{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:48:05Z","timestamp":1747097285234,"version":"3.37.3"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T00:00:00Z","timestamp":1679270400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T00:00:00Z","timestamp":1679270400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61973261","61872311"],"award-info":[{"award-number":["61973261","61872311"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["A2020203010","A2018203088"],"award-info":[{"award-number":["A2020203010","A2018203088"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Project of Hebei Key Laboratory of Software Engineering","award":["22567637H"],"award-info":[{"award-number":["22567637H"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Wireless Netw"],"published-print":{"date-parts":[[2023,7]]},"DOI":"10.1007\/s11276-023-03310-y","type":"journal-article","created":{"date-parts":[[2023,3,20]],"date-time":"2023-03-20T15:02:51Z","timestamp":1679324571000},"page":"2321-2336","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Performance analysis of a Queueing system based on vacation with fault repairable and spare servers in the MP2P network"],"prefix":"10.1007","volume":"29","author":[{"given":"Shunzhi","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4510-6920","authenticated-orcid":false,"given":"Zhanyou","family":"Ma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinying","family":"Niu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yilin","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,20]]},"reference":[{"issue":"8","key":"3310_CR1","doi-asserted-by":"publisher","first-page":"3063","DOI":"10.1007\/s11276-017-1522-1","volume":"24","author":"M Pan","year":"2018","unstructured":"Pan, M., & Lin, Y. (2018). Efficient data dissemination for Wi-Fi peer-to-peer networks by unicasting among Wi-Fi P2P groups. Wireless Networks, 24(8), 3063\u20133081.","journal-title":"Wireless Networks"},{"issue":"3","key":"3310_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2835374","volume":"48","author":"S Brienza","year":"2015","unstructured":"Brienza, S., Cebeci, S. E., Masoumzadeh, S. S., Hlavacs, H., & Anastasi, G. (2015). A survey on energy efficiency in P2P systems: File distribution. content streaming, and epidemics. Acm Computing Surveys, 48(3), 1\u201337.","journal-title":"Acm Computing Surveys"},{"key":"3310_CR3","doi-asserted-by":"crossref","unstructured":"Azzedin, F. (2010). Trust-based taxonomy for free riders in distributed multimedia systems. IEEE International Conference on High Performance Computing & Simulation, pp. 362-369.","DOI":"10.1109\/HPCS.2010.5547108"},{"issue":"3","key":"3310_CR4","doi-asserted-by":"publisher","first-page":"175","DOI":"10.1016\/j.peva.2005.01.005","volume":"63","author":"XY Yang","year":"2006","unstructured":"Yang, X. Y., & Veciana, G. D. (2006). Performance of peer-to-peer networks: Service capacity and role of resource sharing policies. Performance Evaluation, 63(3), 175\u2013194.","journal-title":"Performance Evaluation"},{"issue":"8","key":"3310_CR5","doi-asserted-by":"publisher","first-page":"2313","DOI":"10.1007\/s11276-010-0260-4","volume":"16","author":"Z Zhuang","year":"2010","unstructured":"Zhuang, Z., Kakumanu, S., Jeong, Y., & Velayutham, A. (2010). Mobile hosts participating in peer-to-peer data networks: Challenges and solutions. Wireless Networks, 16(8), 2313\u20132333.","journal-title":"Wireless Networks"},{"issue":"7","key":"3310_CR6","doi-asserted-by":"publisher","first-page":"2465","DOI":"10.1007\/s11276-017-1481-6","volume":"24","author":"CM Liu","year":"2018","unstructured":"Liu, C. M., & Lai, C. C. (2018). A group-based data-driven approach for data synchronization in unstructured mobile P2P systems. Wireless Networks, 24(7), 2465\u20132482.","journal-title":"Wireless Networks"},{"issue":"2","key":"3310_CR7","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1007\/s11276-020-02493-y","volume":"27","author":"SK Singh","year":"2020","unstructured":"Singh, S. K., Kumar, C., & Nath, P. (2020). Analysis and modelling the effects of mobility, Churn rate, node\u2019s life span, intermittent bandwidth and stabilization cost of finger table in structured mobile P2P networks. Wireless Networks, 27(2), 1049\u20131062.","journal-title":"Wireless Networks"},{"issue":"14","key":"3310_CR8","doi-asserted-by":"publisher","first-page":"1889","DOI":"10.1007\/s12083-021-01122-5","volume":"4","author":"S Zhou","year":"2021","unstructured":"Zhou, S., Zhang, T., & Meng, X. F. (2021). IForest: An informed resource search strategy in mobile the P2P networks. Peer-to-Peer Networking and Applications, 4(14), 1889\u20131904.","journal-title":"Peer-to-Peer Networking and Applications"},{"key":"3310_CR9","doi-asserted-by":"crossref","unstructured":"Ge, Z.H., Figueiredo, D.R, Jaiswal, S., & Towsley, D. (2003). Modeling peer-peer file sharing systems. 