學術產出-學位論文

題名 數位網路上多重目標規劃的數學模式
Mathematical Models of Pareto Optimal Path Selection on All-IP Networks
作者 王嘉宏
Wang, Chia-Hung
貢獻者 陸行
Hsing Luh
王嘉宏
Wang, Chia-Hung
關鍵詞 多重目標規劃問題
達成度函數
比例性公平
柏雷托最適
公平的頻寬配置
有序的加權平均法
選徑
延遲
multiple-objective problems
achievement function
proportional fairness
Pareto optimal
fair bandwidth allocation
ordered weighted averaging method
routing
delay
日期 2003
上傳時間 17-九月-2009 13:50:12 (UTC+8)
摘要 面對通訊與資訊科技的大幅進步,通訊網路正在進行一個巨大的變革,要將電信網路與數據網路整合成一個單一的All-IP網路以支援所有網路應用服務。欲達到整合型網路的理想,仍有許多困難尚待克服,而服務品質問題是其中最關鍵的問題之一。因為受限於封包交換網路之原有的特性,All-IP網路有影響服務品質的三項因素:過長的延遲時間、抖動以及封包遺失。首先,我們利用了達成度函數(achievement function)來處理單位的轉換,使得能夠同時考量此三項不同單位的因素。接著,本文中提出一套方法來解決All-IP網路上端對端(end-to-end)的資源配置及路徑規劃問題。在分配資源時,我們企圖提供一種成比例的公平性給各個不同等級。此公平性的精神是要使得所有網路使用者的滿足程度相當,而非各個不同等級的使用者分配到相同的資源。我們將以預算方式控制端對端品質管理以追求使用者之整體最大滿意程度。
本論文的規劃概念是將網路規劃分成兩個階段。第一階段是在一筆給定的總預算底下,以成比例的方式去分配資源給各個不同等級,並建置網路上的頻寬,使各等級能依其需求拿到適當的頻寬,確保滿足程度相當。
接下來第二階段則是在第一部份已完成的規劃基礎下,做路徑規劃,指派新進入的使用者到一條較好的路徑,在滿足此使用者的延遲時間要求下,使此系統的壅塞程度越小越好。路徑規劃的概念為如何挑選最佳網路路徑,以規劃具服務品質之端對端路徑,並可達到資源之最有效利用。網路營運者將可運用此套方法來調校自身所營運的網路以追求使用者最高滿意度。
We present an approach for the fair resource allocation problem
and QoS routing in All-IP networks that offer multiple services to users. The objective of the optimization problem is to determine the amount of required bandwidth for each link and each class to maximize the sum of the users` utility. In this work, we focus on approaches that, while allocating bandwidth, attempt to provide a proportionally fair treatment of all the competing classes. First, we will show that an achievement function can map different criteria subject to various utility onto a normalized scale. It may be interpreted as a measure of QoS (Quality of Service) on All-IP networks. Using the bandwidth allocation model, we can find a Pareto optimal allocation of bandwidth on the network under a limited available budget. This allocation can provide the so-called proportional fairness to every class, that is, this allocation can provide the similar satisfaction to each user. Next, we present a routing scheme under consideration of the delay. Such an optimal path provides the end-to-end QoS guarantees to each user. Finally, a numerical example is given to illustrate how to solve the fair resource allocation problem and how to modify the nonlinear parts.
參考文獻 ""Enabling UMTS/Third Generation Services and Applications", UMTS Forun Report No.11, Oct., 2000.
A. W. Berger, and Y. Kogan, ""Dimensioning Bandwidth for Elastic Traffic in High-Speed Data Networks", IEEE/ACM Transactions on Networking, Vol. 8, No. 5, Oct. 2000.
R. Boutaba, W. Szeto, and Y. Iraqi, ""DORA: Efficient Routing for MPLS Traffic Engineering", Journal of Network and Systems Management, Vol. 10, No. 3, September 2002.
C. T. Chen, ""Budget-Based End-to-End QoS Management for All-IP Networks", Master thesis, Department of Computer Science, National Chengchi University, 2003.
