{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,7]],"date-time":"2026-02-07T13:26:46Z","timestamp":1770470806631,"version":"3.49.0"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T00:00:00Z","timestamp":1708300800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2017S1A5A2A01023654"],"award-info":[{"award-number":["2017S1A5A2A01023654"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100002619","name":"Ajou University","doi-asserted-by":"publisher","award":["2018"],"award-info":[{"award-number":["2018"]}],"id":[{"id":"10.13039\/501100002619","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2024,4]]},"DOI":"10.1007\/s10479-024-05851-7","type":"journal-article","created":{"date-parts":[[2024,2,19]],"date-time":"2024-02-19T13:02:20Z","timestamp":1708347740000},"page":"237-259","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The superposition of Markovian arrival processes: moments and the minimal Laplace transform"],"prefix":"10.1007","volume":"335","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6564-8906","authenticated-orcid":false,"given":"Sunkyo","family":"Kim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,2,19]]},"reference":[{"issue":"2","key":"5851_CR1","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1287\/mnsc.28.2.126","volume":"28","author":"SL Albin","year":"1982","unstructured":"Albin, S. L. (1982). On Poisson approximations for superposition arrival processes in queues. Management Science, 28(2), 126\u2013137.","journal-title":"Management Science"},{"issue":"2","key":"5851_CR2","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1016\/j.ejor.2007.06.020","volume":"190","author":"L Bodrog","year":"2008","unstructured":"Bodrog, L., Heindl, A., Horv\u00e1th, G., & Telek, M. (2008). A Markovian canonical form of second-order matrix-exponential processes. European Journal of Operational Research, 190(2), 459\u2013477.","journal-title":"European Journal of Operational Research"},{"issue":"1","key":"5851_CR3","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/s10479-007-0296-8","volume":"160","author":"L Bodrog","year":"2008","unstructured":"Bodrog, L., Horv\u00e1th, G., & Telek, M. (2008). Moment characterization of matrix exponential and Markovian arrival processes. Annals of Operations Research, 160(1), 51\u201368.","journal-title":"Annals of Operations Research"},{"issue":"2","key":"5851_CR4","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.peva.2009.09.003","volume":"67","author":"G Casale","year":"2010","unstructured":"Casale, G., Zhang, E., & Smirni, E. (2010). Trace data characterization and fitting for Markov modeling. Performance Evaluation, 67(2), 61\u201379.","journal-title":"Performance Evaluation"},{"key":"5851_CR5","volume-title":"The theory of matrices","author":"FR Gantmacher","year":"1960","unstructured":"Gantmacher, F. R. (1960). The theory of matrices. New York: Chelsea Publishing."},{"issue":"9","key":"5851_CR6","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1016\/j.peva.2009.12.006","volume":"67","author":"A Horv\u00e1th","year":"2010","unstructured":"Horv\u00e1th, A., Horv\u00e1th, G., & Telek, M. (2010). A joint moments based analysis of networks of MAP\/MAP\/1 queues. Performance Evaluation, 67(9), 759\u2013778.","journal-title":"Performance Evaluation"},{"issue":"4","key":"5851_CR7","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1109\/26.996078","volume":"50","author":"SH Kang","year":"2002","unstructured":"Kang, S. H., Kim, Y. H., Sung, D. K., & Choi, B. D. (2002). An application of Markovian arrival process (MAP) to modeling superposed ATM cell streams. IEEE Transactions on Communications, 50(4), 633\u2013642.","journal-title":"IEEE Transactions on Communications"},{"key":"5851_CR8","doi-asserted-by":"publisher","first-page":"736","DOI":"10.1016\/S0377-2217(03)00299-6","volume":"157","author":"S Kim","year":"2004","unstructured":"Kim, S. (2004). The heavy-traffic bottleneck phenomenon under splitting and superposition. European Journal of Operational Research, 157, 736\u2013745.","journal-title":"European Journal of Operational Research"},{"issue":"2","key":"5851_CR9","doi-asserted-by":"publisher","first-page":"480","DOI":"10.1287\/opre.1100.0893","volume":"59","author":"S