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Title: | Construction of Fuzzy Queues |
Authors: | 陳奕至 Chen,Yi-Chih |
Contributors: | 陸行 Luh,Hsing 陳奕至 Chen,Yi-Chih |
Keywords: | 模糊 陳奕至 等候系統 陸行 Fuzzy Chen,Yi-Chih Queue Luh,Hsing |
Date: | 2005 |
Issue Date: | 2009-09-18 18:29:22 (UTC+8) |
Abstract: | 近幾年,等候系統開始被廣泛的應用於分析工作上可能產生的延遲。
平均花費在系統中和等候線上的時間成為描述等候系統行為兩個最基本的數量。除了工作的延遲外,我們考慮顧客在等候線上的延遲也會受到滿意度的影響。由於顧客滿意度會影響顧客的到達率,因此系統到達率和系統服務率變成模糊集合。我們建構一個模糊的等候系統並且提出一個去模糊化的方法。這篇論文研究的目的在於呈現一個分析系統的方法,利用此方法解決模糊的系統中最佳化的問題。
關鍵字: 模糊等候,最佳化。 Queueing models for analyzing the possible delay of tasks have
been studied for past several decades. Since then, the average
time spent in the system and the average time spent in queue have become two of the most fundamental quantities describing a
queueing system`s behavior. In additional to the delay of tasks,
we consider the satisfaction of customers affected by several
factors in system. Since the satisfaction reflects the arrival rate and service rate, the arrival rate and the service rate seem more close to the fuzzy sets. We construct a fuzzy queueing model and introduce an optimization problem of a fuzzy queue. The objective of this optimization problem is to present an approach that analyzes the model and decide the optimal number of servers while minimizing the total cost which is a fuzzy set. As a result, we provide a solution procedure to compute the required performance measure in a service-oriented environment.
Keywords: Fuzzy Queue, Optimization Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . . ii
1 Introduction 1
2 Fuzzy Matrices 4
2.1 Research Background . . . . . . . . . . . . . . . . 4
2.2 Convergence of Fuzzy Matrices . . . . . . . . . . . 7
3 A Fuzzy Queueing System 12
3.1 Fuzzy Sets of Service Rates . . . .. . . . . . . . . 12
3.2 Fuzzy Sets of Arrival Rates . . . . . . . . . . . . 13
3.3 Transition Matrix . . . . . . . . . . . . . . . . . 14
4 An Optimization Model 17
4.1 Model Description . . . . . . . . . . . . . . . . . 17
4.2 Defuzzy Methods . . . . . . . . . . . .. . . . . . . 19
4.3 Illustrative Examples . . . . . . . . . . . . . . . 21
4.4 Comparison in Different Defuzzy Methods . . . . . . 27
5 Conclusions 42
References 45
Appendix 1 47
Appendix 2 49
Appendix 3 53 |
Reference: | Avrachenkov, K.E. and Sanchez, E., Fuzzy Markov chains, Fuzzy Optimization and Decision Making, vol. 1, no. 2, pp. 143--159, June 2002. Buckley, J.J., Solving fuzzy equations. Fuzzy Sets and Systems, 50:1-14, 1992. Buckley, J.J., Feuring, T. and Hayashi, Y., Fuzzy queueing theory revisited, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 9(5):527-537, 2001. Bonde, A.R. and Ghoh, S., A comparative study of fuzzy versus "fixed" thresholds for robust queue management in Cell-Switching networks, IEEE/ACM Transactions on Networking. vol. 2, no. 4, pp. 337-344, 1994. Chen, S.P., A membership function approach to single-server fuzzy queues with bulk service, In Proceedings of 2002 Conference on Technology and Management, pp. 299-307, 2002. Chen, S.J. and Hwang, C.L., Fuzzy multiple attribute decision making, Berlin: Springer-Verlag, 1992. Davis, M.M., How long should a customer wait for service? Decision Sciences, vol.\\ 22, no.\\ 2, 324-34, 1991. Davis, M.M. and Maggard, M.J., An analysis of customer satisfaction with waiting times in a two-stage service process, Journal of Operatons Management, vol.\\ 9, no.\\ 3, 324-334, 1990. Dubois, D. and Prade, H., Possibility theory, Plenum Press, New York, 1988. Give`on, Y., Lattice matrices, {\\sl Information and Control}, 7 , 477-484, 1964. Guu, S.M., Lur, Y.Y., and Pang, C.T., On infinite products of fuzzy matrices, Fuzzy sets. SIAM J. Matrix Anal. Appl, vol.\\ 22, no.\\ 4, pp. 1190-1203 Jain, R., Decision making in the presence of fuzzy variables, IEEE Trans. Syst., Man, Cybern., 6, 698-703, 1976 Jain, R., A procedure for multiple-aspect decision making using fuzzy sets, Int. J. Syst. Sci., 8(1), 1-7, 1977. Kao, C., Li, C.C. and Chen, S.P., Parametric programming to the analysis of fuzzy queues, Fuzzy Sets and Systems, 107:93-100, 1999. Luh, H., Wang, C.H. and Chen, Y.C., Queue management with various apects of waiting, In Proceedings of 2005 International Conference on Intelligent Technologies and Applied Statistics, 2005. Sanchez, E., Resolution of composite fuzzy relation equations, {\\sl Information and Control} 30 , 38-48, 1976. Thomason, M.G., Convergence of powers of a fuzzy matrix, {\\sl J. Math. Anal. Appl}. 57 , 476-480, 1977. Yager, R.R., Ranking fuzzy subsets over the unit interval, Proceedings of the 1978 CDC., 1435-1437, 1978. Yager, R.R., On choosing between fuzzy subsets, Kybernetes., 9, 151-154, 1980. Yager, R.R., A procedure for ordering fuzzy subsets of the unit interval, Inf. Sci., 24, 143-161, 1981. Zhang, R. and Phillis, Y.A., Admission control and scheduling in simple series parallel networks using fuzzy logic, IEEE Transactions on Fuzzy Syatems, vol. 9, no. 2, pp. 307-314, 2001. |
Description: | 碩士 國立政治大學 應用數學研究所 92751009 94 |
Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0927510091 |
Data Type: | thesis |
Appears in Collections: | [應用數學系] 學位論文
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