{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T10:15:41Z","timestamp":1783419341276,"version":"3.54.6"},"reference-count":46,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T00:00:00Z","timestamp":1774915200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"},{"start":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T00:00:00Z","timestamp":1783382400000},"content-version":"vor","delay-in-days":98,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2023YFB2906403"],"award-info":[{"award-number":["2023YFB2906403"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. King Saud Univ. Comput. Inf. Sci."],"published-print":{"date-parts":[[2026,7]]},"DOI":"10.1007\/s44443-026-00690-x","type":"journal-article","created":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T14:13:44Z","timestamp":1774966424000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["CPN-HRL :a hierarchical deep reinforcement learning approach for priority\u2013aware task scheduling in CPN enabled by cloud\u2013edge\u2013end environments"],"prefix":"10.1007","volume":"38","author":[{"given":"Qiqiang","family":"Yue","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Le","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xu","family":"Feng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zheng","family":"Yuan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuai","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiqiang","family":"Xia","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuanyan","family":"Song","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ying","family":"Yao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yi","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,3,31]]},"reference":[{"issue":"6","key":"690_CR1","doi-asserted-by":"publisher","first-page":"2370","DOI":"10.1016\/j.jksuci.2020.11.002","volume":"34","author":"SA Alsaidy","year":"2022","unstructured":"Alsaidy SA, Abbood AD, Sahib MA (2022) Heuristic initialization of pso task scheduling algorithm in cloud computing. J King Saud Univ-Comput Inf Sci 34(6):2370\u20132382","journal-title":"J King Saud Univ-Comput Inf Sci"},{"key":"690_CR2","doi-asserted-by":"publisher","first-page":"104766","DOI":"10.1016\/j.jpdc.2023.104766","volume":"183","author":"I Behera","year":"2024","unstructured":"Behera I, Sobhanayak S (2024) Task scheduling optimization in heterogeneous cloud computing environments: A hybrid ga-gwo approach. J Parallel Distrib Comput 183:104766","journal-title":"J Parallel Distrib Comput"},{"issue":"09","key":"690_CR3","first-page":"44","volume":"35","author":"L Bo","year":"2019","unstructured":"Bo L, Zengyi L, Xuliang W, Mingchuan Y, Yunqing C (2019) A new edge computing solution based on the integration of cloud, network, and edge: Computing power network. Telecommun Sci 35(09):44\u201351","journal-title":"Telecommun Sci"},{"key":"690_CR4","doi-asserted-by":"publisher","first-page":"110185","DOI":"10.1016\/j.comnet.2024.110185","volume":"240","author":"Y Cai","year":"2024","unstructured":"Cai Y, Li W, Meng X, Zheng W, Chen C, Liang Z (2024) Adaptive contrastive learning based network latency prediction in 5g urllc scenarios. Comput Netw 240:110185","journal-title":"Comput Netw"},{"issue":"21","key":"690_CR5","doi-asserted-by":"publisher","first-page":"18579","DOI":"10.1007\/s00521-022-07477-x","volume":"34","author":"L Cheng","year":"2022","unstructured":"Cheng L, Kalapgar A, Jain A, Wang Y, Qin Y, Li Y, Liu C (2022) Cost-aware real-time job scheduling for hybrid cloud using deep reinforcement learning. Neural Comput Appl 34(21):18579\u201318593","journal-title":"Neural Comput Appl"},{"key":"690_CR6","doi-asserted-by":"crossref","unstructured":"Feng L, Xie R, Tang Q, Huang