M. C. Chen, ""Distributed Resource Management and Admission Control in Budget-Based QoS Management for All-IP Core Networks", Master thesis, Department of Computer Science, National Chengchi University, 2003.
A. L. Erera, C. F. Daganzo, and D. J. Lovell, ""The Access-Control Problem on Capacitated FIFO Networks with Unique O-D Paths is Hard", Operations Research, Vol. 50, No. 4, pp. 736-743, July-August 2002.
B. Fortz, J. Rexford, and M. Thorup, ""Traffic Engineering with Traditional IP Routing Protocols", IEEE Communications Magazine, October 2002.
R. J. Gibbens, S. K. Sargood, C. V. Eijl, F. P. Kelly, H. Azmoodeh, R. N. Macfadyen, N. W. Macfadyen, ""Fixed-Point Models for the End-to-End Performance Analysis of IP Networks", 13th ITC Specialist Seminar: IP Traffic Measurement, Modeling and Management, Monterey, California, Sep. 2000.
K. Gopalan and T. Chiueh, ""Delay Budget Allocation for Delay-Guaranteed Network Paths", Technical Report TR-113, Experimental Computer Systems Labs, Dept. of Computer Science, State University of New York, Stony Brook, NY, June 2002.
J. Gozdecki, A. Jajszczyk, and R. Stankiewicz, ""Quality of Service Terminology in IP Networks", IEEE Communications Magazine, no. 3, pp. 153-159, Mar. 2003.
D. Granot, J. Kuipers, and S. Chopra, ""Cost allocation for a tree network with heterogeneous cutomers", Mathematics of Operations Research, Vol. 27, Iss. 4, pp. 647-661, Nov. 2002.
R. A. Guerin and A. Orda, ""QoS Routing in Networks with Inaccurate Information: Theory and Algorithms", IEEE/ACM TRANSACTIONS ON NETWORKING, Vol. 7, No. 3, June 1999.
P. V. Hentenryck, ILOG OPL Studio 3.5: The Optimization Language, Massachusetts Institute of Technology, April 2001.
R. Johari and D. K. H. Tan, ""End-to-End Congestion Control for the Internet: Delays and Stability", IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 9, NO. 6, pp. 818-832, Dec. 2001.
F. P. Kelly, ""Charging and Rate Control for Elastic Traffic", European Transactions on Telecommunications, volume 8, pages 33-37, 1997.
F. P. Kelly, A. K. Maulloo and D. K. H. Tan, ""Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability", Journal of the Operational Research Society, Vol. 49, 237-252, 1998.
F. P. Kelly, ""Mathematical modelling of the Internet", Mathematics Unlimited - 2001 and Beyond, Springer-Verlag, Berlin, pp. 685-702, 2001.
F. P. Kelly, ""Fairness and Stability of End-to-End Congestion Control", European Journal of Control, vol. 9, pp. 159-176, 2003.
T. H. Li, ""Path Planning in Budget-Based QoS Management for All-IP Core Networks", Master thesis, Department of Computer Science, National Chengchi University, 2003.
Y. N. Lien, H. C. Jang, T. C. Tsai, and H. Luh, ""BBQ: A QoS Management Infrastructure for All-IP Networks", Communications of Institute of Information and Computing Machinery: Mobile Communications and Wireless Networks, Vol.7, No. 1, pp. 89-115, Mar. 2004.
A. W. Marshall, I. Olkin, Inequalties: Theory of Majorization and Its Applications, New York: Academic Press, 1979.
A. Muller, D. Stoyan, Comparison Methods for Stochastic Models and Risks, Wiley, Chichester, 2002.
M. Minoux, Mathematical Programming: Theory and Algorithms, Wiley, Chichester, 1986.
G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, New York : Wiley, 1988.
W. Ogryczak, T. Sliwinski and A. Wierzbicki, ""Fair Resource Allocation Schemes and Network Dimensioning Problems", Journal of Telecommunications and Information Technology, pp. 34-42, 3/2003.
