政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32581

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/32581

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政大典藏 > College of Science > Department of Mathematical Sciences > Theses > Item 140.119/32581

Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/32581

Title:	權重效用在網路問題上之研究 A Study on Weighted Utilizations of Network Dimensioning Problems
Authors:	程雅惠 Cheng,Ya Hui
Contributors:	陸行 Luh,Hsing 程雅惠 Cheng,Ya Hui
Keywords:	權重效用函數權重公平資源分配最佳權重 weighted utility functions weight fair bandwidth allocation optimal weights
Date:	2006
Issue Date:	2009-09-17 13:47:28 (UTC+8)
Abstract:	我們以公平頻寬配置考慮網路上多重等級與多重服務品質的效用函數，利用權重效用函數提出兩種數學最佳化模型。這兩個模型的目標都是要尋找權重效用函數總和值的最大值。本篇論文特別以權重為決策變數，研究最佳權重的行為模式，並求得最佳權重分佈公式。我們發現模型I的總權重效用只看重某個效用值最大的等級，完全忽略其他效用值較小的等級；即最大效用函數的最佳權重為1，其他效用較小的最佳權重為0。在最佳化過程中，模型II的數值資料呈現出最佳權重架構為：最佳權重中的每個權重均相等，且總和為1。我們隨後證明這些結果，並利用GAMS軟體來呈現數值資料。 We propose two mathematical models with weighted utility functions for the fair bandwidth allocation and QoS routing in communication networks which offer multiple services for several classes of users. The formulation and numerical experiments are carried out in a general utility-maximizing framework. In this work, instead of being fixed, the weight for each utility function is taken as a free variable. The objective of this thesis is to find the structure of optimal weights that maximize the weighted sum of utilities of the bandwidth allocation for each class. We solve it by proposing two models in terms of fairness. Model I and II are constructed to compare different choices for optimal weights. For Model I, the structure of optimal weights form a vector which consists of one for a class and zero otherwise. For Model II, the form of optimal weights is that each weight of utility function is equally assigned. The results are proved and illustrated by software GAMS numerically.
Reference:	Birbil, S. I. and Fang, S. C., An Electromagnetism-like Mechanism for Global Optimazation, Journal of Global Optimization 25, 263-282, (2003). Hentenryck, P.V., ILOG OPL Studio 3.5: The Optimization Language, Massachusetts Institute of Technology, April (2001). Kelly, F. P., Fairness and Stability of End-to-End Congestion Control, European Journal of Control 9, 159-176, (2003). Kelly, F. P., Maulloo, A. K. and Tan, D.K.H., Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability, Journal of the Operational Research Society 3, 49, 237-252, (1998). Luh, H. and Wang, C. H., Mathematical Models of Pareto Optimal Path Selection on All-IP Networks, Proceedings of The First Sino-International Symposium on Probability, Statistics and Quantitative Management, 185-197, (2004). Luh, H. and Wang, C. H., Proportional Bandwidth Allocation for Unicasting in All-IP Networks, Proceedings of the 2nd Sino-International Symposium on Probability, Statistics and Quantitative Management, 111-130, (2005). Maher, M., Stewart, K. and Rosa, A., Stochastic Social Optimum Traffic Assignment, Transportation Research Part 3, B 39, 753-767, (2005). Nsakanda, A. L., Diaby, M. and Price, W. L., Hybrid Genetic Appoach for Solving Large-scale Capacitated Cell Formation Problems with Ultiple Routings, European Journal of Operational Research 171, 1051-1070, (2006). Ogryczak, W., \\`{S}liwi\\`{n}ski, T. and Wierzbicki, A., Fair Resource Allocation Schemes and Network Dimensioning Problems, Journal of Telecommunications and Information Technology 3, 34-42, (2003). Pi\\`{o}ro, M., Malicsk\\`{o}, G. and Fodor, G., Optimal Link Capacity Dimensioning in Proportionally Fair Networks, NETWORKING 2002, LNCS 2345, 277-288, (2002). Rosenthal, R. E., GAMS, A USER`S GUIDE, GAMS Development Corporation, (1998). Sahinidis, N. and Tawarmalani, M., BARON Solver Manual, GAMS Development Corporation, (2004). Stockman, A. C., Introduction to Economics, 2nd ed., Fort Worth, Dryden Press, (1999). Wang, C. H. and Luh, H., A Fair QoS Scheme for Bandwidth Allocation by Precomputation-Based Approach, International Journal of Information and Management Sciences, Vol. 19, No. 3, Accepted for Publication, (2008). Wang, C. H. and Luh, H., A Precomputation-Based Scheme for QoS Routing and Fair Bandwidth Allocation, Lecture Notes in Computer Science, Vol. 4297, 595-606, (2006). Wang, C. H. and Luh, H., A Two-Phase Scheme for Fair Bandwidth Allocation and QoS Routing in All-IP Networks. Proc. of the Third Sino-International Symposium on Probability, Statistics, and Quantitative Management, 49-63, Oct. (2006). Wang, C. H. and Luh, H., Fair Budget Allocation of Precomputation in All-IP Networks, in Proc. of IFORS International Triennial Conference, Honolulu, Hawaii, July (2005). Wang, C. H. and Luh, H., Network Dimensioning Problem of Applying Achievement Function, Lecture Notes in Operations Research, Operations Research and Its Applications 6, 35-59, (2006). Wang, C. H., and Luh, H., Two-Phase Modeling of QoS Routing in Communication Networks, submitted to International Workshop on Performance Modeling and Evaluation in Computer and Telecommunication Networks (PMECT07) in conjunction with IEEE ICCCN2007, Honolulu, Hawaii, USA, August 16, (2007). Wang, C. H., Mathematical Models of Pareto Optimal Path Selection on All-IP Networks, Master`s Thesis, Department of Mathematical Sciences, National Chengchi University, July (2004). Wang, C. H., Yue, W. and Luh, H., Performance Evaluation of Predetermined Bandwidth Allocation for Heterogeneous Networks. Technical Report of IEICE, Vol. 107, No. 6, 37-42, (2007). Wierzbicki, A.P., A Mathematical Basis for Satisficing Decision Making, Math. Modelling, Vol. 3, 391-405, (1982).
Description:	碩士國立政治大學應用數學研究所 93751016 95
Source URI:	http://thesis.lib.nccu.edu.tw/record/#G0093751016
Data Type:	thesis
Appears in Collections:	[Department of Mathematical Sciences] Theses

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