{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:07:58Z","timestamp":1750306078759,"version":"3.41.0"},"reference-count":55,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2017,6,29]],"date-time":"2017-06-29T00:00:00Z","timestamp":1498694400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Perform. Eval. Comput. Syst."],"published-print":{"date-parts":[[2017,9,30]]},"abstract":"<jats:p>\n            The Markov Modulated Poisson Process (MMPP) has been extensively studied in random process theory and widely applied in various applications involving Poisson arrivals whose rate varies following a Markov process. Despite the rich literature on MMPP, very little is known on its intricate temporal dependence structure. No exact solution is available so far to capture the\n            <jats:italic>functional<\/jats:italic>\n            temporal dependence of MMPP at the stationary state over slotted times.\n          <\/jats:p>\n          <jats:p>This article tackles the above challenges with copula analysis. It not only presents a novel analytical framework to capture the temporal dependence of MMPP but also provides the exact copula-based solutions for single MMPP as well as the aggregate of independent MMPP. This theoretical contribution discloses functional dependence structure of MMPP. It also lays the foundation for many applications that rely on the temporal dependence of MMPP for adaptive control or predictive resource provisioning. We demonstrate case studies, with real-world trace data as well as simulation, to illustrate the practical significance of our analytical results.<\/jats:p>","DOI":"10.1145\/3089254","type":"journal-article","created":{"date-parts":[[2017,6,30]],"date-time":"2017-06-30T12:36:19Z","timestamp":1498826179000},"page":"1-28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Copula Analysis of Temporal Dependence Structure in Markov Modulated Poisson Process and Its Applications"],"prefix":"10.1145","volume":"2","author":[{"given":"Fang","family":"Dong","sequence":"first","affiliation":[{"name":"University of Victoria, BC, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kui","family":"Wu","sequence":"additional","affiliation":[{"name":"University of Victoria, BC, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Venkatesh","family":"Srinivasan","sequence":"additional","affiliation":[{"name":"University of Victoria, BC, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,6,29]]},"reference":[{"volume-title":"Proceedings of INFOCOM\u201997","author":"Allan","key":"e_1_2_2_2_1"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/49.700908"},{"key":"e_1_2_2_4_1","first-page":"1","article-title":"Distribution and dependence of extremes in network sampling processes","volume":"2","author":"Avrachenkov Konstantin","year":"2015","journal-title":"Computat. Soc. Netw."},{"key":"e_1_2_2_5_1","unstructured":"Kazim Azam and Michael K. Pitt. 2014. Bayesian inference for a semi-parametric copula-based Markov chain. Working Paper University of Warwick. (2014).  Kazim Azam and Michael K. Pitt. 2014. Bayesian inference for a semi-parametric copula-based Markov chain. Working Paper University of Warwick. (2014)."},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/26.223775"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2007.061619"},{"key":"e_1_2_2_8_1","unstructured":"Khalid Begain Gunter Bolch and Helmut Herold. 2012. Practical Performance Modeling: Application of the MOSEL Language. Springer Science 8 Business Media U.S.  Khalid Begain Gunter Bolch and Helmut Herold. 2012. Practical Performance Modeling: Application of the MOSEL Language. Springer Science 8 Business Media U.S."},{"key":"e_1_2_2_9_1","unstructured":"Martina Beil. 2013. Modeling Dependencies Among Financial Asset Returns Using Copulas. Ph.D. Dissertation. Technische Universit\u00e4t M\u00fcnchen.  Martina Beil. 2013. Modeling Dependencies Among Financial Asset Returns Using Copulas. Ph.D. Dissertation. Technische Universit\u00e4t M\u00fcnchen."},{"key":"e_1_2_2_10_1","first-page":"420","article-title":"A short note on multivariate dependence modeling","volume":"49","author":"B\u00edna Vladislav","year":"2013","journal-title":"Kybernetika"},{"key":"e_1_2_2_11_1","doi-asserted-by":"crossref","unstructured":"Eric Bouy\u00e9 Valdo Durrleman Ashkan Nikeghbali Ga\u00ebl Riboulet and Thierry Roncalli. 2000. Copulas for finance-a reading guide and some applications. Available at SSRN 1032533 (2000).  Eric Bouy\u00e9 Valdo Durrleman Ashkan Nikeghbali Ga\u00ebl Riboulet and Thierry Roncalli. 2000. Copulas for finance-a reading guide and some applications. Available at SSRN 1032533 (2000).","DOI":"10.2139\/ssrn.1032533"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12104-3_19"},{"volume-title":"Information Technologies and Mathematical Modelling-Queueing Theory and Applications","author":"Burkatovskaya Yulia","key":"e_1_2_2_13_1"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1214\/09-AOS719"},{"key":"e_1_2_2_15_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.entcs.2015.10.022"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.03.030"},{"key":"e_1_2_2_17_1","first-page":"1","article-title":"Modeling poisson error process on wireless channels","volume":"7","author":"Cs\u00f3ka Tibor","year":"2015","journal-title":"Int. J. Commun. Netw. Inform. Secur."},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCCN.2016.7568503"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1109\/INFOCOM.2015.7218532"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.2307\/3215223"},{"key":"e_1_2_2_21_1","doi-asserted-by":"crossref","unstructured":"Valdo Durrleman Ashkan Nikeghbali Thierry Roncalli and others. 2000. Which copula is the right one? Working paper Cr\u00e9dit Lyonnais. (2000).  Valdo Durrleman Ashkan Nikeghbali Thierry Roncalli and others. 