A. Orda, ""Routing with End-to-End QoS Guarantees in Broadband Networks", IEEE/ACM Transactions on Networking, Vol. 7, No. 3, June 1999.
M. Pioro, G. Malicsko, and G. Fodor, ""Optimal Link Capacity Dimensioning in Proportionally Fair Networks", NETWORKING 2002, LNCS 2345, pp.277-288, 2002.
R. L. Rardin, Optimization in Operations Research, Prentice-Hall, 1998.
R. E., Steuer, Multiple Criteria Optimization : Theory, Computation, and Application, New York, Wiley, 1986.
A. C. Stockman, Introduction to Economics, 2nd ed., the Dryden Press, 1999.
P. Thomas, D. Teneketzis, J. K. Mackie-Mason, ""A Market-Based Approach to Optimal Resource Allocation in Integrated-Services Connection-Oriented Networks", Operations Research, Vol. 50, No. 4, pp. 603-616, July-August, 2002.
S. T. Waller, A. K. Ziliaskopoulos, ""A Dynamic and Stochastic Approach to Network Design", Journal of the Transportation Research Board, No. 1771, pp. 106-114, 2001.
P. Whittle, Optimization Under Constraints, Wiley, Chichester, 1971.
W. Willinger and V. Paxson, ""Where Mathematics meets the Internet", Notices of the American Mathematical Society, pp. 961-970, Sep. 1998.
W. L. Winston, Operations Research: Applications and Algorithms, 3rd ed., Duxbury, 1994.
X. Xiao and L. M. Ni, ""Internet QoS: A Big Picture", IEEE Network, March/April, 1999.
R. R. Yager, ""On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making", IEEE Transactions on Systems, Man and Cybernetics, vol. 18, No. 1, pp. 183-190, 1988.
R. R. Yager, ""On the analytic representation of the Leximin ordering and its application to flexible constraint propagation", European Journal of Operational Research, vol. 102, pp. 176-192, 1997.
描述 碩士
國立政治大學
應用數學研究所
91751008
92
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0917510081
資料類型 thesis
dc.contributor.advisor 陸行zh_TW
dc.contributor.advisor Hsing Luhen_US
dc.contributor.author (作者) 王嘉宏zh_TW
dc.contributor.author (作者) Wang, Chia-Hungen_US
dc.creator (作者) 王嘉宏zh_TW
dc.creator (作者) Wang, Chia-Hungen_US
dc.date (日期) 2003en_US
dc.date.accessioned 17-九月-2009 13:50:12 (UTC+8)-
dc.date.available 17-九月-2009 13:50:12 (UTC+8)-
dc.date.issued (上傳時間) 17-九月-2009 13:50:12 (UTC+8)-
dc.identifier (其他 識別碼) G0917510081en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/32606-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學研究所zh_TW
dc.description (描述) 91751008zh_TW
dc.description (描述) 92zh_TW
dc.description.abstract (摘要) 面對通訊與資訊科技的大幅進步,通訊網路正在進行一個巨大的變革,要將電信網路與數據網路整合成一個單一的All-IP網路以支援所有網路應用服務。欲達到整合型網路的理想,仍有許多困難尚待克服,而服務品質問題是其中最關鍵的問題之一。因為受限於封包交換網路之原有的特性,All-IP網路有影響服務品質的三項因素:過長的延遲時間、抖動以及封包遺失。首先,我們利用了達成度函數(achievement function)來處理單位的轉換,使得能夠同時考量此三項不同單位的因素。接著,本文中提出一套方法來解決All-IP網路上端對端(end-to-end)的資源配置及路徑規劃問題。在分配資源時,我們企圖提供一種成比例的公平性給各個不同等級。此公平性的精神是要使得所有網路使用者的滿足程度相當,而非各個不同等級的使用者分配到相同的資源。我們將以預算方式控制端對端品質管理以追求使用者之整體最大滿意程度。
本論文的規劃概念是將網路規劃分成兩個階段。第一階段是在一筆給定的總預算底下,以成比例的方式去分配資源給各個不同等級,並建置網路上的頻寬,使各等級能依其需求拿到適當的頻寬,確保滿足程度相當。
接下來第二階段則是在第一部份已完成的規劃基礎下,做路徑規劃,指派新進入的使用者到一條較好的路徑,在滿足此使用者的延遲時間要求下,使此系統的壅塞程度越小越好。路徑規劃的概念為如何挑選最佳網路路徑,以規劃具服務品質之端對端路徑,並可達到資源之最有效利用。網路營運者將可運用此套方法來調校自身所營運的網路以追求使用者最高滿意度。
zh_TW
dc.description.abstract (摘要) We present an approach for the fair resource allocation problem
