, Chen Z, Li S (2020) Dynamic pricing for smart mobile edge computing: a reinforcement learning approach. IEEE Wireless Commun Lett 10(4):700\u2013704","journal-title":"IEEE Wireless Commun Lett"},{"issue":"1","key":"1926_CR34","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1109\/TNSE.2021.3068340","volume":"9","author":"J Du","year":"2021","unstructured":"Du J, Cheng W, Lu G, Cao H, Chu X, Zhang Z, Wang J (2021) Resource pricing and allocation in mec enabled blockchain systems: an a3c deep reinforcement learning approach. IEEE Trans Netw Sci Eng 9(1):33\u201344","journal-title":"IEEE Trans Netw Sci Eng"},{"issue":"17","key":"1926_CR35","doi-asserted-by":"publisher","first-page":"15969","DOI":"10.1109\/JIOT.2022.3150955","volume":"9","author":"Y Li","year":"2022","unstructured":"Li Y, Yang B, Wu H, Han Q, Chen C, Guan X (2022) Joint offloading decision and resource allocation for vehicular fog-edge computing networks: a contract-stackelberg approach. IEEE Internet of Things J 9(17):15969\u201315982","journal-title":"IEEE Internet of Things J"},{"key":"1926_CR36","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1016\/j.future.2021.08.029","volume":"127","author":"X Huang","year":"2022","unstructured":"Huang X, Gong S, Yang J, Zhang W, Yang L, Yeo CK (2022) Hybrid market-based resources allocation in mobile edge computing systems under stochastic information. Fut Gener Comput Syst 127:80\u201391","journal-title":"Fut Gener Comput Syst"},{"key":"1926_CR37","doi-asserted-by":"crossref","unstructured":"Zheng Y, Zou L, Zhang W, Yang J, Yang L, Lin Z (2023) Contract-based cooperative computation and communication resources sharing in mobile edge computing. J Grid Comput 21(1):14","DOI":"10.1007\/s10723-023-09649-y"},{"issue":"4","key":"1926_CR38","doi-asserted-by":"publisher","first-page":"2494","DOI":"10.1109\/COMST.2023.3315374","volume":"25","author":"Y Zuo","year":"2023","unstructured":"Zuo Y, Guo J, Gao N, Zhu Y, Jin S, Li X (2023) A survey of blockchain and artificial intelligence for 6g wireless communications. IEEE Commun Survey Tutor 25(4):2494\u20132528","journal-title":"IEEE Commun Survey Tutor"},{"key":"1926_CR39","doi-asserted-by":"crossref","unstructured":"Tang C, Wu H (2021) Optimal computational resource pricing in vehicular edge computing: a stackelberg game approach. J Syst Arch 121:102331","DOI":"10.1016\/j.sysarc.2021.102331"},{"issue":"17","key":"1926_CR40","doi-asserted-by":"publisher","first-page":"16510","DOI":"10.1109\/JIOT.2022.3153089","volume":"9","author":"H Zhou","year":"2022","unstructured":"Zhou H, Wang Z, Cheng N, Zeng D, Fan P (2022) Stackelberg-game-based computation offloading method in cloud-edge computing networks. IEEE Internet of Things J 9(17):16510\u201316520","journal-title":"IEEE Internet of Things J"}],"container-title":["Peer-to-Peer Networking and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12083-025-01926-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12083-025-01926-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12083-025-01926-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T02:32:36Z","timestamp":1746844356000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12083-025-01926-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,19]]},"references-count":40,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["1926"],"URL":"https:\/\/doi.org\/10.1007\/s12083-025-01926-9","relation":{},"ISSN":["1936-6442","1936-6450"],"issn-type":[{"value":"1936-6442","type":"print"},{"value":"1936-6450","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,19]]},"assertion":[{"value":"8 May 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for publication"}}],"article-number":"102"}}