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By examining unobservable queues (fully unobservable and almost unobservable cases), it is possible to formulate an equilibrium joining strategy as well as the socially optimal probability of joining a fully unobservable queue. This paper also presents numerical examples illustrating how system parameters affect mixed equilibrium and socially optimal balking strategies.<\/jats:p>","DOI":"10.1051\/ro\/2024083","type":"journal-article","created":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T18:57:18Z","timestamp":1712343438000},"page":"2569-2589","source":"Crossref","is-referenced-by-count":4,"title":["Equilibrium balking strategies in unobservable queues with multiple vacations and an optional service"],"prefix":"10.1051","volume":"58","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0527-0961","authenticated-orcid":false,"given":"Dong-Yuh","family":"Yang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0007-6304-5395","authenticated-orcid":false,"given":"Yin-Ying","family":"Dai","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2155-2026","authenticated-orcid":false,"given":"Chia-Huang","family":"Wu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2024,6,25]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"685","DOI":"10.1080\/16843703.2020.1736365","volume":"17","author":"Aghsami","year":"2020","journal-title":"Qual. 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