and QoS routing in All-IP networks that offer multiple services to users. The objective of the optimization problem is to determine the amount of required bandwidth for each link and each class to maximize the sum of the users` utility. In this work, we focus on approaches that, while allocating bandwidth, attempt to provide a proportionally fair treatment of all the competing classes. First, we will show that an achievement function can map different criteria subject to various utility onto a normalized scale. It may be interpreted as a measure of QoS (Quality of Service) on All-IP networks. Using the bandwidth allocation model, we can find a Pareto optimal allocation of bandwidth on the network under a limited available budget. This allocation can provide the so-called proportional fairness to every class, that is, this allocation can provide the similar satisfaction to each user. Next, we present a routing scheme under consideration of the delay. Such an optimal path provides the end-to-end QoS guarantees to each user. Finally, a numerical example is given to illustrate how to solve the fair resource allocation problem and how to modify the nonlinear parts.
en_US
dc.description.tableofcontents Abstract (in Chinese) i
Abstract ii
Acknowledgment iii
Structure of this Work iv
List of Figures viii
List of Tables ix
1 Introduction 1
2 QoS on All-IP Networks 6
2.1 Quality of Service 6
2.2 Resource Allocation Routing with QoS Guarantees 8
3 Achievement Function 11
3.1 Construction 11
3.2 Implication 12
4 Formulation of the Bandwidth Allocation Model with
Proportional Fairness 16
4.1 Notations 16
4.2 Objective Functions 18
4.3 Constraints 22
4.4 A Mathematical Model 24
4.5 Modifications of Nonlinear Parts 25
4.5.1 Objectives 25
4.5.2 Constraints 26
4.5.3 A Mixed-Integer Programming Model 31
4.6 Pareto Optimal Solutions 32
4.7 A Routing Scheme with End-to-End QoS Guarantees 34
4.7.1 QoS Guarantees in Deterministic Case 34
4.7.2 Optimization of the Path Selection 35
5 A Numerical Example 37
5.1 Problem Statements 37
5.2 A Mathematical Programming 40
5.3 Numerical Experiments with ILOG 41
5.3.1 Modifications of the Objective Functions 41
5.3.2 Modifications of the Constraints 47
5.3.3 A Mixed-Integer Programming Model 50
6 Conclusions and Future Studies 53
6.1 Conclusions 53
6.2 Future Studies 54
Bibliography 55
zh_TW
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dc.language.iso en_US-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0917510081en_US
dc.subject (關鍵詞) 多重目標規劃問題zh_TW
dc.subject (關鍵詞) 達成度函數zh_TW
dc.subject (關鍵詞) 比例性公平zh_TW
dc.subject (關鍵詞) 柏雷托最適zh_TW
dc.subject (關鍵詞) 公平的頻寬配置zh_TW
dc.subject (關鍵詞) 有序的加權平均法zh_TW
dc.subject (關鍵詞) 選徑zh_TW
dc.subject (關鍵詞) 延遲zh_TW
dc.subject (關鍵詞) multiple-objective problemsen_US
dc.subject (關鍵詞) achievement functionen_US
dc.subject (關鍵詞) proportional fairnessen_US
dc.subject (關鍵詞) Pareto optimalen_US
dc.subject (關鍵詞) fair bandwidth allocationen_US
dc.subject (關鍵詞) ordered weighted averaging methoden_US
dc.subject (關鍵詞) routingen_US
dc.subject (關鍵詞) delayen_US
dc.title (題名) 數位網路上多重目標規劃的數學模式zh_TW
