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題名 以二維度馬可夫鏈的排隊模型研究客戶服務中心之等候機制
A queueing model of call center by two-dimensional Markov chain approach in a case study作者 黃瀚陞 貢獻者 陸行
黃瀚陞關鍵詞 客戶服務中心
排隊模型
二維度馬可夫鏈日期 2010 上傳時間 9-May-2016 16:39:28 (UTC+8) 摘要 在這篇論文中，藉由一個二維度的馬可夫鏈， 建立保護VIP線路同時允許重試現象的一般客戶線路的數學模型。 我們提出一個融合階段演算法以處理此二維度的馬可夫鏈，並且提出管理成本函數以研究在客服中心中最適當的服務人員數目 。藉由逼近法，找出一般顧客在重試群裡的平均等候時間和等候時間機率分配函數的上界與下界。 數值結果說明逼近方法對於計算一個很大的系統時可以省下很多計算時間，而且不失準確性。 最後，我們探討逼近法和實際解之間的誤差，數值結果也說明隨著系統容量或顧客到達率的增加，逼近法將更為準確。
In this thesis, we model a call center with guard channel scheme for VIP calls and retrial phenomenon for regular calls by a 2-dimensional Markov chain. We present a phase merging algorithm to solve the 2-dimensional Markov chain and a managerial cost function corresponding to studying the optimum number of servers in a call center. Also we will obtain upper and lower bounds with probability distribution functions of waiting time by using approximation. Numerical results show the approximation can save computational time without losing precision in the case of a call center with large capacity. Moreover, errors of the approximation are discussed, and it shows that the approximation is more accurate when the capacity of system or the arrival rate is large.
Abstract 中文摘要 List of Figures List of Tables 1. Introduction 2. System description 2.1 A queueing model 2.2 Waiting time 2.3 Computation of stationary probability distribution 3. Approximation and its computing procedure 3.1 Approximation of pi-method 3.2 Applications 3.3 Errors between Approximation and pi-method 4. Conclusion Appendix A Appendix B Bibliography參考文獻 [1] Abate J., Whitt W., Numberical inversion of Laplace transforms of probability distribution. ORSA. Journal on computing 7. 1995; 36-43. [2] Artalejo J.R., Gomez-corral A, Neuts MF., Numerical analysis of multiserver retrial queues operating under a full access policy. In: Latouche G. and Taylor P.(Eds), Advances in Algorithmic Methods for Stochastic Models. Notable Publications Inc., NJ. 2000; 1-19. [3] Artalejo J.R., Orlovsky D.S, Dudin A.N., Multiserver retrial model with variable number of active servers. Computer and Industrial Engineering. 2005; 48(2); 273-288. [4] Chen B.P.K., Henderson S.G., Two Issues in Setting Call Centre Staffing Levels. Annals of Operations Research. 2001; 108; 157-192. [5] Choi B.D., Chang Y., Single server retrial queues with priority calls. Mathematical and Computer Modeling. 1999; 30(3); 7-32. [6] Choi B.D., Melikov A., Amir velibekov., A simple numerical approximation of joint probabilities of calls in service and calls in the retrial group in a picocell. Appl. Comput. Math. 7(2008); no.1; 21-30. [7] Korolyuk, V.S., Korolyuk, V.V., Stochastic models of systems. Kluwer Academic Pluishers, Boston, 2009. 50 [8] Liang, C.C., Hsu, P.Y., Leu, J.D., Luh, H., An effective approach for content delivery in an evolving intranet environment- a case study of the largest telecom company in Taiwan. Lect Notes Comp Sci. 2005; 3806: 740-49. [9] Liang, C.C., Wang, C.H., Luh, H., Hsu, P.Y., Disaster Avoidance Mechanism for Content-Delivering. Service, Copmputer and Oper Res. 2009; 36(1): 27-39. [10] Mushko V.V., Klimenok V.I., Ramakrishnan K.O., Krishnamoorthy A, Dudin A.N., Multiserver queue with addressed retrials. Annals of Operations Reserch. 2006; 141(1); 283-301. [11] Matlab 7. The MathWorks, Inc.. 2009. [12] Servi L.D., Algorithmic solutions to two-dimensional birth-death processes with application to capacity planning. Telecommunication Systems. 2002; 21(2-4); 205-212. [13] Ross S., A First Course in Probability. Sixth edition, by Prentice-Hall, Inc.. 2002. [14] Taha H.A., Operations Research an introduction. Seventh edition, by Pearson Education, Inc.. 2003. [15] Takayuki O., Analysis of a QBD process that depends on backgroumd QBD processes. Septemer, CMU-CS-04-163. 2004. 描述 碩士
