{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T19:50:24Z","timestamp":1779306624805,"version":"3.51.4"},"reference-count":21,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,27]],"date-time":"2022-09-27T00:00:00Z","timestamp":1664236800000},"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>The concept of a single server retrial queueing system with delayed repair and feedback under a working vacation policy, along with the asymmetric transition representation, is discussed in this article. In addition, consumers are entitled to balk and renege in some situations. The steady-state probability generating function for system size and orbit size is derived by using the approach of supplementary variables. Discussions include key metrics of the system and a few significant special conditions. Moreover, the impact of system parameters is examined through the analysis of some numerical examples.<\/jats:p>","DOI":"10.3390\/sym14102024","type":"journal-article","created":{"date-parts":[[2022,9,29]],"date-time":"2022-09-29T01:23:16Z","timestamp":1664414596000},"page":"2024","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":28,"title":["Analysis of an M\/G\/1 Retrial Queue with Delayed Repair and Feedback under Working Vacation policy with Impatient Customers"],"prefix":"10.3390","volume":"14","author":[{"given":"Micheal Mathavavisakan Nicholas","family":"GnanaSekar","sequence":"first","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632 014, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7765-094X","authenticated-orcid":false,"given":"Indhira","family":"Kandaiyan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore-632 014, Tamil Nadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Artalejo, J.R., and G\u00f3mez-Corral, A. 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