2000. Which copula is the right one? Working paper Cr\u00e9dit Lyonnais. (2000).","DOI":"10.2139\/ssrn.1032545"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.914305"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044450896-6.50010-8"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-5316(93)90035-S"},{"key":"e_1_2_2_25_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2007.10.005"},{"key":"e_1_2_2_26_1","article-title":"Statistical analysis of different traffic types effect on QoS of wireless ad hoc networks","volume":"3","author":"Gharehajlu Mahmood Mollaei","year":"2015","journal-title":"J. Inform. Syst. Telecommun."},{"key":"e_1_2_2_27_1","doi-asserted-by":"publisher","DOI":"10.1109\/GLOCOM.2007.499"},{"key":"e_1_2_2_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comcom.2008.11.022"},{"key":"e_1_2_2_29_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2003.820252"},{"key":"e_1_2_2_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1297332.1297337"},{"key":"e_1_2_2_31_1","first-page":"2134","article-title":"Internet traffic modeling: Markovian approach to self-similar traffic and prediction of loss probability for finite queues","volume":"84","author":"Kasahara Shoji","year":"2001","journal-title":"IEICE Trans. Commun."},{"key":"e_1_2_2_32_1","doi-asserted-by":"crossref","unstructured":"Natalia Markovich. 2008. Nonparametric Analysis of Univariate Heavy-tailed Data: Research and Practice. Vol. 753. John Wiley 8 Sons England.  Natalia Markovich. 2008. Nonparametric Analysis of Univariate Heavy-tailed Data: Research and Practice. Vol. 753. John Wiley 8 Sons England.","DOI":"10.1002\/9780470723609"},{"key":"e_1_2_2_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/1815396.1815470"},{"key":"e_1_2_2_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.comcom.2005.02.012"},{"key":"e_1_2_2_35_1","unstructured":"Roger B. Nelson. 2006. An Introduction to Copulas. Springer New York.   Roger B. Nelson. 2006. An Introduction to Copulas. Springer New York."},{"volume-title":"Analytical and Stochastic Modeling Techniques and Applications","author":"Neuh\u00e4user David","key":"e_1_2_2_36_1"},{"key":"e_1_2_2_37_1","unstructured":"Marcel F. Neuts. 1989. Structured Stochastic Matrices of M\/G\/1 Type and Their Applications. Taylor 8 Francis New York.  Marcel F. Neuts. 1989. Structured Stochastic Matrices of M\/G\/1 Type and Their Applications. Taylor 8 Francis New York."},{"volume-title":"High-Speed Networks and Multimedia Communications","author":"Nogueira Ant\u00f3nio","key":"e_1_2_2_38_1"},{"key":"e_1_2_2_39_1","doi-asserted-by":"publisher","DOI":"10.1109\/TNET.2008.2008750"},{"key":"e_1_2_2_40_1","doi-asserted-by":"publisher","DOI":"10.1109\/CLOUD.2011.100"},{"key":"e_1_2_2_41_1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-444-62731-5.00016-6"},{"key":"e_1_2_2_42_1","doi-asserted-by":"publisher","DOI":"10.1109\/MASCOTS.2012.22"},{"key":"e_1_2_2_43_1","doi-asserted-by":"publisher","DOI":"10.1109\/MASCOTS.2014.27"},{"key":"e_1_2_2_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmva.2012.03.001"},{"key":"e_1_2_2_45_1","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2006.871709"},{"key":"e_1_2_2_46_1","unstructured":"Sheldon M. Ross. 2003. Introduction to Probability Models. Academic Press Burlington.  Sheldon M. Ross. 2003. Introduction to Probability Models. Academic Press Burlington."},{"key":"e_1_2_2_47_1","doi-asserted-by":"publisher","DOI":"10.1080\/15326349408807323"},{"key":"e_1_2_2_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-9473(95)00025-9"},{"key":"e_1_2_2_49_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1023672904130"},{"key":"e_1_2_2_50_1","unstructured":"Steven L. Scott. 2000. Detecting network intrusion using a Markov modulated nonhomogeneous poisson process. Available Online (2000). https:\/\/astro.temple.edu\/&sim;msobel\/courses_files\/scott-smythe.pdf.  Steven L. Scott. 2000. Detecting network intrusion using a Markov modulated nonhomogeneous poisson process. Available Online (2000). https:\/\/astro.temple.edu\/&sim;msobel\/courses_files\/scott-smythe.pdf."},{"key":"e_1_2_2_51_1","doi-asserted-by":"publisher","DOI":"10.1093\/ietcom\/e88-b.4.1493"},{"key":"e_1_2_2_52_1","unstructured":"Pravin K. Trivedi and David M. Zimmer. 2007. Copula Modeling: An Introduction for Practitioners. Now Publishers Inc. Boston.  Pravin K. Trivedi and David M. Zimmer. 2007. Copula Modeling: An Introduction for Practitioners. Now Publishers Inc. Boston."},{"key":"e_1_2_2_53_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.econlet.2012.04.016"},{"key":"e_1_2_2_54_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.19.3.722"},{"key":"e_1_2_2_55_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1016616406118"},{"key":"e_1_2_2_56_1","doi-asserted-by":"publisher","DOI":"10.1109\/LCOMM.2006.1613754"}],"container-title":["ACM Transactions on Modeling and Performance Evaluation of Computing Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3089254","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3089254","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:30:07Z","timestamp":1750217407000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3089254"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,29]]},"references-count":55,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,9,30]]}},"alternative-id":["10.1145\/3089254"],"URL":"https:\/\/doi.org\/10.1145\/3089254","relation":{},"ISSN":["2376-3639","2376-3647"],"issn-type":[{"type":"print","value":"2376-3639"},{"type":"electronic","value":"2376-3647"}],"subject":[],"published":{"date-parts":[[2017,6,29]]},"assertion":[{"value":"2016-04-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-04-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-06-29","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}