22th Annual Joint Conference of the IEEE Computer and Communications Societies, San Francisco, pp. 2188-2198.","DOI":"10.1109\/INFCOM.2003.1209239"},{"issue":"1","key":"3310_CR10","first-page":"296","volume":"46","author":"SF Jin","year":"2016","unstructured":"Jin, S. F., Li, Y., Liu, J. P., & Huo, Z. Q. (2016). Strategies of nash equilibrium and social optimization for online mechanisms of P2P nodes. Journal of Jilin University (Engineering and Technology Edition), 46(1), 296\u2013302 ((in Chinese)).","journal-title":"Journal of Jilin University (Engineering and Technology Edition)"},{"issue":"2","key":"3310_CR11","doi-asserted-by":"publisher","first-page":"1431","DOI":"10.1007\/s11276-020-02512-y","volume":"27","author":"ZY Ma","year":"2021","unstructured":"Ma, Z. Y., Yu, X. R., Guo, S. S., & Zhang, Y. (2021). Analysis of wireless sensor networks with sleep mode and threshold activation. Wireless Networks, 27(2), 1431\u20131443.","journal-title":"Wireless Networks"},{"issue":"4","key":"3310_CR12","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1504\/IJCNDS.2021.119215","volume":"27","author":"FJ Liu","year":"2021","unstructured":"Liu, F. J., Ma, Z. Y., Si, Q. N., & Yan, M. (2021). Performance analysis of peer-to-peer networks based on two-phase service queuing theory. International Journal Communication Networks and Distributed Systems, 27(4), 349\u2013365.","journal-title":"International Journal Communication Networks and Distributed Systems"},{"issue":"5","key":"3310_CR13","doi-asserted-by":"publisher","first-page":"3287","DOI":"10.1007\/s11276-021-02659-2","volume":"27","author":"QN Si","year":"2021","unstructured":"Si, Q. N., Ma, Z. Y., Liu, F. J., & Wang, R. (2021). Performance analysis of P2P network with dynamic changes of servers based on M\/M\/c queueing model. Wireless Networks, 27(5), 3287\u20133297.","journal-title":"Wireless Networks"},{"issue":"4","key":"3310_CR14","first-page":"6","volume":"17","author":"TT Ling","year":"2018","unstructured":"Ling, T. T., Ding, B. L., & Zhu, Y. J. (2018). Asynchronous restricted vacation queue with two standby servers. Journal of Taiyuan Normal University (Natural Science), 17(4), 6\u201311 ((in Chinese)).","journal-title":"Journal of Taiyuan Normal University (Natural Science)"},{"issue":"3","key":"3310_CR15","first-page":"28","volume":"53","author":"ZY Ma","year":"2017","unstructured":"Ma, Z. Y., Xu, M. J., Zheng, X. M., & Wang, W. B. (2017). The Geom\/Geom\/1+1 queue system with server breakdowns and a spare server with setup time. Journal of Northwest Normal University (Natural Science), 53(3), 28\u201333 ((in Chinese)).","journal-title":"Journal of Northwest Normal University (Natural Science)"},{"issue":"1","key":"3310_CR16","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1016\/j.jmsy.2017.05.010","volume":"44","author":"DY Yang","year":"2017","unstructured":"Yang, D. Y., & Wu, Y. Y. (2017). Analysis of a finite-capacity system with working breakdowns and retention of impatient customers. Journal of Manufacturing Systems, 44(1), 207\u2013216.","journal-title":"Journal of Manufacturing Systems"},{"issue":"4","key":"3310_CR17","doi-asserted-by":"publisher","first-page":"214","DOI":"10.3923\/ajms.2011.214.223","volume":"4","author":"MG Subramania","year":"2011","unstructured":"Subramania, M. G., Ayyappan, & Sekar, G. (2011). M\/M\/c retrial queueing system with breakdown and repair of services. Asian Journal of Mathematics & Statistics, 4(4), 214\u2013223.","journal-title":"Asian Journal of Mathematics & Statistics"},{"issue":"3","key":"3310_CR18","first-page":"85","volume":"5","author":"NS Tian","year":"2001","unstructured":"Tian, N. S., Li, Q. L., & Cao, J. H. (2001). M\/M\/c queue with synchronous multiple vacation of partial servers. Operations Research Transactions, 5(3), 85\u201394.","journal-title":"Operations Research Transactions"},{"issue":"35","key":"3310_CR19","first-page":"96","volume":"3","author":"ZY Ma","year":"2018","unstructured":"Ma, Z. Y., Wang, W. B., & Zheng, X. M. (2018). The M\/M\/c queueing model with preemptive priority and multiple synchronous working vacation. Journal of Chongqing Normal University (Natural Science), 3(35), 96\u2013100 ((in Chinese)).","journal-title":"Journal of Chongqing Normal University (Natural