{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,7]],"date-time":"2026-03-07T18:09:18Z","timestamp":1772906958090,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T00:00:00Z","timestamp":1739232000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Sciences and Engineering Research Council of Canada"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>An Erlang loss system, which is an M\/G\/s\/s queue, is a model used in various applications. In this paper, a controlled version of the process is defined. The objective is to maximize the expected time until the system is full when the service time is exponentially distributed. The control variable is the service rate. The dynamic programming equation satisfied by the value function F, from which the optimal control follows at once, is derived, and F is found explicitly when s=2 and s=3. The problem of minimising the probability of the system being saturated is also considered.<\/jats:p>","DOI":"10.3390\/axioms14020130","type":"journal-article","created":{"date-parts":[[2025,2,11]],"date-time":"2025-02-11T05:34:32Z","timestamp":1739252072000},"page":"130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Optimal Control Problems for Erlang Loss Systems"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9451-543X","authenticated-orcid":false,"given":"Mario","family":"Lefebvre","sequence":"first","affiliation":[{"name":"Department of Mathematics and Industrial Engineering, Polytechnique Montr\u00e9al, P.O. Box 6079, Station Centre-Ville, Montr\u00e9al, QC H3C 3A7, Canada"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,11]]},"reference":[{"key":"ref_1","unstructured":"Smith, P.J., Sathyendran, A., and Murch, A.R. (1999, January 16\u201320). Analysis of traffic distribution in cellular networks. Proceedings of the 1999 IEEE 49th Vehicular Technology Conference, Houston, TX, USA."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"814740","DOI":"10.1155\/2008\/814740","article-title":"An Erlang loss queue with time-phased batch arrivals as a model for traffic control in communication networks","volume":"2008","author":"Lee","year":"2008","journal-title":"Math. Probl. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s10729-008-9077-4","article-title":"Erlang loss models for the static deployment of ambulances","volume":"12","author":"Restrepo","year":"2009","journal-title":"Health Care Manag. 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[13th ed.]."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/130\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:31:06Z","timestamp":1760027466000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/130"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,11]]},"references-count":20,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["axioms14020130"],"URL":"https:\/\/doi.org\/10.3390\/axioms14020130","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,11]]}}}