T (2024) Delay-prioritized task scheduling with load balancing in computing power networks. In: 2024 IEEE Wireless Communications and Networking Conference (WCNC), pp 1\u20136. IEEE","DOI":"10.1109\/WCNC57260.2024.10570622"},{"key":"690_CR7","doi-asserted-by":"crossref","unstructured":"Feng L, Xie R, Tang Q, Huang T, Xiong Z, Chen T, Zhang R, Tan S, Fang Z (2025) Carcs: Joint optimization of computing-aware routing and collaborative scheduling in computing power networks. IEEE Network","DOI":"10.1109\/MNET.2025.3548419"},{"issue":"16","key":"690_CR8","doi-asserted-by":"publisher","first-page":"2557","DOI":"10.3390\/electronics11162557","volume":"11","author":"S Gupta","year":"2022","unstructured":"Gupta S, Iyer S, Agarwal G, Manoharan P, Algarni AD, Aldehim G, Raahemifar K (2022) Efficient prioritization and processor selection schemes for heft algorithm: A makespan optimizer for task scheduling in cloud environment. Electronics 11(16):2557","journal-title":"Electronics"},{"key":"690_CR9","doi-asserted-by":"crossref","unstructured":"Han Y, Zhao Z, Mo J, Shu C, Min G (2019) Efficient task offloading with dependency guarantees in ultra-dense edge networks. In: 2019 IEEE Global Communications Conference (GLOBECOM), pp 1\u20136. IEEE","DOI":"10.1109\/GLOBECOM38437.2019.9013142"},{"key":"690_CR10","doi-asserted-by":"crossref","unstructured":"He G, Li X, Lv S, Zhou Y, Ni Z, Chen X (2024) Task scheduling algorithm for heterogeneous computing power network. In: 2024 IEEE 99th Vehicular Technology Conference (VTC2024-Spring), pp 1\u20135. IEEE","DOI":"10.1109\/VTC2024-Spring62846.2024.10683650"},{"issue":"3","key":"690_CR11","first-page":"7","volume":"27","author":"Y Huijuan","year":"2021","unstructured":"Huijuan Y, Lu L, Xiaodong D (2021) Computing power aware network: Architecture and key technologies. ZTE Commun 27(3):7\u201311","journal-title":"ZTE Commun"},{"key":"690_CR12","doi-asserted-by":"crossref","unstructured":"Jamil SU, Khan MA, Rahman M, Paracha MA, Zia T, Rahman SS, Ahmed SB (2025) How intelligence is reshaping today: Ioe edge networks? Internet Things 101717","DOI":"10.1016\/j.iot.2025.101717"},{"key":"690_CR13","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1016\/j.future.2023.09.018","volume":"150","author":"GP Koslovski","year":"2024","unstructured":"Koslovski GP, Pereira K, Albuquerque PR (2024) Dag-based workflows scheduling using actor-critic deep reinforcement learning. Futur Gener Comput Syst 150:354\u2013363","journal-title":"Futur Gener Comput Syst"},{"issue":"6","key":"690_CR14","doi-asserted-by":"publisher","first-page":"3103","DOI":"10.1109\/TCYB.2020.2977661","volume":"51","author":"K Li","year":"2020","unstructured":"Li K, Zhang T, Wang R (2020) Deep reinforcement learning for multiobjective optimization. IEEE Trans Cybern 51(6):3103\u20133114","journal-title":"IEEE Trans Cybern"},{"key":"690_CR15","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/j.future.2022.04.032","volume":"135","author":"J Li","year":"2022","unstructured":"Li J, Zhang X, Wei J, Ji Z, Wei Z (2022) Garlsched: Generative adversarial deep reinforcement learning task scheduling optimization for large-scale high performance computing systems. Futur Gener Comput Syst 135:259\u2013269","journal-title":"Futur Gener Comput Syst"},{"issue":"10","key":"690_CR16","doi-asserted-by":"publisher","first-page":"14599","DOI":"10.1109\/JIOT.2025.3526599","volume":"12","author":"X Lin","year":"2025","unstructured":"Lin X, Yao Y, Hu B, Yang W, Zhou X, Li G, Zhang W (2025) A real-time anomaly detection method for industrial control systems based on long-short period deterministic finite automaton. IEEE Internet Things J 12(10):14599\u201314621","journal-title":"IEEE Internet Things