dc.title (題名) Mathematical Models of Pareto Optimal Path Selection on All-IP Networksen_US
dc.type (資料類型) thesisen
dc.relation.reference (參考文獻) ""Enabling UMTS/Third Generation Services and Applications", UMTS Forun Report No.11, Oct., 2000.zh_TW
dc.relation.reference (參考文獻) A. W. Berger, and Y. Kogan, ""Dimensioning Bandwidth for Elastic Traffic in High-Speed Data Networks", IEEE/ACM Transactions on Networking, Vol. 8, No. 5, Oct. 2000.zh_TW
dc.relation.reference (參考文獻) R. Boutaba, W. Szeto, and Y. Iraqi, ""DORA: Efficient Routing for MPLS Traffic Engineering", Journal of Network and Systems Management, Vol. 10, No. 3, September 2002.zh_TW
dc.relation.reference (參考文獻) C. T. Chen, ""Budget-Based End-to-End QoS Management for All-IP Networks", Master thesis, Department of Computer Science, National Chengchi University, 2003.zh_TW
dc.relation.reference (參考文獻) M. C. Chen, ""Distributed Resource Management and Admission Control in Budget-Based QoS Management for All-IP Core Networks", Master thesis, Department of Computer Science, National Chengchi University, 2003.zh_TW
dc.relation.reference (參考文獻) A. L. Erera, C. F. Daganzo, and D. J. Lovell, ""The Access-Control Problem on Capacitated FIFO Networks with Unique O-D Paths is Hard", Operations Research, Vol. 50, No. 4, pp. 736-743, July-August 2002.zh_TW
dc.relation.reference (參考文獻) B. Fortz, J. Rexford, and M. Thorup, ""Traffic Engineering with Traditional IP Routing Protocols", IEEE Communications Magazine, October 2002.zh_TW
dc.relation.reference (參考文獻) R. J. Gibbens, S. K. Sargood, C. V. Eijl, F. P. Kelly, H. Azmoodeh, R. N. Macfadyen, N. W. Macfadyen, ""Fixed-Point Models for the End-to-End Performance Analysis of IP Networks", 13th ITC Specialist Seminar: IP Traffic Measurement, Modeling and Management, Monterey, California, Sep. 2000.zh_TW
dc.relation.reference (參考文獻) K. Gopalan and T. Chiueh, ""Delay Budget Allocation for Delay-Guaranteed Network Paths", Technical Report TR-113, Experimental Computer Systems Labs, Dept. of Computer Science, State University of New York, Stony Brook, NY, June 2002.zh_TW
dc.relation.reference (參考文獻) J. Gozdecki, A. Jajszczyk, and R. Stankiewicz, ""Quality of Service Terminology in IP Networks", IEEE Communications Magazine, no. 3, pp. 153-159, Mar. 2003.zh_TW
dc.relation.reference (參考文獻) D. Granot, J. Kuipers, and S. Chopra, ""Cost allocation for a tree network with heterogeneous cutomers", Mathematics of Operations Research, Vol. 27, Iss. 4, pp. 647-661, Nov. 2002.zh_TW
dc.relation.reference (參考文獻) R. A. Guerin and A. Orda, ""QoS Routing in Networks with Inaccurate Information: Theory and Algorithms", IEEE/ACM TRANSACTIONS ON NETWORKING, Vol. 7, No. 3, June 1999.zh_TW
dc.relation.reference (參考文獻) P. V. Hentenryck, ILOG OPL Studio 3.5: The Optimization Language, Massachusetts Institute of Technology, April 2001.zh_TW
dc.relation.reference (參考文獻) R. Johari and D. K. H. Tan, ""End-to-End Congestion Control for the Internet: Delays and Stability", IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 9, NO. 6, pp. 818-832, Dec. 2001.zh_TW
dc.relation.reference (參考文獻) F. P. Kelly, ""Charging and Rate Control for Elastic Traffic", European Transactions on Telecommunications, volume 8, pages 33-37, 1997.zh_TW
