{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T06:45:05Z","timestamp":1770273905133,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T00:00:00Z","timestamp":1553126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this investigation, a novel sort of retrial queueing system with working breakdown services is introduced. Two distinct kinds of customers are considered, which are priority and ordinary customers. The normal busy server may become inadequate due to catastrophes at any time which cause the major server to fail. At a failure moment, the major server is sent to be fixed and the server functions at a lower speed (called the working breakdown period) during the repair period. The probability generating functions (PGF) of the system size is found using the concepts of the supplementary variable technique (SVT). The impact of parameters in system performance measures and cost optimization are examined numerically.<\/jats:p>","DOI":"10.3390\/sym11030419","type":"journal-article","created":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T12:28:01Z","timestamp":1553171281000},"page":"419","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Performance Analysis of Preemptive Priority Retrial Queueing System with Disaster under Working Breakdown Services"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9027-2354","authenticated-orcid":false,"given":"Sherif I.","family":"Ammar","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Madinah Munawwarah 414111, Saudi Arabia"},{"name":"Department of Mathematics, Menoufia University, Shebin El Koum 32511, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2305-7881","authenticated-orcid":false,"given":"Pakkirisamy","family":"Rajadurai","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam 612001, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1016\/j.mcm.2009.12.011","article-title":"Accessible bibliography on retrial queues: Progress in 2000\u20132009","volume":"51","author":"Artalejo","year":"2010","journal-title":"Math. Comput. Model."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Artalejo, J.R., and Corral, A.G. (2008). Retrial Queueing Systems, Springer.","DOI":"10.1007\/978-3-540-78725-9"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF01158476","article-title":"The M\/G\/1 retrial queue with Bernoulli schedule","volume":"7","author":"Choi","year":"1990","journal-title":"Queueing Syst."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1016\/j.cie.2012.08.015","article-title":"A single-server retrial G-queue with priority and unreliable server under Bernoulli vacation schedule","volume":"64","author":"Wu","year":"2013","journal-title":"Comp. Ind. Eng."},{"key":"ref_5","first-page":"233","article-title":"A preemptive priority retrial queue with two classes of customers and general retrial times","volume":"15","author":"Gao","year":"2015","journal-title":"Oper. Res."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"116","DOI":"10.1007\/s12597-015-0218-5","article-title":"On the discrete-time Geo\/G\/1 retrial queueing system with preemptive resume and Bernoulli feedback","volume":"53","author":"Peng","year":"2016","journal-title":"Opsearch"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/S0166-5316(02)00057-3","article-title":"M\/M\/1 queues with working vacations","volume":"50","author":"Servi","year":"2002","journal-title":"Perform. Eval."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"654","DOI":"10.1016\/j.peva.2005.05.005","article-title":"M\/G\/1 queue with multiple working vacations","volume":"63","author":"Wu","year":"2006","journal-title":"Perform. Eval."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s00236-009-0110-y","article-title":"M\/M\/1 retrial queue with working vacations","volume":"47","year":"2010","journal-title":"Acta Inform."},{"key":"ref_10","first-page":"33","article-title":"A survey on working vacation queueing models","volume":"106","author":"Chandrasekaran","year":"2016","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"434","DOI":"10.1007\/s12597-013-0154-1","article-title":"Performance analysis of a single server retrial queue with working vacation","volume":"51","author":"Arivudainambi","year":"2014","journal-title":"Opsearch"},{"key":"ref_12","first-page":"06","article-title":"An M\/G\/1 retrial queue with general retrial times, working vacations and vacation interruption","volume":"31","author":"Gao","year":"2014","journal-title":"Asia-Pac. J. Oper. Res."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.asej.2016.03.008","article-title":"Analysis of an unreliable retrial G-queue with working vacations and vacation interruption under Bernoulli schedule","volume":"9","author":"Rajadurai","year":"2018","journal-title":"Ain Shams Eng. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1564","DOI":"10.1016\/j.apm.2012.04.045","article-title":"An M\/G\/1 queue with single working vacation and vacation interruption under Bernoulli schedule","volume":"37","author":"Gao","year":"2013","journal-title":"Appl. Math. Model."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1007\/s12597-014-0183-4","article-title":"An M\/G\/1 G-queue with server breakdown, working vacations and vacation interruption","volume":"52","author":"Zhan","year":"2015","journal-title":"Opsearch"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1016\/j.cie.2012.04.018","article-title":"A queue with working breakdowns","volume":"63","author":"Kalidass","year":"2012","journal-title":"Comput. Ind. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1788","DOI":"10.1016\/j.apm.2013.09.016","article-title":"The M\/G\/1 queue with disasters and working breakdowns","volume":"38","author":"Kim","year":"2014","journal-title":"Appl. Math. Model."},{"key":"ref_18","first-page":"1545","article-title":"M\/M\/1 vacation queueing system with working breakdowns and variable arrival rate","volume":"11","author":"Ma","year":"2015","journal-title":"J. Comput. Inf. Syst."},{"key":"ref_19","first-page":"859","article-title":"An M\/M\/1\/N Queue with Working Breakdowns and Vacations","volume":"119","author":"Deepa","year":"2018","journal-title":"Int. J. Pure Appl. Math."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"707","DOI":"10.1080\/00207160.2015.1128531","article-title":"The GI\/M\/1 queue in a multi-phase service environment with disasters and working breakdowns","volume":"94","author":"Jiang","year":"2017","journal-title":"Int. J. Comput. Math."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1051\/ro\/2014014","article-title":"The MX\/M\/1 queue with working breakdown","volume":"48","author":"Liu","year":"2014","journal-title":"Rairo Oper. Res. Rech. Op\u00e9r."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1051\/ro\/2017091","article-title":"Sensitivity analysis of an M\/G\/1 retrial queueing system with disaster under working vacations and working breakdowns","volume":"52","author":"Rajadurai","year":"2018","journal-title":"Rairo Oper. Res."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"863","DOI":"10.1007\/s11277-016-3581-5","article-title":"PRIN: A Priority-Based Energy Efficient MAC Protocol for Wireless Sensor Networks Varying the Sample Inter-Arrival Time","volume":"92","author":"Anandakumar","year":"2017","journal-title":"Wirel. Pers. Commun."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.cie.2015.01.017","article-title":"Cost-minimization analysis of a working vacation queue with N-policy and server breakdowns","volume":"82","author":"Yang","year":"2015","journal-title":"Comp. Ind. Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1058","DOI":"10.1287\/opre.17.6.1058","article-title":"Some conditions for Ergodicity and recurrence of Markov chains","volume":"17","author":"Pakes","year":"1969","journal-title":"Oper. Res."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1287\/opre.31.4.783","article-title":"Mean drifts and the non Ergodicity of Markov chains","volume":"31","author":"Sennott","year":"1983","journal-title":"Oper. Res."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/419\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:39:47Z","timestamp":1760186387000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/3\/419"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,21]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["sym11030419"],"URL":"https:\/\/doi.org\/10.3390\/sym11030419","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,21]]}}}