J"},{"key":"690_CR17","doi-asserted-by":"publisher","first-page":"107588","DOI":"10.1016\/j.future.2024.107588","volume":"164","author":"L Liu","year":"2025","unstructured":"Liu L, Zhang Y (2025) Task offloading optimization for multi-objective based on cloud-edge-end collaboration in maritime networks. Futur Gener Comput Syst 164:107588","journal-title":"Futur Gener Comput Syst"},{"key":"690_CR18","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1016\/j.jpdc.2022.10.003","volume":"172","author":"J Liu","year":"2023","unstructured":"Liu J, Yang P, Chen C (2023) Intelligent energy-efficient scheduling with ant colony techniques for heterogeneous edge computing. J Parall Distrib Comput 172:84\u201396","journal-title":"J Parall Distrib Comput"},{"key":"690_CR19","doi-asserted-by":"crossref","unstructured":"Liu X, Li W, Cao B, Wang S, Lyu Z (2025) Large-scale multiobjective vehicle task offloading optimization based on cloud-edge-end collaboration for 6g enabled transport systems. IEEE Trans Intell Transport Syst","DOI":"10.1109\/TITS.2025.3579164"},{"issue":"04","key":"690_CR20","first-page":"107","volume":"40","author":"X Mande","year":"2024","unstructured":"Mande X, Zhufang H, Hao S (2024) Multi-user fine-grained task offloading and scheduling strategy in cloud-edge-end collaborative computing. Telecommun Sci 40(04):107\u2013121","journal-title":"Telecommun Sci"},{"issue":"2","key":"690_CR21","doi-asserted-by":"publisher","first-page":"2144","DOI":"10.1109\/TCC.2022.3188926","volume":"11","author":"S Mousavi","year":"2022","unstructured":"Mousavi S, Mood SE, Souri A, Javidi MM (2022) Directed search: a new operator in nsga-ii for task scheduling in iot based on cloud-fog computing. IEEE Trans Cloud Comput 11(2):2144\u20132157","journal-title":"IEEE Trans Cloud Comput"},{"key":"690_CR22","doi-asserted-by":"crossref","unstructured":"Mustafa E, Shuja J, Rehman F, Namoun A, Bilal M, Iqbal A (2025) Computation offloading in vehicular communications using ppo-based deep reinforcement learning: E. mustafa et al. J Supercomput 81(4):547","DOI":"10.1007\/s11227-025-07009-z"},{"key":"690_CR23","doi-asserted-by":"publisher","first-page":"146379","DOI":"10.1109\/ACCESS.2019.2946216","volume":"7","author":"S Pang","year":"2019","unstructured":"Pang S, Li W, He H, Shan Z, Wang X (2019) An eda-ga hybrid algorithm for multi-objective task scheduling in cloud computing. IEEE Access 7:146379\u2013146389","journal-title":"IEEE Access"},{"issue":"23","key":"690_CR24","doi-asserted-by":"publisher","first-page":"4611","DOI":"10.3390\/electronics13234611","volume":"13","author":"MA Paracha","year":"2024","unstructured":"Paracha MA, Jamil SU, Shahzad K, Khan MA, Rasheed A (2024) Leveraging ai for network threat detection\u2014a conceptual overview. Electronics 13(23):4611","journal-title":"Electronics"},{"key":"690_CR25","doi-asserted-by":"crossref","unstructured":"Rajak A, Tripathi R (2025) An attention-enhanced lstm model for efficient network slicing in beyond 5g networks. Ad Hoc Networks 104070","DOI":"10.1016\/j.adhoc.2025.104070"},{"issue":"5","key":"690_CR26","doi-asserted-by":"publisher","first-page":"1666","DOI":"10.3390\/s21051666","volume":"21","author":"S Sheng","year":"2021","unstructured":"Sheng S, Chen P, Chen Z, Wu L, Yao Y (2021) Deep reinforcement learning-based task scheduling in iot edge computing. Sensors 21(5):1666","journal-title":"Sensors"},{"issue":"2","key":"690_CR27","doi-asserted-by":"publisher","first-page":"175","DOI":"10.23919\/JCC.2021.02.011","volume":"18","author":"X Tang","year":"2021","unstructured":"Tang X, Cao C, Wang Y, Zhang S, Liu Y, Li M, He T (2021) Computing power network: The architecture of convergence of computing and networking towards 6g requirement. China