{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T23:57:34Z","timestamp":1780444654707,"version":"3.54.1"},"reference-count":10,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2019,1,25]],"date-time":"2019-01-25T00:00:00Z","timestamp":1548374400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGMETRICS Perform. Eval. Rev."],"published-print":{"date-parts":[[2019,1,25]]},"abstract":"<jats:p>Mean field approximation is a powerful tool to study the performance of large stochastic systems that is known to be exact as the system's size N goes to infinity. Recently, it has been shown that, when one wants to compute expected performance metric in steady-state, mean field approximation can be made more accurate by adding a term in 1\/N to the original approximation. This is called the refined mean field approximation in [7]. In this paper, we show how to obtain the same result for the transient regime and we provide a further refinement by expanding the term in 1\/N2 (both for transient and steady-state regime). Our derivations are inspired by moment-closure approximation. We provide a number of examples that show this new approximation is usable in practice for systems with up to a few tens of dimensions.<\/jats:p>","DOI":"10.1145\/3308897.3308909","type":"journal-article","created":{"date-parts":[[2019,1,28]],"date-time":"2019-01-28T14:01:39Z","timestamp":1548684099000},"page":"25-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["Size Expansions of Mean Field Approximation"],"prefix":"10.1145","volume":"46","author":[{"given":"Nicolas","family":"Gast","sequence":"first","affiliation":[{"name":"Univ. Grenoble Alpes, Grenoble, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luca","family":"Bortolussi","sequence":"additional","affiliation":[{"name":"University of Trieste, Trieste, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mirco","family":"Tribastone","sequence":"additional","affiliation":[{"name":"IMT School for Advanced Studies, Lucca, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2019,1,25]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2008.03.005"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2013.08.012"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/3084454"},{"key":"e_1_2_1_4_1","volume-title":"Refined mean field tool. https:\/\/github.com\/ngast\/rmf_tool","author":"Gast Nicolas","year":"2018","unstructured":"Nicolas Gast . Refined mean field tool. https:\/\/github.com\/ngast\/rmf_tool , 2018 . Nicolas Gast. Refined mean field tool. https:\/\/github.com\/ngast\/rmf_tool, 2018."},{"key":"e_1_2_1_5_1","volume-title":"Size expansions of mean field approximation: Transient and steady-state analysis. https:\/\/github.com\/ngast\/sizeExpansionMeanField","author":"Gast Nicolas","year":"2018","unstructured":"Nicolas Gast , Luca Bortolussi , and Mirco Tribastone . Size expansions of mean field approximation: Transient and steady-state analysis. https:\/\/github.com\/ngast\/sizeExpansionMeanField , 2018 . Nicolas Gast, Luca Bortolussi, and Mirco Tribastone. Size expansions of mean field approximation: Transient and steady-state analysis. https:\/\/github.com\/ngast\/sizeExpansionMeanField, 2018."},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/2745844.2745850"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/3154491"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.2307\/3212147"},{"issue":"1","key":"e_1_2_1_10_1","first-page":"20","article-title":"Queueing system with selection of the shortest of two queues: An asymptotic approach","volume":"32","author":"Vvedenskaya Nikita Dmitrievna","year":"1996","unstructured":"Nikita Dmitrievna Vvedenskaya , Roland L'vovich Dobrushin , and Fridrikh Izrailevich Karpelevich . Queueing system with selection of the shortest of two queues: An asymptotic approach . Problemy Peredachi Informatsii , 32 ( 1 ): 20 -- 34 , 1996 . Nikita Dmitrievna Vvedenskaya, Roland L'vovich Dobrushin, and Fridrikh Izrailevich Karpelevich. Queueing system with selection of the shortest of two queues: An asymptotic approach. Problemy Peredachi Informatsii, 32(1):20--34, 1996.","journal-title":"Problemy Peredachi Informatsii"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1145\/2896377.2901463"}],"container-title":["ACM SIGMETRICS Performance Evaluation Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3308897.3308909","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3308897.3308909","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T00:58:03Z","timestamp":1750208283000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3308897.3308909"}},"subtitle":["Transient and Steady-State Analysis"],"short-title":[],"issued":{"date-parts":[[2019,1,25]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,1,25]]}},"alternative-id":["10.1145\/3308897.3308909"],"URL":"https:\/\/doi.org\/10.1145\/3308897.3308909","relation":{},"ISSN":["0163-5999"],"issn-type":[{"value":"0163-5999","type":"print"}],"subject":[],"published":{"date-parts":[[2019,1,25]]},"assertion":[{"value":"2019-01-25","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}