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Here, we construct very accurate approximations of the workload distribution of the MAP\/G\/1 queue that capture the tail behavior of the exact workload distribution and provide a small relative error. Motivated by statistical analysis, we assume that the service times are a mixture of a phase-type and a heavy-tailed distribution. With the aid of perturbation analysis, we derive our approximations as a sum of the workload distribution of the MAP\/PH\/1 queue and a heavytailed component that depends on the perturbation parameter. We refer to our approximations as corrected phase-type approximations, and we exhibit their performance with a numerical study.<\/jats:p>","DOI":"10.1145\/2518025.2518036","type":"journal-article","created":{"date-parts":[[2013,9,3]],"date-time":"2013-09-03T11:57:11Z","timestamp":1378209431000},"page":"53-55","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Corrected phase-type approximations for the workload of the MAP\/G\/1 queue with heavy-tailed service times"],"prefix":"10.1145","volume":"41","author":[{"given":"Eleni","family":"Vatamidou","sequence":"first","affiliation":[{"name":"EURANDOM and Eindhoven University of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ivo","family":"Adan","sequence":"additional","affiliation":[{"name":"EURANDOM and Eindhoven University of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maria","family":"Vlasiou","sequence":"additional","affiliation":[{"name":"EURANDOM, CWI, and Eindhoven University of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bert","family":"Zwart","sequence":"additional","affiliation":[{"name":"EURANDOM, CWI, VU University Amsterdam, Georgia Institute of Technology, and Eindhoven University of Technology"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2013,8,27]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-6377(99)00014-0"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1026093622185"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","DOI":"10.1142\/2779","volume-title":"Ruin Probabilities","author":"Asmussen S.","year":"2000","unstructured":"Asmussen , S. ( 2000 ). Ruin Probabilities Asmussen, S. (2000). Ruin Probabilities"},{"key":"e_1_2_1_4_1","volume-title":"Applied Probability and Queues","author":"Asmussen S.","year":"2003","unstructured":"Asmussen , S. ( 2003 ). Applied Probability and Queues . Springer-Verlag , New York . Asmussen, S. (2003). Applied Probability and Queues. Springer-Verlag, New York."},{"key":"e_1_2_1_5_1","first-page":"419","article-title":"Fitting phase-type distributions via the EM algorithm","volume":"23","author":"Asmussen S.","year":"1996","unstructured":"Asmussen , S. , Nerman , O. and Olson , M. ( 1996 ). Fitting phase-type distributions via the EM algorithm . Scand. J. Stat. 23 , 419 -- 441 . Asmussen, S., Nerman, O. and Olson, M. (1996). Fitting phase-type distributions via the EM algorithm. Scand. J. Stat. 23, 419--441.","journal-title":"Scand. J. Stat."},{"key":"e_1_2_1_6_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-33483-2","volume-title":"Modelling Extremal Events Springer-Verlag","author":"Embrechts P.","year":"1997","unstructured":"Embrechts , P. , Kl\u00fcppelberg , C. and Mikosch , T . ( 1997 ). Modelling Extremal Events Springer-Verlag , Berlin . Embrechts, P., Kl\u00fcppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events Springer-Verlag, Berlin."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0167-6687(82)90021-X"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-5316(97)00003-5"},{"key":"e_1_2_1_9_1","volume-title":"The BMAP\/G\/1 queue: A tutorial","author":"Lucantoni D. M.","year":"1993","unstructured":"Lucantoni , D. M. ( 1993 ). The BMAP\/G\/1 queue: A tutorial . Lucantoni, D. M. (1993). The BMAP\/G\/1 queue: A tutorial."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02411476"},{"key":"e_1_2_1_11_1","volume-title":"Heavy-Tail Phenomena: Probabilistic and Statistical Modeling","author":"Resnick S. I.","year":"2007","unstructured":"Resnick , S. I. ( 2007 ). Heavy-Tail Phenomena: Probabilistic and Statistical Modeling . Springer , NY. Resnick, S. I. (2007). Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. Springer, NY."},{"key":"e_1_2_1_12_1","doi-asserted-by":"crossref","DOI":"10.1002\/9780470317044","volume-title":"Stochastic Processes for Insurance and Finance","author":"Rolski T.","year":"1999","unstructured":"Rolski , T. , Schmidli , H. , Schmidt , V. and Teugels , J . ( 1999 ). Stochastic Processes for Insurance and Finance . John Wiley & Sons Ltd . Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999). Stochastic Processes for Insurance and Finance. 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