Commun 18(2):175\u2013185","journal-title":"China Commun"},{"issue":"3","key":"690_CR28","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1109\/TSC.2023.3326539","volume":"17","author":"T Wang","year":"2023","unstructured":"Wang T, Shen L, Fan Q, Xu T, Liu T, Xiong H (2023) Joint admission control and resource allocation of virtual network embedding via hierarchical deep reinforcement learning. IEEE Trans Serv Comput 17(3):1001\u20131015","journal-title":"IEEE Trans Serv Comput"},{"issue":"9","key":"690_CR29","doi-asserted-by":"publisher","first-page":"1990","DOI":"10.3390\/electronics12091990","volume":"12","author":"Z Wang","year":"2023","unstructured":"Wang Z, Yu Y, Liu D, Li W, Xiong A, Song Y (2023) A resource allocation scheme with the best revenue in the computing power network. Electronics 12(9):1990","journal-title":"Electronics"},{"key":"690_CR30","doi-asserted-by":"publisher","first-page":"110337","DOI":"10.1016\/j.engappai.2025.110337","volume":"148","author":"Z Wang","year":"2025","unstructured":"Wang Z, Zhan W, Duan H, Huang H (2025) Multiobjective optimization deep reinforcement learning for dependent task scheduling based on spatio-temporal fusion graph neural network. Eng Appl Artif Intell 148:110337","journal-title":"Eng Appl Artif Intell"},{"key":"690_CR31","unstructured":"Wang T, Fan Q, Wang C, Yang L, Ding L, Yuan NJ, Xiong H (2024) Flagvne: A flexible and generalizable reinforcement learning framework for network resource allocation. arXiv:2404.12633"},{"key":"690_CR32","doi-asserted-by":"crossref","unstructured":"Wei D, Wen J, Xu P, Shi H, Pan C (2025) Dependent tasks joint scheduling and offloading for edge computing based on deep reinforcement learning. Ad Hoc Networks 104111","DOI":"10.1016\/j.adhoc.2025.104111"},{"key":"690_CR33","doi-asserted-by":"publisher","first-page":"104249","DOI":"10.1016\/j.jnca.2025.104249","volume":"242","author":"J Wu","year":"2025","unstructured":"Wu J, Zhu Z (2025) Intelligent routing optimization for sdn based on ppo and gnn. J Netw Comput Appl 242:104249","journal-title":"J Netw Comput Appl"},{"key":"690_CR34","doi-asserted-by":"crossref","unstructured":"Wu J, Cao Z, Zhang Y, Zhang X (2019) Edge-cloud collaborative computation offloading model based on improved partical swarm optimization in mec. In: 2019 IEEE 25th International Conference on Parallel and Distributed Systems (ICPADS), pp 959\u2013962. IEEE","DOI":"10.1109\/ICPADS47876.2019.00144"},{"key":"690_CR35","doi-asserted-by":"publisher","first-page":"2701","DOI":"10.1109\/TON.2025.3649656","volume":"34","author":"Y Xia","year":"2025","unstructured":"Xia Y, He Q, Fang H, Wang X, Bi Y, Hawbani A, Yu K (2025) Mprof: Multi-dimensional preference-driven resource optimization framework for cloud-edge-end collaboration. IEEE Trans Network 34:2701\u20132716","journal-title":"IEEE Trans Network"},{"key":"690_CR36","doi-asserted-by":"crossref","unstructured":"Xie R, Feng L, Tang Q, Zhu H, Huang T, Zhang R, Yu FR, Xiong Z (2025) Priority-aware task scheduling in computing power network-enabled edge computing systems. IEEE Trans Netw Sci Eng","DOI":"10.1109\/TNSE.2025.3557385"},{"key":"690_CR37","doi-asserted-by":"crossref","unstructured":"Xiong X, Li M, Yu FR, Zhang H, Wang K, Si P (2025) Cloud-edge-end collaborative computing-enabled intelligent sharding blockchain for industrial iot based on ppo approach. IEEE Trans Mobile Comput","DOI":"10.1109\/TMC.2025.3554568"},{"key":"690_CR38","doi-asserted-by":"crossref","unstructured":"Yang J, Jiang B, Lv Z, Choo K-KR (2020) A task scheduling algorithm considering game theory designed for energy management in cloud computing. Future Gener Comput Syst 