{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:19:56Z","timestamp":1773656396965,"version":"3.50.1"},"publisher-location":"Cham","reference-count":27,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030430238","type":"print"},{"value":"9783030430245","type":"electronic"}],"license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020]]},"DOI":"10.1007\/978-3-030-43024-5_11","type":"book-chapter","created":{"date-parts":[[2020,3,8]],"date-time":"2020-03-08T20:02:15Z","timestamp":1583697735000},"page":"173-189","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Parallelization of EM-Algorithms for Markovian Arrival Processes"],"prefix":"10.1007","author":[{"given":"Andreas","family":"Blume","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Buchholz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jan","family":"Kriege","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,3,9]]},"reference":[{"key":"11_CR1","unstructured":"The internet traffic archive. \nhttp:\/\/ita.ee.lbl.gov\/"},{"key":"11_CR2","unstructured":"The parmap software. \nhttps:\/\/github.com\/minbraz\/parmap\/"},{"issue":"4","key":"11_CR3","first-page":"419","volume":"23","author":"S Asmussen","year":"1996","unstructured":"Asmussen, S., Nerman, O., Olsson, M.: Fitting phase-type distributions via the EM-algorithm. Scand. J. Stat. 23(4), 419\u2013441 (1996)","journal-title":"Scand. J. Stat."},{"key":"11_CR4","doi-asserted-by":"crossref","unstructured":"Bause, F., Buchholz, P., Kriege, J.: ProFiDo - the processes fitting toolkit Dortmund. In: QEST 2010, Seventh International Conference on the Quantitative Evaluation of Systems, Williamsburg, Virginia, USA, 15\u201318 September 2010, pp. 87\u201396. IEEE Computer Society (2010)","DOI":"10.1109\/QEST.2010.20"},{"key":"11_CR5","unstructured":"Blume, A.: Parallelisierung von Methoden zur Parameteranpassung von MAPs. Master\u2019s thesis, Fakult\u00e4t f\u00fcr Informatik, TU Dortmund (2019)"},{"key":"11_CR6","doi-asserted-by":"publisher","first-page":"50","DOI":"10.1016\/j.peva.2018.05.001","volume":"123\u2013124","author":"M Brazenas","year":"2018","unstructured":"Brazenas, M., Horvath, G., Telek, M.: Parallel algorithms for fitting Markov arrival processes. Perform. Eval. 123\u2013124, 50\u201367 (2018)","journal-title":"Perform. Eval."},{"issue":"1\u20134","key":"11_CR7","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1023\/A:1020981005544","volume":"112","author":"L Breuer","year":"2002","unstructured":"Breuer, L.: An EM algorithm for batch Markovian arrival processes and its comparison to a simpler estimation procedure. Ann. OR 112(1\u20134), 123\u2013138 (2002)","journal-title":"Ann. OR"},{"key":"11_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1007\/978-3-540-45232-4_14","volume-title":"Computer Performance Evaluation. Modelling Techniques and Tools","author":"P Buchholz","year":"2003","unstructured":"Buchholz, P.: An EM-algorithm for MAP fitting from real traffic data. In: Kemper, P., Sanders, W.H. (eds.) TOOLS 2003. LNCS, vol. 2794, pp. 218\u2013236. Springer, Heidelberg (2003). \nhttps:\/\/doi.org\/10.1007\/978-3-540-45232-4_14"},{"issue":"11","key":"11_CR9","doi-asserted-by":"publisher","first-page":"1092","DOI":"10.1016\/j.peva.2010.08.006","volume":"67","author":"P Buchholz","year":"2010","unstructured":"Buchholz, P., Kemper, P., Kriege, J.: Multi-class Markovian arrival processes and their parameter fitting. Perform. Eval. 67(11), 1092\u20131106 (2010)","journal-title":"Perform. Eval."