{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T06:20:05Z","timestamp":1774765205792,"version":"3.50.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T00:00:00Z","timestamp":1709942400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,3,9]],"date-time":"2024-03-09T00:00:00Z","timestamp":1709942400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Oper. Res. Forum"],"DOI":"10.1007\/s43069-024-00295-y","type":"journal-article","created":{"date-parts":[[2024,3,11]],"date-time":"2024-03-11T09:01:32Z","timestamp":1710147692000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods"],"prefix":"10.1007","volume":"5","author":[{"given":"Anis","family":"Chettouf","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Amina Angelika","family":"Bouchentouf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Boualem","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,3,9]]},"reference":[{"issue":"1","key":"295_CR1","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/BF01149327","volume":"1","author":"BT Doshi","year":"1986","unstructured":"Doshi BT (1986) Queueing systems with vacations-a survey. Queueing Syst 1(1):29\u201366","journal-title":"Queueing Syst"},{"key":"295_CR2","volume-title":"Queueing analysis: a foundation of performance analysis, vol 1: Vacation and priority systems, Part 1","author":"H Takagi","year":"1991","unstructured":"Takagi H (1991) Queueing analysis: a foundation of performance analysis, vol 1: Vacation and priority systems, Part 1. Elsevier Science Publishers B.V., Amsterdam"},{"key":"295_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-33723-4","volume-title":"Vacation queueing models theory and applications","author":"N Tian","year":"2006","unstructured":"Tian N, Zhang ZG (2006) Vacation queueing models theory and applications. Springer, New York"},{"issue":"18","key":"295_CR4","doi-asserted-by":"publisher","first-page":"9152","DOI":"10.1002\/mma.5119","volume":"41","author":"F Afroun","year":"2018","unstructured":"Afroun F, Aissani D, Hamadouche D, Boualem M (2018) Q-matrix method for the analysis and performance evaluation of unreliable $${M\/M\/1\/N}$$ queueing model. Math Methods Appl Sci 41(18):9152\u20139163. https:\/\/doi.org\/10.1002\/mma.5119","journal-title":"Math Methods Appl Sci"},{"issue":"1","key":"295_CR5","doi-asserted-by":"publisher","first-page":"9","DOI":"10.1007\/s40819-022-01481-4","volume":"9","author":"A Begum","year":"2023","unstructured":"Begum A, Choudhury G (2023) Analysis of an $$M\/\\begin{pmatrix}G_1\\ G_2\\end{pmatrix}\/1$$ Queue with Bernoulli Vacation and Server Breakdown. Int J Appl Comput Math 9(1):9. https:\/\/doi.org\/10.1007\/s40819-022-01481-4","journal-title":"Int J Appl Comput Math"},{"key":"295_CR6","doi-asserted-by":"publisher","unstructured":"Jain M, Meena RK (2017) Markovian analysis of unreliable multi-components redundant fault tolerant system with working vacation and F-policy. Cogent Math 4(1). https:\/\/doi.org\/10.1080\/23311835.2017.1306961","DOI":"10.1080\/23311835.2017.1306961"},{"key":"295_CR7","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1016\/j.apm.2007.02.013","volume":"32","author":"M Jain","year":"2008","unstructured":"Jain M, Sharma GC, Sharma S (2008) Performance modeling of state dependent system with mixed standbys and two modes of failure. Appl Math Model 32:712\u2013724","journal-title":"Appl Math Model"},{"issue":"1","key":"295_CR8","first-page":"53","volume":"14","author":"PV Laxmi","year":"2019","unstructured":"Laxmi PV, Rajesh P, Kassahun TW (2019) Performance measures of variant working vacations on batch arrival queue with server breakdowns. Int J Manag Sci Eng Manag 14(1):53\u201363","journal-title":"Int J Manag Sci Eng Manag"},{"key":"295_CR9","doi-asserted-by":"publisher","first-page":"588","DOI":"10.1016\/S0377-2217(02)00451-4","volume":"149","author":"O Nakdimon","year":"2003","unstructured":"Nakdimon O, Yechiali U (2003) Polling systems with breakdowns and repairs. Eur J Oper Res 149:588\u2013613","journal-title":"Eur J Oper Res"},{"issue":"11","key":"295_CR10","doi-asserted-by":"publisher","first-page":"2047","DOI":"10.1177\/0954405414540649","volume":"229","author":"DY Yang","year":"2015","unstructured":"Yang DY, Wu ZR, Tsou CS (2015) Reliability analysis of a repairable system with geometric reneging and threshold-based recovery policy. Proc Inst Mech Eng B J Eng Manuf 229(11):2047\u20132062","journal-title":"Proc Inst Mech Eng B J Eng Manuf"},{"issue":"6","key":"295_CR11","doi-asserted-by":"publisher","first-page":"672","DOI":"10.1080\/16843703.2018.1510359","volume":"16","author":"D Zirem","year":"2019","unstructured":"Zirem D, Boualem M, Adel-Aissanou K, Aissani D (2019) Analysis of a single server batch arrival unreliable queue with balking and general retrial time. Qual Technol Quant Manag 16(6):672\u2013695","journal-title":"Qual Technol Quant Manag"},{"issue":"1","key":"295_CR12","first-page":"101","volume":"28","author":"D Yue","year":"2006","unstructured":"Yue D, Zhang Y, Yue W (2006) Optimal performance analysis of an $${M\/M\/1\/N}$$ queue system with balking, reneging and server vacation. Int J Pure Appl Math 28(1):101\u2013115","journal-title":"Int J Pure Appl Math"},{"key":"295_CR13","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s11134-007-9031-z","volume":"56","author":"U Yechiali","year":"2007","unstructured":"Yechiali U (2007) Queues with system disasters and impatient customers when system is down. Queueing Syst 56:195\u2013202","journal-title":"Queueing Syst"},{"issue":"3","key":"295_CR14","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1016\/j.cor.2005.05.013","volume":"34","author":"K-H