105:985\u2013992","DOI":"10.1016\/j.future.2017.03.024"},{"key":"690_CR39","doi-asserted-by":"publisher","first-page":"103961","DOI":"10.1016\/j.aei.2025.103961","volume":"69","author":"Y Yin","year":"2026","unstructured":"Yin Y, Yang B, Wang S, Kang L, Peng Q (2026) A multi-layer dynamic production scheduling method for manufacturing systems with cloud-edge-end architecture. Adv Eng Inform 69:103961","journal-title":"Adv Eng Inform"},{"issue":"9","key":"690_CR40","doi-asserted-by":"publisher","first-page":"109","DOI":"10.23919\/JCC.ja.2021-0776","volume":"21","author":"S Yukun","year":"2024","unstructured":"Yukun S, Bo L, Junlin L, Haonan H, Xing Z, Jing P, Wenbo W (2024) Computing power network: A survey. China Commun 21(9):109\u2013145","journal-title":"China Commun"},{"issue":"13","key":"690_CR41","first-page":"3821","volume":"9","author":"S Zhan","year":"2012","unstructured":"Zhan S, Huo H (2012) Improved pso-based task scheduling algorithm in cloud computing. J Inf Computat Sci 9(13):3821\u20133829","journal-title":"J Inf Computat Sci"},{"key":"690_CR42","doi-asserted-by":"crossref","unstructured":"Zhang Z.-Q., Huang T, Qian B, Hu R (2025) Mamhsan: A multi-agent deep reinforcement learning framework based on multi-head self-attention network with heterogeneous graph embedding for flexible job shop scheduling. Comput Indust Eng 111466","DOI":"10.1016\/j.cie.2025.111466"},{"issue":"21","key":"690_CR43","doi-asserted-by":"publisher","first-page":"34364","DOI":"10.1109\/JIOT.2024.3382682","volume":"11","author":"M Zhao","year":"2024","unstructured":"Zhao M, Zhang X, He Z, Chen Y, Zhang Y (2024) Dependency-aware task scheduling and layer loading for mobile edge computing networks. IEEE Internet Things J 11(21):34364\u201334381","journal-title":"IEEE Internet Things J"},{"key":"690_CR44","doi-asserted-by":"crossref","unstructured":"Zhao F, Jia Y (2025) A multi-agent reinforcement learning with multi-task learning and graph edge attention networks for dynamic flexible job shop scheduling. Applied Soft Comput 114277","DOI":"10.1016\/j.asoc.2025.114277"},{"key":"690_CR45","doi-asserted-by":"crossref","unstructured":"Zhou Y, Li X, Luo J, Yuan M, Zeng J, Yao J (2022) Learning to optimize dag scheduling in heterogeneous environment. In: 2022 23rd IEEE International Conference on Mobile Data Management (MDM), pp 137\u2013146. IEEE","DOI":"10.1109\/MDM55031.2022.00040"},{"key":"690_CR46","doi-asserted-by":"crossref","unstructured":"Zou Z, Xie R, Ren Y, Yu FR, Huang T (2022) Task scheduling for icn-based computing first network: A deep reinforcement learning approach. In: 2022 IEEE 8th International Conference on Computer and Communications (ICCC), pp 1615\u20131620. IEEE","DOI":"10.1109\/ICCC56324.2022.10065638"}],"container-title":["Journal of King Saud University Computer and Information Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s44443-026-00690-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-026-00690-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s44443-026-00690-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,7]],"date-time":"2026-07-07T09:39:20Z","timestamp":1783417160000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s44443-026-00690-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,31]]},"references-count":46,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2026,7]]}},"alternative-id":["690"],"URL":"https:\/\/doi.org\/10.1007\/s44443-026-00690-x","relation":{},"ISSN":["1319-1578","2213-1248"],"issn-type":[{"value":"1319-1578","type":"print"},{"value":"2213-1248","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,31]]},"assertion":[{"value":"20 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"31 March 2026","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"}}],"article-number":"290"}}