},{"key":"11_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06674-5","volume-title":"Input Modeling with Phase-Type Distributions and Markov Models - Theory and Applications","author":"P Buchholz","year":"2014","unstructured":"Buchholz, P., Kriege, J., Felko, I.: Input Modeling with Phase-Type Distributions and Markov Models - Theory and Applications. Springer, New York (2014)"},{"key":"11_CR11","doi-asserted-by":"crossref","unstructured":"Casale, G.: Building accurate workload models using Markovian arrival processes. In: Merchant, A., Keeton, K., Rubenstein, D. (eds.) Proceedings of the 2011 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems SIGMETRICS 2011, San Jose, CA, USA, 07\u201311 June 2011 (Co-located with FCRC 2011), pp. 357\u2013358. ACM (2011)","DOI":"10.1145\/1993744.1993783"},{"key":"11_CR12","doi-asserted-by":"crossref","unstructured":"Casale, G., Zhang, E.Z., Smirni, E.: KPC-toolbox: simple yet effective trace fitting using Markovian arrival processes. In: QEST, pp. 83\u201392 (2008)","DOI":"10.1109\/QEST.2008.33"},{"issue":"4","key":"11_CR13","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1145\/42404.42409","volume":"31","author":"BL Fox","year":"1988","unstructured":"Fox, B.L., Glynn, P.W.: Computing poisson probabilities. Commun. ACM 31(4), 440\u2013445 (1988)","journal-title":"Commun. ACM"},{"key":"11_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"119","DOI":"10.1007\/978-3-642-40725-3_10","volume-title":"Computer Performance Engineering","author":"G Horv\u00e1th","year":"2013","unstructured":"Horv\u00e1th, G., Okamura, H.: A fast EM algorithm for fitting marked markovian arrival processes with a new special structure. In: Balsamo, M.S., Knottenbelt, W.J., Marin, A. (eds.) EPEW 2013. LNCS, vol. 8168, pp. 119\u2013133. Springer, Heidelberg (2013). \nhttps:\/\/doi.org\/10.1007\/978-3-642-40725-3_10"},{"key":"11_CR15","doi-asserted-by":"crossref","unstructured":"Horv\u00e1th, G., Telek, M., Buchholz, P.: A MAP fitting approach with independent approximation of the inter-arrival time distribution and the lag-correlation. In: QEST, pp. 124\u2013133. IEEE CS Press (2005)","DOI":"10.1109\/QEST.2005.1"},{"issue":"2","key":"11_CR16","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/S0166-5316(03)00067-1","volume":"54","author":"A Klemm","year":"2003","unstructured":"Klemm, A., Lindemann, C., Lohmann, M.: Modeling IP traffic using the batch Markovian arrival process. Perform. Eval. 54(2), 149\u2013173 (2003)","journal-title":"Perform. Eval."},{"key":"11_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1007\/978-3-642-12104-3_20","volume-title":"Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance","author":"J Kriege","year":"2010","unstructured":"Kriege, J., Buchholz, P.: An empirical comparison of MAP fitting algorithms. In: M\u00fcller-Clostermann, B., Echtle, K., Rathgeb, E.P. (eds.) MMB&DFT 2010. LNCS, vol. 5987, pp. 259\u2013273. Springer, Heidelberg (2010). \nhttps:\/\/doi.org\/10.1007\/978-3-642-12104-3_20"},{"key":"11_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-319-05359-2_1","volume-title":"Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance","author":"J Kriege","year":"2014","unstructured":"Kriege, J., Buchholz, P.: PH and MAP fitting with aggregated traffic traces. In: Fischbach, K., Krieger, U.R. (eds.) MMB&DFT 2014. LNCS, vol. 8376, pp. 1\u201315. Springer, Cham (2014). \nhttps:\/\/doi.org\/10.1007\/978-3-319-05359-2_1"},{"issue":"4","key":"11_CR19","doi-asserted-by":"publisher","first-page":"831","DOI":"10.1145\/322217.322232","volume":"27","author":"RE Ladner","year":"1980","unstructured":"Ladner, R.E., Fischer, M.J.: Parallel prefix computation. J. ACM 27(4), 831\u2013838 (1980)","journal-title":"J. ACM"},{"issue":"3","key":"11_CR20","doi-asserted-by":"publisher","first-page":"676","DOI":"10.2307\/1427464","volume":"22","author":"DM Lucantoni","year":"1990","unstructured":"Lucantoni, D.M., Meier-Hellstern, K.S., Neuts, M.F.: A single-server queue with server vacations and a class of non-renewal arrival processes. Adv. Appl. Probab. 