{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T14:13:22Z","timestamp":1769696002392,"version":"3.49.0"},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T00:00:00Z","timestamp":1728518400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We consider an <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"https:\/\/linproxy.fan.workers.dev:443\/http\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S0021900224000780_inline3.png\"\/><jats:tex-math>\n$\\mathrm{M}\/\\mathrm{G}\/\\infty$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> queue with infinite expected service time. We then provide the transience\/recurrence classification of the states (the system is said to be at state <jats:italic>n<\/jats:italic> if there are <jats:italic>n<\/jats:italic> customers being served), observing also that here (unlike irreducible Markov chains, for example) it is possible for recurrent and transient states to coexist. We also prove a lower bound on the growth speed in the transient case.<\/jats:p>","DOI":"10.1017\/jpr.2024.78","type":"journal-article","created":{"date-parts":[[2024,10,10]],"date-time":"2024-10-10T12:35:04Z","timestamp":1728563704000},"page":"572-575","update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["On transience of \n$\\mathrm{M}\/\\mathrm{G}\/\\infty$\n queues"],"prefix":"10.1017","volume":"62","author":[{"ORCID":"https:\/\/linproxy.fan.workers.dev:443\/https\/orcid.org\/0000-0002-5076-8048","authenticated-orcid":false,"given":"Serguei","family":"Popov","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,10,10]]},"reference":[{"key":"S0021900224000780_ref2","unstructured":"[2] Menshikov, M. , Popov, S. and Wade, A. (2024). Semi-infinite particle systems with exclusion interaction and heterogeneous jump rates. Available at arXiv:2405.05246."},{"key":"S0021900224000780_ref1","unstructured":"[1] Foucart, C. and Y., Linglong (2023). Extremal shot noise processes and random cutout sets. Available at arXiv:2302.03082 (to appear in Bernoulli)."},{"key":"S0021900224000780_ref3","doi-asserted-by":"publisher","DOI":"10.1137\/0114007"}],"container-title":["Journal of Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0021900224000780","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,23]],"date-time":"2025-04-23T09:47:17Z","timestamp":1745401637000},"score":1,"resource":{"primary":{"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/www.cambridge.org\/core\/product\/identifier\/S0021900224000780\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,10]]},"references-count":3,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,6]]}},"alternative-id":["S0021900224000780"],"URL":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1017\/jpr.2024.78","relation":{},"ISSN":["0021-9002","1475-6072"],"issn-type":[{"value":"0021-9002","type":"print"},{"value":"1475-6072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,10,10]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/linproxy.fan.workers.dev:443\/https\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}