Science)"},{"issue":"10","key":"3310_CR20","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1016\/j.jpdc.2021.06.009","volume":"157","author":"ZY Ma","year":"2021","unstructured":"Ma, Z. Y., Zhang, C. Z., Zhang, L. Y., & Wang, S. Z. (2021). Energy saving strategy and nash equilibrium of hybrid P2P network. Journal of Parallel and Distributed Computing, 157(10), 145\u2013156.","journal-title":"Journal of Parallel and Distributed Computing"},{"issue":"13","key":"3310_CR21","doi-asserted-by":"publisher","first-page":"3166","DOI":"10.1002\/cpe.3213","volume":"27","author":"P Trunfio","year":"2015","unstructured":"Trunfio, P. (2015). A two-layer model for improving the energy efficiency of file sharing peer-to-peer networks. Concurrency Computation: Practice and Experience, 27(13), 3166\u20133183.","journal-title":"Concurrency Computation: Practice and Experience"},{"key":"3310_CR22","first-page":"115","volume-title":"A task scheduling strategy with a sleep-delay timer and a waking-up threshold in cloud computing queueing theory and network applications","author":"SF Jin","year":"2018","unstructured":"Jin, S. F., Wang, X. S., & Yue, W. Y. (2018). A task scheduling strategy with a sleep-delay timer and a waking-up threshold in cloud computing queueing theory and network applications (pp. 115\u2013123). Cham: Springer."},{"issue":"4","key":"3310_CR23","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1145\/964723.383071","volume":"31","author":"I Stoica","year":"2001","unstructured":"Stoica, I. (2001). Chord: A scalable peer-to-peer lookup protocol for internet applications. Acm Sigcomm Computer Communication Review, 31(4), 149\u2013160.","journal-title":"Acm Sigcomm Computer Communication Review"},{"key":"3310_CR24","volume-title":"The quasi birth and death process and matrix-geometric solution","author":"NS Tian","year":"2002","unstructured":"Tian, N. S., & Yue, D. Q. (2002). The quasi birth and death process and matrix-geometric solution. Beijing: Science Press. (in Chinese)."},{"key":"3310_CR25","volume-title":"Matrix-geometric solution in stochastic models","author":"MF Neuts","year":"1981","unstructured":"Neuts, M. F. (1981). Matrix-geometric solution in stochastic models. Johns Hopkins University Press."},{"issue":"4","key":"3310_CR26","doi-asserted-by":"publisher","first-page":"690","DOI":"10.2307\/1425930","volume":"8","author":"MF Neuts","year":"1976","unstructured":"Neuts, M. F. (1976). Moment formulas for the markov renewal branching process advance applied probability. Advances in Applied Probability, 8(4), 690\u2013711.","journal-title":"Advances in Applied Probability"},{"issue":"2","key":"3310_CR27","doi-asserted-by":"publisher","first-page":"256","DOI":"10.1137\/1030046","volume":"30","author":"V Ramaswami","year":"1988","unstructured":"Ramaswami, V. (1988). Nonlinear matrix equations in applied probability-solution techniques and open problems. Siam Review, 30(2), 256\u2013263.","journal-title":"Siam Review"},{"issue":"7","key":"3310_CR28","first-page":"99","volume":"21","author":"E Isaacson","year":"1967","unstructured":"Isaacson, E., & Keller, H. B. (1967). Analysis of numerical methods. Mathematics of Computation, 21(7), 99\u201399.","journal-title":"Mathematics of Computation"},{"issue":"1","key":"3310_CR29","doi-asserted-by":"publisher","first-page":"221","DOI":"10.2307\/1427244","volume":"18","author":"MF Neuts","year":"1986","unstructured":"Neuts, M. F. (1986). The caudal characteristic curve of queues. Advances in Applied Probability, 18(1), 221\u2013254.","journal-title":"Advances in Applied Probability"}],"container-title":["Wireless Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11276-023-03310-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11276-023-03310-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11276-023-03310-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T09:09:31Z","timestamp":1686733771000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11276-023-03310-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,20]]},"references-count":29,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,7]]}},"alternative-id":["3310"],"URL":"https:\/\/doi.org\/10.1007\/s11276-023-03310-y","relation":{},"ISSN":["1022-0038","1572-8196"],"issn-type":[{"type":"print","value":"1022-0038"},{"type":"electronic","value":"1572-8196"}],"subject":[],"published":{"date-parts":[[2023,3,20]]},"assertion":[{"value":"27 February 2023","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2023","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declaration"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}