22(3), 676\u2013705 (1990)","journal-title":"Adv. Appl. Probab."},{"key":"11_CR21","doi-asserted-by":"publisher","first-page":"764","DOI":"10.2307\/3213143","volume":"16","author":"MF Neuts","year":"1979","unstructured":"Neuts, M.F.: A versatile Markovian point process. J. Appl. Probab. 16, 764\u2013779 (1979)","journal-title":"J. Appl. Probab."},{"key":"11_CR22","doi-asserted-by":"crossref","unstructured":"Okamura, H., Dohi, T.: Faster maximum likelihood estimation algorithms for Markovian arrival processes. In: 2009 Sixth International Conference on the Quantitative Evaluation of Systems, pp. 73\u201382, September 2009","DOI":"10.1109\/QEST.2009.28"},{"issue":"10","key":"11_CR23","doi-asserted-by":"publisher","first-page":"938","DOI":"10.1016\/j.peva.2011.04.001","volume":"68","author":"H Okamura","year":"2011","unstructured":"Okamura, H., Dohi, T., Trivedi, K.S.: A refined EM algorithm for PH distributions. Perform. Eval. 68(10), 938\u2013954 (2011)","journal-title":"Perform. Eval."},{"issue":"7\u20138","key":"11_CR24","doi-asserted-by":"publisher","first-page":"629","DOI":"10.1016\/j.peva.2006.09.002","volume":"64","author":"A Panchenko","year":"2007","unstructured":"Panchenko, A., Th\u00fcmmler, A.: Efficient phase-type fitting with aggregated traffic traces. Perform. Eval. 64(7\u20138), 629\u2013645 (2007)","journal-title":"Perform. Eval."},{"key":"11_CR25","volume-title":"Introduction to the Numerical Solution of Markov Chains","author":"WJ Stewart","year":"1994","unstructured":"Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)"},{"issue":"3","key":"11_CR26","doi-asserted-by":"publisher","first-page":"245","DOI":"10.1109\/TDSC.2006.27","volume":"3","author":"A Th\u00fcmmler","year":"2006","unstructured":"Th\u00fcmmler, A., Buchholz, P., Telek, M.: A novel approach for phase-type fitting with the EM algorithm. IEEE Trans. Dep. Sec. Comput. 3(3), 245\u2013258 (2006)","journal-title":"IEEE Trans. Dep. Sec. Comput."},{"key":"11_CR27","unstructured":"Wu, C., Yang, C., Zhao, H., Zhu, J.: On the convergence of the EM algorithm: a data-adaptive analysis (2016)"}],"container-title":["Lecture Notes in Computer Science","Measurement, Modelling and Evaluation of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-43024-5_11","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,3,8]],"date-time":"2020-03-08T20:04:59Z","timestamp":1583697899000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-030-43024-5_11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"ISBN":["9783030430238","9783030430245"],"references-count":27,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-43024-5_11","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020]]},"assertion":[{"value":"9 March 2020","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"MMB","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Measurement, Modelling and Evaluation of Computing Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Saarbr\u00fccken","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Germany","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2020","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16 March 2020","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18 March 2020","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"20","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mmb2020","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/www.mmb2020.de\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"easychair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"32","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"16","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"50% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.375","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.27","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}