請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/45839完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 謝南瑞 | |
| dc.contributor.author | Meng-Ching Hu | en |
| dc.contributor.author | 胡孟青 | zh_TW |
| dc.date.accessioned | 2021-06-15T04:47:05Z | - |
| dc.date.available | 2011-08-10 | |
| dc.date.copyright | 2010-08-10 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-08-04 | |
| dc.identifier.citation | [1] H. Furrer. Risk theory and heavy-tailed Lèvy processes, Diss. ETH 12408, Ph.D. thesis, Eidgenössische Technische Hochschule. Zurich, (1997)
[2] K. Maulik, S. I. Resnick. The self-similar and multifractal nature of a network traffic model, Stochastic Models, 19-4 (2003), 549-577 [3] K. Park, W. Willinger. Self-similar network traffic and performance evaluation. John Wiley & Sons, Inc. (2000) [4] L. de Haan. On regular variation and its application to the weak convergence of sample Extremes, Mathematisch Centrum, Amsterdam, (1970). [5] M. S. Taqqu, W. Willinger, and R. Sherman. Proof of a fundamental result in self-similar traffic modeling, Comput. Comm. Rev., 27 (1997), 5-23 [6] O. Boxma and J. W. Cohen. Heavy traffic analysis for the GI/G/1 queue with heavy- tailed distributions. Queuing Systems Theory Appl., 33-1-3 (1999), 177-204 [7] S. I. Resnick and H. Rootzén. Self-similar communication models and very heavy tails, Ann. Appl. Probab., 10 (2000), 753-778 [8] S. I. Resnick and G. Samorodnitsky. A heavy traffic approximation for workload processes with heavy tailed service requirements, Management Sci., 46 (2000), 1236- 1248 [9] S. I. Resnick. A probability path, Birkhäuser Boston, Cambridge, MA, (1998). [10] S. I. Resnick. Heavy-tail Phenomena: probabilistic and statistical modeling, Springer. (2007) [11] T. Mikosch, S. I. Resnick, H. Rootzén, and A. W. Stegeman. Is network approxi- mated by stable Lèvy motion or fractional Brownian motion?, Ann. Appl. Probab., 12-1 (2002), 23-68. [12] T.Lindvall, Weak convergence of probability measures and random functions in the function space . J. Appl. Probab. ,10 (1973), 109-121 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/45839 | - |
| dc.description.abstract | 近年來在網路資料傳輸的研究上，發現許多與傳統網路模型不同的特點，其中主要有自我相似性(self-similarity)，長期相依性(long-range dependence)，以及厚尾現象(heavy-tail)。本文首先解釋傳輸檔案的厚尾現象與長期相依性之間的關聯性，接著用數學方法解釋在假設傳輸檔案具有厚尾現象且傳輸速度為定值的情況下，累積的傳輸量將近似穩定Lèvy運動(stable Lèvy motion) 或碎形布朗運動(Fractional Brownian motion)，其差別在於傳輸成長速率的不同。最後一段討論在只有一個伺服器的情況下，當傳輸交通繁重時，在某些假設條件下，用戶端等待時間將會趨近一個特殊的Mittag-Leffler分布。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2021-06-15T04:47:05Z (GMT). No. of bitstreams: 1 ntu-99-R95221029-1.pdf: 578591 bytes, checksum: 37bf1b166886033b0cae5d2511816598 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | 致謝 I
摘要 II Abstract III Contents IV 1.Introduction 1 2.Some Math Tools 4 2.1 The Infinite Node Poisson Model 4 2.2 Regular Variation 5 2.3 Stable Lèvy Motion 6 2.4 Lyapunov’s Limit Theorem 8 2.5 The space D[0,1] and D[0,∞) 8 3. Long Range Dependence 12 4.Cumulative Traffic on Large Time Scale Under Slow Growth15 4.1 Slow Growth Condition 16 4.2 Basic decomposition 18 4.3 Approximation to Stable Levy motion 20 5.Cumulative Traffic on Large Time Scale Under Fast Growth25 5.1 Fast Growth Condition 25 5.2 Approximation to Fractional Brownian motion 25 6. Heavy Traffic Limit Theorem 31 6.1 Waiting Time Process 31 6.2 Approximation to a negative-drift random walk 34 6.3 Approximation to supremum of a negative-drift random walk 37 6.4 Heavy-tail Approximation for Queues with Heavy-Tail Services 40 6.5 Examples for Heavy Traffic Approximation 47 Reference 49 | |
| dc.language.iso | zh-TW | |
| dc.title | 厚尾理論於網路傳輸模型之應用 | zh_TW |
| dc.title | Heavy-Tail Applications to Internet Models | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王振男,張志中 | |
| dc.subject.keyword | 厚尾現象,碎形布朗運動,Levy過程, | zh_TW |
| dc.subject.keyword | heavy-tail,Fractional Brownian Motion,Levy Process, | en |
| dc.relation.page | 50 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-08-05 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-99-1.pdf 目前未授權公開取用 | 565.03 kB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。