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We develop minimax optimal estimators of <jats:italic>G<\/jats:italic> and study behavior of the minimax pointwise risk over a suitable family of service time distribution functions. In addition, we address the problem of adaptive estimation and propose a data\u2013driven estimation procedure that adapts to unknown smoothness of the service time distribution function\u00a0<jats:italic>G<\/jats:italic>. Lastly, a numerical study is presented to illustrate practical performance of the developed adaptive procedure.\n<\/jats:p>","DOI":"10.1007\/s11134-024-09921-2","type":"journal-article","created":{"date-parts":[[2024,7,27]],"date-time":"2024-07-27T19:01:24Z","timestamp":1722106884000},"page":"81-123","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive minimax estimation of service time distribution in the $$M_t\/G\/\\infty $$ queue from departure data"],"prefix":"10.1007","volume":"108","author":[{"given":"Wenwen","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5496-5583","authenticated-orcid":false,"given":"Alexander","family":"Goldenshluger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,7,27]]},"reference":[{"key":"9921_CR1","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1214\/13-EJS796","volume":"7","author":"F Abramovich","year":"2013","unstructured":"Abramovich, F., Pensky, M., Rozenholc, Y.: Laplace deconvolution with noisy observations. 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