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The probability generating function and marginal generating function of orbit size are obtained in a steady state. The stability condition for each vacation model is derived. Performance measures such as mean orbit size, mean system size, mean waiting time of a customer, and the probabilities of the server being in different states have also been determined. Based on performance characteristics, a comparative analysis is performed among the three vacations. Numerical illustrations are displayed to establish the consistency of the theory developed.<\/jats:p>","DOI":"10.1051\/ro\/2022042","type":"journal-article","created":{"date-parts":[[2022,3,10]],"date-time":"2022-03-10T19:53:05Z","timestamp":1646941985000},"page":"1089-1117","source":"Crossref","is-referenced-by-count":5,"title":["Performance analysis of discrete-time <i>Geo<\/i><sup><i>X<\/i><\/sup>\/<i>G<\/i>\/1 retrial queue with various vacation policies and impatient customers"],"prefix":"10.1051","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7868-8090","authenticated-orcid":false,"given":"Rajasudha","family":"R","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4877-2400","authenticated-orcid":false,"given":"Arumuganathan","family":"R","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2892-0864","authenticated-orcid":false,"given":"Dharmaraja","family":"S","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2022,5,12]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1016\/j.jkss.2008.04.006","volume":"37","author":"Aboul-Hassan","year":"2008","journal-title":"J. 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