Wang","year":"2007","unstructured":"Wang K-H, Ke J-B, Ke J-C (2007) Profit analysis of the $${M\/M\/R}$$ machine repair problem with balking, reneging, and standby switching failures. Comput Oper Res 34(3):835\u2013847","journal-title":"Comput Oper Res"},{"key":"295_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-09703-9","volume-title":"Advances in Queueing Theory and Network Applications","author":"D Yue","year":"2009","unstructured":"Yue D, Yue W (2009) Analysis of an $${M\/M\/c\/N}$$ queueing system with balking, reneging, and synchronous vacations. In: Yue W, Takahashi Y, Takagi H (eds) Advances in Queueing Theory and Network Applications. Springer, New York"},{"issue":"6","key":"295_CR16","doi-asserted-by":"publisher","first-page":"11","DOI":"10.4236\/ajor.2013.36054","volume":"3","author":"M Baruah","year":"2013","unstructured":"Baruah M, Kailash C, Madan T (2013) Eldabi: a two stage batch arrival queue with reneging during vacation and breakdown periods. Am J Oper Res 3(6):11. https:\/\/doi.org\/10.4236\/ajor.2013.36054","journal-title":"Am J Oper Res"},{"key":"295_CR17","doi-asserted-by":"publisher","first-page":"380","DOI":"10.1016\/j.amc.2014.05.025","volume":"241","author":"X Li","year":"2014","unstructured":"Li X, Wang J, Zhang F (2014) New results on equilibrium balking strategies in the single-server queue with breakdowns and repairs. Appl Math Comput 241:380\u2013388. https:\/\/doi.org\/10.1016\/j.amc.2014.05.025","journal-title":"Appl Math Comput"},{"issue":"4","key":"295_CR18","doi-asserted-by":"publisher","first-page":"651","DOI":"10.12732\/ijpam.v115i4.1","volume":"115","author":"SH Rao","year":"2017","unstructured":"Rao SH, Vasanta Kumar V, Srinivasa Kumar B, Srinivasa Rao T (2017) Analysis of two-phase queuing system with impatient customers, server breakdowns and delayed repair. Int J Pure Appl Math 115(4):651\u2013663","journal-title":"Int J Pure Appl Math"},{"issue":"6","key":"295_CR19","first-page":"104","volume":"57","author":"AA Bouchentouf","year":"2018","unstructured":"Bouchentouf AA, Guendouzi A (2018) Sensitivity analysis of multiple vacation feedback queuing system with differentiated vacations, vacation interruptions and impatient customers. Int J Appl Math Stat 57(6):104\u2013121","journal-title":"Int J Appl Math Stat"},{"issue":"1","key":"295_CR20","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1007\/s12597-019-00357-4","volume":"56","author":"AA Bouchentouf","year":"2019","unstructured":"Bouchentouf AA, Cherfaoui M, Boualem M (2019) Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers. Opsearch 56(1):300\u2013320","journal-title":"Opsearch"},{"issue":"4","key":"295_CR21","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1504\/IJOR.2023.129959","volume":"46","author":"M Cherfaoui","year":"2023","unstructured":"Cherfaoui M, Bouchentouf AA, Boualem M (2023) Modelling and simulation of Bernoulli feedback queue with general customers\u2019 impatience under variant vacation policy. Int J Oper Res 46(4):451\u2013480","journal-title":"Int J Oper Res"},{"issue":"6","key":"295_CR22","doi-asserted-by":"publisher","first-page":"766","DOI":"10.1080\/16843703.2022.2054088","volume":"19","author":"AA Bouchentouf","year":"2022","unstructured":"Bouchentouf AA, Boualem M, Yahiaoui L, Ahmad H (2022) A multi-station unreliable machine model with working vacation policy and customers impatience. Qual Technol Quant Manag 19(6):766\u2013796","journal-title":"Qual Technol Quant Manag"},{"key":"295_CR23","doi-asserted-by":"publisher","first-page":"133","DOI":"10.1007\/s40305-021-00361-w","volume":"11","author":"S Majid","year":"2023","unstructured":"Majid S (2023) Performance analysis of a Markovian queue with impatient customers and working vacation. J Oper Res Soc China 11:133\u2013156. https:\/\/doi.org\/10.1007\/s40305-021-00361-w","journal-title":"J Oper Res Soc China"},{"key":"295_CR24","volume-title":"Matrix-geometric solutions in stochastic models: an algorithmic approach","author":"MF Neuts","year":"1981","unstructured":"Neuts MF (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. The John Hopkins University Press, Baltimore"},{"issue":"12","key":"295_CR25","doi-asserted-by":"publisher","first-page":"2165","DOI":"10.1080\/00207721.2013.859326","volume":"46","author":"C-D Liou","year":"2015","unstructured":"Liou C-D (2015) Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers. Int J Syst Sci 46(12):2165\u20132182","journal-title":"Int J Syst Sci"}],"container-title":["Operations Research Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-024-00295-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s43069-024-00295-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s43069-024-00295-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,26]],"date-time":"2024-03-26T06:25:32Z","timestamp":1711434332000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s43069-024-00295-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,9]]},"references-count":25,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["295"],"URL":"https:\/\/doi.org\/10.1007\/s43069-024-00295-y","relation":{},"ISSN":["2662-2556"],"issn-type":[{"value":"2662-2556","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,9]]},"assertion":[{"value":"23 July 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 March 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent to Participate"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Consent for Publication"}},{"value":"The authors declare no competing interests.","order":5,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing Interests"}}],"article-number":"22"}}