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Queue length distributions can provide insight into the impact of system design changes that go beyond simple averages, but conventional queueing theory lacks efficient techniques for estimating the long-run queue length distribution when service times are not exponential. The approximate queue lengths depend on only the first and second moments of the service time rather than the full service time distribution, resulting in a model that is applicable to a wide variety of systems. Validation results show that the new approximation is highly accurate for light-tailed service time distributions. Work in progress includes developing accurate approximations for multi-server queues and heavy-tailed service distributions.<\/jats:p>","DOI":"10.1145\/2425248.2425268","type":"journal-article","created":{"date-parts":[[2013,1,8]],"date-time":"2013-01-08T15:34:16Z","timestamp":1357659256000},"page":"77-79","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Estimating queue length distributions for queues with random arrivals"],"prefix":"10.1145","volume":"40","author":[{"given":"Daniel S.","family":"Myers","sequence":"first","affiliation":[{"name":"University of Wisconsin-Madison"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mary K.","family":"Vernon","sequence":"additional","affiliation":[{"name":"University of Wisconsin-Madison"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,1,4]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Conditional ages and residual service times in the M\/G\/1 queue. 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Ross . Stochastic Processes . John Wiley and Sons , New York , 1983 . S. Ross. Stochastic Processes. John Wiley and Sons, New York, 1983."},{"key":"e_1_2_1_7_1","volume-title":"Stochastic Modelling and Analysis: A Computational Approach","author":"Tijms H.C.","year":"1986","unstructured":"H.C. Tijms . Stochastic Modelling and Analysis: A Computational Approach . John Wiley and Sons , Great Britain , 1986 . H.C. Tijms. Stochastic Modelling and Analysis: A Computational Approach. John Wiley and Sons, Great Britain, 1986."}],"container-title":["ACM SIGMETRICS Performance Evaluation Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2425248.2425268","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2425248.2425268","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T20:14:09Z","timestamp":1750277649000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2425248.2425268"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,4]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2012,12,4]]}},"alternative-id":["10.1145\/2425248.2425268"],"URL":"https:\/\/doi.org\/10.1145\/2425248.2425268","relation":{},"ISSN":["0163-5999"],"issn-type":[{"type":"print","value":"0163-5999"}],"subject":[],"published":{"date-parts":[[2012,1,4]]},"assertion":[{"value":"2012-01-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}