dc.relation.reference (參考文獻) F. P. Kelly, A. K. Maulloo and D. K. H. Tan, ""Rate Control for Communication Networks: Shadow Prices, Proportional Fairness and Stability", Journal of the Operational Research Society, Vol. 49, 237-252, 1998.zh_TW
dc.relation.reference (參考文獻) F. P. Kelly, ""Mathematical modelling of the Internet", Mathematics Unlimited - 2001 and Beyond, Springer-Verlag, Berlin, pp. 685-702, 2001.zh_TW
dc.relation.reference (參考文獻) F. P. Kelly, ""Fairness and Stability of End-to-End Congestion Control", European Journal of Control, vol. 9, pp. 159-176, 2003.zh_TW
dc.relation.reference (參考文獻) T. H. Li, ""Path Planning in Budget-Based QoS Management for All-IP Core Networks", Master thesis, Department of Computer Science, National Chengchi University, 2003.zh_TW
dc.relation.reference (參考文獻) Y. N. Lien, H. C. Jang, T. C. Tsai, and H. Luh, ""BBQ: A QoS Management Infrastructure for All-IP Networks", Communications of Institute of Information and Computing Machinery: Mobile Communications and Wireless Networks, Vol.7, No. 1, pp. 89-115, Mar. 2004.zh_TW
dc.relation.reference (參考文獻) A. W. Marshall, I. Olkin, Inequalties: Theory of Majorization and Its Applications, New York: Academic Press, 1979.zh_TW
dc.relation.reference (參考文獻) A. Muller, D. Stoyan, Comparison Methods for Stochastic Models and Risks, Wiley, Chichester, 2002.zh_TW
dc.relation.reference (參考文獻) M. Minoux, Mathematical Programming: Theory and Algorithms, Wiley, Chichester, 1986.zh_TW
dc.relation.reference (參考文獻) G. L. Nemhauser and L. A. Wolsey, Integer and Combinatorial Optimization, New York : Wiley, 1988.zh_TW
dc.relation.reference (參考文獻) W. Ogryczak, T. Sliwinski and A. Wierzbicki, ""Fair Resource Allocation Schemes and Network Dimensioning Problems", Journal of Telecommunications and Information Technology, pp. 34-42, 3/2003.zh_TW
dc.relation.reference (參考文獻) A. Orda, ""Routing with End-to-End QoS Guarantees in Broadband Networks", IEEE/ACM Transactions on Networking, Vol. 7, No. 3, June 1999.zh_TW
dc.relation.reference (參考文獻) M. Pioro, G. Malicsko, and G. Fodor, ""Optimal Link Capacity Dimensioning in Proportionally Fair Networks", NETWORKING 2002, LNCS 2345, pp.277-288, 2002.zh_TW
dc.relation.reference (參考文獻) R. L. Rardin, Optimization in Operations Research, Prentice-Hall, 1998.zh_TW
dc.relation.reference (參考文獻) R. E., Steuer, Multiple Criteria Optimization : Theory, Computation, and Application, New York, Wiley, 1986.zh_TW
dc.relation.reference (參考文獻) A. C. Stockman, Introduction to Economics, 2nd ed., the Dryden Press, 1999.zh_TW
dc.relation.reference (參考文獻) P. Thomas, D. Teneketzis, J. K. Mackie-Mason, ""A Market-Based Approach to Optimal Resource Allocation in Integrated-Services Connection-Oriented Networks", Operations Research, Vol. 50, No. 4, pp. 603-616, July-August, 2002.zh_TW
dc.relation.reference (參考文獻) S. T. Waller, A. K. Ziliaskopoulos, ""A Dynamic and Stochastic Approach to Network Design", Journal of the Transportation Research Board, No. 1771, pp. 106-114, 2001.zh_TW
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