{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:28:29Z","timestamp":1740144509007,"version":"3.37.3"},"reference-count":23,"publisher":"EDP Sciences","license":[{"start":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T00:00:00Z","timestamp":1614643200000},"content-version":"vor","delay-in-days":60,"URL":"https:\/\/www.edpsciences.org\/en\/authors\/copyright-and-licensing"}],"funder":[{"name":"Sun Yat-sen University Youth Teacher Cultivation Project","award":["19wkpy15"],"award-info":[{"award-number":["19wkpy15"]}]},{"DOI":"10.13039\/501100002858","name":"China Postdoctoral Science Foundation","doi-asserted-by":"publisher","award":["No. 2019M663197"],"award-info":[{"award-number":["No. 2019M663197"]}],"id":[{"id":"10.13039\/501100002858","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671404"],"award-info":[{"award-number":["11671404"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2020,4,3]]},"published-print":{"date-parts":[[2021]]},"abstract":"<jats:p>This paper considers a single-server queueing system with server breakdowns. When the server fails, it is sent to repair immediately and its maintenance rate is allowed to be adjustable. The goal is to find the optimal maintenance rates that minimize the long-run average cost of the system. We address the static and dynamic maintenance control problems respectively. For the static control model, we derive the stationary system performances and the explicit solution of the optimal maintenance rate. Then regarding the dynamic maintenance problem, we formulate it as a Markov decision process (MDP) and the optimal dynamic policy is proved to be a threshold policy. Based on the structure of optimal dynamic policy, we construct a performance evaluation for computing efficiently the optimal threshold and average cost. Finally, a comparative study of the dynamic and static policies is presented by numerical experiment which shows the impact of system parameters on the optimal maintenance policies.<\/jats:p>","DOI":"10.1051\/ro\/2020034","type":"journal-article","created":{"date-parts":[[2020,4,4]],"date-time":"2020-04-04T18:53:34Z","timestamp":1586026414000},"page":"S1339-S1354","source":"Crossref","is-referenced-by-count":1,"special_numbering":"Supplement","title":["Dynamic vs. static maintenance rate policies for multi-state queueing systems"],"prefix":"10.1051","volume":"55","author":[{"given":"Gang","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zaiming","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuqing","family":"Chu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2021,3,2]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"3194","DOI":"10.1109\/TPWRS.2012.2237042","volume":"28","author":"Abeygunawardane","year":"2013","journal-title":"IEEE Trans. Power Syst"},{"key":"R2","doi-asserted-by":"crossref","first-page":"545","DOI":"10.1016\/j.ejor.2013.02.011","volume":"228","author":"Borrero","year":"2013","journal-title":"Eur. J. Oper. Res"},{"key":"R3","doi-asserted-by":"crossref","first-page":"834","DOI":"10.1016\/j.ejor.2016.06.021","volume":"255","author":"Chen","year":"2016","journal-title":"Eur. J. Oper. Res"},{"key":"R4","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.ress.2004.11.001","volume":"90","author":"Chen","year":"2005","journal-title":"Reliab. Eng. Sys. Saf"},{"key":"R5","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1007\/s10479-009-0646-9","volume":"178","author":"Creemers","year":"2010","journal-title":"Ann. Oper. Res"},{"key":"R6","doi-asserted-by":"crossref","first-page":"1197","DOI":"10.1051\/ro\/2018057","volume":"53","author":"Gao","year":"2019","journal-title":"RAIRO:OR"},{"key":"R7","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.apnum.2006.11.010","volume":"58","author":"Kenne","year":"2008","journal-title":"Appl. Numer. Math"},{"key":"R8","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0895-7177(03)90093-8","volume":"38","author":"Kenn\u00e9","year":"2003","journal-title":"Math. Comput. Model"},{"key":"R9","doi-asserted-by":"crossref","first-page":"4583","DOI":"10.1080\/00207543.2014.998791","volume":"53","author":"Khalili","year":"2015","journal-title":"Int. J. Prod. Res"},{"key":"R10","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.cie.2008.11.023","volume":"57","author":"Kim","year":"2009","journal-title":"Comput. Ind. Eng"},{"issue":"1","key":"R11","first-page":"1","volume":"1","author":"Koole","year":"2007","journal-title":"Foundations and Trends[circleR] in Stochastic Systems"},{"key":"R12","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1287\/msom.1030.0030","volume":"6","author":"Lariviere","year":"2004","journal-title":"Manuf. Serv. Oper. Manage"},{"key":"R13","doi-asserted-by":"crossref","unstructured":"Latouche G. and Ramaswami V., Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM 5 (1999).","DOI":"10.1137\/1.9780898719734"},{"key":"R14","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s10845-009-0354-y","volume":"23","author":"Njike","year":"2012","journal-title":"J. Intell. Manuf"},{"key":"R15","unstructured":"Puterman M.L., Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley & Sons Inc., New York, NY (2014)."},{"key":"R16","doi-asserted-by":"crossref","first-page":"665","DOI":"10.1007\/s00170-016-9127-x","volume":"89","author":"Salari","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol"},{"key":"R17","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/s10479-016-2217-1","volume":"247","author":"Taleb","year":"2016","journal-title":"Ann. Oper. Res"},{"key":"R18","unstructured":"Tijms H.C., Stochastic Models: An Algorithmic Approach. In Vol. 303 of Probability and Statistics - Applied Probability and Statistics Section. John Wiley & Sons Inc., New York, NY (1994)."},{"key":"R19","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.cam.2009.07.043","volume":"233","author":"Wang","year":"2009","journal-title":"J. Comput. Appl. Math"},{"key":"R20","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.cor.2014.03.018","volume":"49","author":"Wu","year":"2014","journal-title":"Comput. Oper. Res"},{"key":"R21","doi-asserted-by":"crossref","first-page":"304","DOI":"10.1016\/j.cie.2008.11.025","volume":"57","author":"Yeh","year":"2009","journal-title":"Comput. Ind. Eng"},{"key":"R22","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1016\/j.proeng.2011.12.756","volume":"29","author":"Yingkui","year":"2012","journal-title":"Proc. Eng"},{"key":"R23","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1016\/j.cie.2016.05.007","volume":"98","author":"Zheng","year":"2016","journal-title":"Comput. Ind. Eng"}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2020034\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T09:50:23Z","timestamp":1614678623000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2020034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":23,"alternative-id":["ro190368"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2020034","relation":{},"ISSN":["0399-0559","1290-3868"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"1290-3868"}],"subject":[],"published":{"date-parts":[[2021]]}}}