Kim","year":"2011","unstructured":"Kim, S. (2011). Modeling cross correlation in three-moment four-parameter decomposition approximation of queueing networks. Operations Research, 59(2), 480\u2013497.","journal-title":"Operations Research"},{"issue":"7","key":"5851_CR10","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1002\/nav.21719","volume":"63","author":"S Kim","year":"2017","unstructured":"Kim, S. (2017). Minimal LST representations of MAP($$n$$)s: Moment fittings and queueing approximations. Naval Research Logistics, 63(7), 549\u2013561.","journal-title":"Naval Research Logistics"},{"issue":"5","key":"5851_CR11","doi-asserted-by":"publisher","first-page":"261","DOI":"10.1007\/s11134-005-6967-8","volume":"49","author":"S Kim","year":"2005","unstructured":"Kim, S., Muralidharan, R., & O\u2019Cinneide, C. (2005). Taking account of correlations between streams in queueing network approximations. Queueing Systems, 49(5), 261\u2013281.","journal-title":"Queueing Systems"},{"issue":"6","key":"5851_CR12","doi-asserted-by":"publisher","first-page":"833","DOI":"10.1109\/JSAC.1986.1146402","volume":"4","author":"K Sriram","year":"1986","unstructured":"Sriram, K., & Whitt, W. (1986). Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, 4(6), 833\u2013846.","journal-title":"IEEE Journal on Selected Areas in Communications"},{"key":"5851_CR13","doi-asserted-by":"publisher","first-page":"1080","DOI":"10.1287\/mnsc.36.9.1080","volume":"36","author":"S Suresh","year":"1990","unstructured":"Suresh, S., & Whitt, W. (1990). Arranging queues in series: A simulation experiment. Management Science, 36, 1080\u20131091.","journal-title":"Management Science"},{"key":"5851_CR14","doi-asserted-by":"publisher","first-page":"355","DOI":"10.1016\/0167-6377(90)90054-9","volume":"9","author":"S Suresh","year":"1990","unstructured":"Suresh, S., & Whitt, W. (1990). The heavy-traffic bottleneck phenomenon in open queueing networks. Operations Research Letters, 9, 355\u2013362.","journal-title":"Operations Research Letters"},{"issue":"9\u201312","key":"5851_CR15","doi-asserted-by":"publisher","first-page":"1153","DOI":"10.1016\/j.peva.2007.06.001","volume":"64","author":"M Telek","year":"2007","unstructured":"Telek, M., & Horv\u00e1th, G. (2007). A minimal representation of Markov arrival processes and a moments matching method. Performance Evaluation, 64(9\u201312), 1153\u20131168.","journal-title":"Performance Evaluation"},{"issue":"9","key":"5851_CR16","doi-asserted-by":"publisher","first-page":"2779","DOI":"10.1002\/j.1538-7305.1983.tb03204.x","volume":"62","author":"W Whitt","year":"1983","unstructured":"Whitt, W. (1983). The queueing network analyzer. The Bell System Technical Journal, 62(9), 2779\u20132815.","journal-title":"The Bell System Technical Journal"},{"issue":"1","key":"5851_CR17","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1016\/0304-4149(85)90378-3","volume":"21","author":"W Whitt","year":"1985","unstructured":"Whitt, W. (1985). Queues with superposition arrival processes in heavy traffic. Stochastic Processes and their Applications, 21(1), 81\u201391.","journal-title":"Stochastic Processes and their Applications"},{"key":"5851_CR18","doi-asserted-by":"crossref","unstructured":"Whitt, W., & You, W. (2021). A robust queueing network analyzer based on indices of dispersion. Naval Research Logistics, 69(1), 36\u201356.","DOI":"10.1002\/nav.22010"}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-024-05851-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-024-05851-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-024-05851-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T16:25:57Z","timestamp":1711729557000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-024-05851-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,19]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,4]]}},"alternative-id":["5851"],"URL":"https:\/\/doi.org\/10.1007\/s10479-024-05851-7","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,19]]},"assertion":[{"value":"28 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 February 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}