{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:26:33Z","timestamp":1750307193518,"version":"3.41.0"},"reference-count":3,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2012,3,9]],"date-time":"2012-03-09T00:00:00Z","timestamp":1331251200000},"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":[[2012,3,9]]},"abstract":"<jats:p>The Laplace-Stieltjes transform of a matrix-exponential distribution is a rational function. If there are no common factors between the numerator and denominator polynomials, then the order of the matrix-exponential distribution is the degree of the denominator polynomial. Given a rational Laplace-Stieltjes transform, it is unknown, in general, when it corresponds to a matrix-exponential distribution. Matrix-exponential distributions of order 3 have been completely characterized in this manner, but in this talk we look at the problem of characterizing matrix-exponential distributions of order 4.<\/jats:p>","DOI":"10.1145\/2185395.2185408","type":"journal-article","created":{"date-parts":[[2012,4,24]],"date-time":"2012-04-24T18:41:10Z","timestamp":1335292870000},"page":"26-26","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Characterizing matrix-exponential distributions of order 4 (abstract only)"],"prefix":"10.1145","volume":"39","author":[{"given":"Mark","family":"Fackrell","sequence":"first","affiliation":[{"name":"University of Melbourne"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2012,4,9]]},"reference":[{"key":"e_1_2_1_1_1","series-title":"Lecture Notes in Pure and Applied Mathematics","first-page":"313","volume-title":"Matrix-analytic Methods in Stochastic Models","author":"ASMUSSEN S.","year":"1997"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100030231"},{"key":"e_1_2_1_3_1","first-page":"20","volume-title":"Summer Computer Simulation Conference","author":"LIPSKY L.","year":"1986"}],"container-title":["ACM SIGMETRICS Performance Evaluation Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2185395.2185408","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T10:06:02Z","timestamp":1750241162000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2185395.2185408"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,3,9]]},"references-count":3,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2012,3,9]]}},"alternative-id":["10.1145\/2185395.2185408"],"URL":"https:\/\/doi.org\/10.1145\/2185395.2185408","relation":{},"ISSN":["0163-5999"],"issn-type":[{"type":"print","value":"0163-5999"}],"subject":[],"published":{"date-parts":[[2012,3,9]]},"assertion":[{"value":"2012-04-09","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}