{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T14:02:03Z","timestamp":1768744923147,"version":"3.49.0"},"reference-count":33,"publisher":"Association for Computing Machinery (ACM)","issue":"1","license":[{"start":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T00:00:00Z","timestamp":1677456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-19-CE23-0015"],"award-info":[{"award-number":["ANR-19-CE23-0015"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Proc. ACM Meas. Anal. Comput. Syst."],"published-print":{"date-parts":[[2023,2,27]]},"abstract":"<jats:p>Mean field approximation is a powerful technique which has been used in many settings to study large-scale stochastic systems. In the case of two-timescale systems, the approximation is obtained by a combination of scaling arguments and the use of the averaging principle. This paper analyzes the approximation error of this 'average' mean field model for a two-timescale model (X, Y), where the slow component X describes a population of interacting particles which is fully coupled with a rapidly changing environment Y. The model is parametrized by a scaling factor N, e.g. the population size, which as N gets large decreases the jump size of the slow component in contrast to the unchanged dynamics of the fast component. We show that under relatively mild conditions, the 'average' mean field approximation has a bias of order O(1\/N) compared to E[X]. This holds true under any continuous performance metric in the transient regime, as well as for the steady-state if the model is exponentially stable. To go one step further, we derive a bias correction term for the steady-state, from which we define a new approximation called the refined 'average' mean field approximation whose bias is of order O(1\/N2). This refined 'average' mean field approximation allows computing an accurate approximation even for small scaling factors, i.e., N ~10 -50. We illustrate the developed framework and accuracy results through an application to a random access CSMA model.<\/jats:p>","DOI":"10.1145\/3579336","type":"journal-article","created":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T23:50:57Z","timestamp":1677801057000},"page":"1-29","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Bias and Refinement of Multiscale Mean Field Models"],"prefix":"10.1145","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4629-6348","authenticated-orcid":false,"given":"Sebastian","family":"Allmeier","sequence":"first","affiliation":[{"name":"Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, Grenoble, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6884-8698","authenticated-orcid":false,"given":"Nicolas","family":"Gast","sequence":"additional","affiliation":[{"name":"Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, Grenoble, France"}]}],"member":"320","published-online":{"date-parts":[[2023,3,2]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1214\/105051606000000420"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2008.03.005"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCOM.1987.1096769"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2010.5.31"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/stsy.2021.0085"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1214\/16-AAP1211"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1214\/15-SSY212"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1214\/20-AAP1609"},{"key":"e_1_2_1_9_1","doi-asserted-by":"crossref","unstructured":"F. Cecchi. 2018. Mean-field limits for ultra-dense random-access networks. Technische Universiteit Eindhoven. Proefschrift.","DOI":"10.1145\/3199524.3199545"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1287\/stsy.2021.0068"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1239\/aap"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/3084454"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2018.09.005"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1177\/075910639203700105"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1145\/3154491"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","unstructured":"P.J. Hunt and T.G. Kurtz. 1994. Large loss networks. Stochastic Processes and their Applications 53 2 (oct 1994) 363--378. https:\/\/doi.org\/10.1016\/0304--4149(94)90071-X","DOI":"10.1016\/0304--4149(94)90071-X"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024--3795(82)90218-X"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479892237562"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1214\/12-AAP841"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/13-AAP934"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.2307\/3212147"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304--4149(78)90020-0"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/QEST.2007.8"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.7717\/peerj-cs.103"},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/71.963420"},{"key":"e_1_2_1_26_1","volume-title":"Stuart","author":"Pavliotis Grigorios A.","year":"2008","unstructured":"Grigorios A. Pavliotis and Andrew M. Stuart. 2008. Multiscale Methods: Averaging and Homogenization. Texts Applied in Mathematics, Vol. 53. Springer New York, New York, NY."},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/978--1--4612--5561--1"},{"key":"e_1_2_1_28_1","volume-title":"Differential Equations and Dynamical Systems","author":"Perko Lawrence","unstructured":"Lawrence Perko. 2001. Differential Equations and Dynamical Systems (3rd ed.). Number 7 in Texts in Applied Mathematics. Springer-Verlag, Berlin, Heidelberg.","edition":"3"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1137\/20M1382891"},{"key":"e_1_2_1_30_1","volume-title":"Approximate Computation of Expectations","author":"Stein Charles","unstructured":"Charles Stein. 1986. Approximate Computation of Expectations. Vol. 7. Institute of Mathematical Statistics. i--164 pages. http:\/\/www.jstor.org\/stable\/4355512"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2010.08.011"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/INFCOM.2005.1497875"},{"key":"e_1_2_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/2896377.2901463"}],"container-title":["Proceedings of the ACM on Measurement and Analysis of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3579336","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3579336","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:49:27Z","timestamp":1750182567000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3579336"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,27]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2023,2,27]]}},"alternative-id":["10.1145\/3579336"],"URL":"https:\/\/doi.org\/10.1145\/3579336","relation":{},"ISSN":["2476-1249"],"issn-type":[{"value":"2476-1249","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,27]]},"assertion":[{"value":"2023-03-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}