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Rev."],"published-print":{"date-parts":[[2007,12]]},"abstract":"<jats:p>\n            We consider the stationary solution of large ergodic continuous-time Markov chains (CTMCs) with a finite state space\n            <jats:italic>S<\/jats:italic>\n            , i.e., the computation of \u03c0 as solution of \u03c0 \u00b7\n            <jats:bold>Q<\/jats:bold>\n            = 0 subject to \u2211\n            <jats:sub>\n              <jats:bold>i<\/jats:bold>\n              \u03b5\n              <jats:italic>s<\/jats:italic>\n            <\/jats:sub>\n            \u03c0[\n            <jats:bold>i<\/jats:bold>\n            ] = 1, where\n            <jats:bold>Q<\/jats:bold>\n            coincides with transition rate matrix\n            <jats:bold>R<\/jats:bold>\n            except in its diagonal elements,\n            <jats:bold>Q<\/jats:bold>\n            [\n            <jats:bold>i, i<\/jats:bold>\n            ] = - \u2211\n            <jats:sub>\n              <jats:bold>j<\/jats:bold>\n              \u03b5\n              <jats:italic>s<\/jats:italic>\n            <\/jats:sub>\n            <jats:bold>R<\/jats:bold>\n            [\n            <jats:bold>i, j<\/jats:bold>\n            ].\n          <\/jats:p>","DOI":"10.1145\/1328690.1328697","type":"journal-article","created":{"date-parts":[[2008,1,3]],"date-time":"2008-01-03T18:20:10Z","timestamp":1199384410000},"page":"16-18","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["Approximating stationary measures of structured continuous-time Markov models using matrix diagrams"],"prefix":"10.1145","volume":"35","author":[{"given":"Gianfranco","family":"Ciardo","sequence":"first","affiliation":[{"name":"University of California at Riverside"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrew S.","family":"Miner","sequence":"additional","affiliation":[{"name":"Iowa State University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Wan","sequence":"additional","affiliation":[{"name":"University of California at Riverside"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andy Jinqing","family":"Yu","sequence":"additional","affiliation":[{"name":"University of California at Riverside"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2007,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/TR.1981.5221004"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.12.3.203.12634"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.peva.2005.06.001"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.5555\/826035.826829"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/278298.278303"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/882474.883484"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/339331.339417"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCAD.1990.129849"},{"key":"e_1_2_1_9_1","volume-title":"Introduction to the Numerical Solution of Markov Chains","author":"Stewart W. J.","year":"1994","unstructured":"W. J. Stewart . Introduction to the Numerical Solution of Markov Chains . Princeton University Press , 1994 . W. J. Stewart. Introduction to the Numerical Solution of Markov Chains. Princeton University Press, 1994."}],"container-title":["ACM SIGMETRICS Performance Evaluation Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1328690.1328697","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1328690.1328697","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:51:58Z","timestamp":1750258318000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1328690.1328697"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12]]},"references-count":9,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,12]]}},"alternative-id":["10.1145\/1328690.1328697"],"URL":"https:\/\/doi.org\/10.1145\/1328690.1328697","relation":{},"ISSN":["0163-5999"],"issn-type":[{"value":"0163-5999","type":"print"}],"subject":[],"published":{"date-parts":[[2007,12]]},"assertion":[{"value":"2007-12-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}