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These probabilities arise in many applications including in PERT networks where our interest may be in measuring the probability of large project delays. We also develop provably asymptotically optimal importance sampling techniques to efficiently estimate these probabilities. In the light-tailed settings we show that an appropriate mixture of exponentially twisted distributions efficiently estimates these probabilities. As is well known, exponential twisting based methods are not applicable in the heavy-tailed settings. To remedy this, we develop techniques that rely on \u201casymptotic hazard rate twisting\u201d and prove their effectiveness in both light and heavy-tailed settings. We show that in many cases the latter may have implementation advantages over exponential twisting based methods in the light-tailed settings. However, our experiments suggest that when easily implementable, the exponential twisting based methods significantly outperform asymptotic hazard rate twisting based methods.<\/jats:p>","DOI":"10.1145\/1225275.1225278","type":"journal-article","created":{"date-parts":[[2007,6,6]],"date-time":"2007-06-06T14:37:11Z","timestamp":1181140631000},"page":"7","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":20,"title":["Asymptotics and fast simulation for tail probabilities of maximum of sums of few random variables"],"prefix":"10.1145","volume":"17","author":[{"given":"S.","family":"Juneja","sequence":"first","affiliation":[{"name":"Tata Institute of Fundamental Research, Mumbai, India"}]},{"given":"R. L.","family":"Karandikar","sequence":"additional","affiliation":[{"name":"Indian Statistical Institute, Delhi, India"}]},{"given":"P.","family":"Shahabuddin","sequence":"additional","affiliation":[{"name":"Columbia University, New York"}]}],"member":"320","published-online":{"date-parts":[[2007,4]]},"reference":[{"key":"e_1_2_1_1_1","first-page":"272","article-title":"A classified bibliography of research on stochastic PERT networks","volume":"27","author":"Adalakha V. G.","year":"1989","unstructured":"Adalakha , V. G. and Kulkarni , V. G. 1989 . A classified bibliography of research on stochastic PERT networks . INFOR 27 , 3, 272 -- 296 . Adalakha, V. G. and Kulkarni, V. G. 1989. A classified bibliography of research on stochastic PERT networks. INFOR 27, 3, 272--296.","journal-title":"INFOR"},{"key":"e_1_2_1_2_1","unstructured":"Crovella M. Taqqu M. S. and Bestavros A. 1998. Heavy tails in the world wide web. In Practical Guide to Heavy Tails R. Adler R. Feldman and M. S. Taqqu Eds. Birkhauser Boston MA 24--31.  Crovella M. Taqqu M. S. and Bestavros A. 1998. Heavy tails in the world wide web. In Practical Guide to Heavy Tails R. Adler R. Feldman and M. S. Taqqu Eds. Birkhauser Boston MA 24--31."},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","unstructured":"Dembo A. and Zeitouni O. 1998. Large Deviations Techniques and Applications Second ed. Springer New York NY.  Dembo A. and Zeitouni O. 1998. Large Deviations Techniques and Applications Second ed. Springer New York NY.","DOI":"10.1007\/978-1-4612-5320-4"},{"key":"e_1_2_1_4_1","volume-title":"Activity Networks: Project Planning and Control by Network Models","author":"Elmaghraby S. E.","year":"1977","unstructured":"Elmaghraby , S. E. 1977 . Activity Networks: Project Planning and Control by Network Models . Wiley , New York, NY . Elmaghraby, S. E. 1977. Activity Networks: Project Planning and Control by Network Models. 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