國立政治大學
應用數學系
967510091資料來源 http://thesis.lib.nccu.edu.tw/record/#G0967510091 資料類型 thesis dc.contributor.advisor 陸行 zh_TW dc.contributor.author (Authors) 黃瀚陞 zh_TW dc.creator (作者) 黃瀚陞 zh_TW dc.date (日期) 2010 en_US dc.date.accessioned 9-May-2016 16:39:28 (UTC+8) - dc.date.available 9-May-2016 16:39:28 (UTC+8) - dc.date.issued (上傳時間) 9-May-2016 16:39:28 (UTC+8) - dc.identifier (Other Identifiers) G0967510091 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/95624 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用數學系 zh_TW dc.description (描述) 967510091 zh_TW dc.description.abstract (摘要) 在這篇論文中，藉由一個二維度的馬可夫鏈， 建立保護VIP線路同時允許重試現象的一般客戶線路的數學模型。 我們提出一個融合階段演算法以處理此二維度的馬可夫鏈，並且提出管理成本函數以研究在客服中心中最適當的服務人員數目 。藉由逼近法，找出一般顧客在重試群裡的平均等候時間和等候時間機率分配函數的上界與下界。 數值結果說明逼近方法對於計算一個很大的系統時可以省下很多計算時間，而且不失準確性。 最後，我們探討逼近法和實際解之間的誤差，數值結果也說明隨著系統容量或顧客到達率的增加，逼近法將更為準確。 zh_TW dc.description.abstract (摘要) In this thesis, we model a call center with guard channel scheme for VIP calls and retrial phenomenon for regular calls by a 2-dimensional Markov chain. We present a phase merging algorithm to solve the 2-dimensional Markov chain and a managerial cost function corresponding to studying the optimum number of servers in a call center. Also we will obtain upper and lower bounds with probability distribution functions of waiting time by using approximation. Numerical results show the approximation can save computational time without losing precision in the case of a call center with large capacity. Moreover, errors of the approximation are discussed, and it shows that the approximation is more accurate when the capacity of system or the arrival rate is large. en_US dc.description.abstract (摘要) Abstract 中文摘要 List of Figures List of Tables 1. Introduction 2. System description 2.1 A queueing model 2.2 Waiting time 2.3 Computation of stationary probability distribution 3. Approximation and its computing procedure 3.1 Approximation of pi-method 3.2 Applications 3.3 Errors between Approximation and pi-method 4. Conclusion Appendix A Appendix B Bibliography - dc.description.tableofcontents Abstract 中文摘要 List of Figures List of Tables 1. Introduction 2. System description 2.1 A queueing model 2.2 Waiting time 2.3 Computation of stationary probability distribution 3. Approximation and its computing procedure 3.1 Approximation of pi-method 3.2 Applications 3.3 Errors between Approximation and pi-method 4. Conclusion Appendix A Appendix B Bibliography zh_TW dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0967510091 en_US dc.subject (關鍵詞) 客戶服務中心 zh_TW dc.subject (關鍵詞) 排隊模型 zh_TW dc.subject (關鍵詞) 二維度馬可夫鏈 zh_TW dc.title (題名) 以二維度馬可夫鏈的排隊模型研究客戶服務中心之等候機制 zh_TW dc.title (題名) A queueing model of call center by two-dimensional Markov chain approach in a case study en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Abate J., Whitt W., Numberical inversion of Laplace transforms of probability distribution. ORSA. Journal on computing 7. 1995; 36-43. [2] Artalejo J.R., Gomez-corral A, Neuts MF., Numerical analysis of multiserver retrial queues operating under a full access policy. In: Latouche G. and Taylor P.(Eds), Advances in Algorithmic Methods for Stochastic Models. Notable Publications Inc., NJ. 2000; 1-19. [3] Artalejo J.R., Orlovsky D.S, Dudin A.N., Multiserver retrial model with variable number of active servers. Computer and Industrial Engineering. 2005; 48(2); 273-288. [4] Chen B.P.K., Henderson S.G., Two Issues in Setting Call Centre Staffing Levels. Annals of Operations Research. 2001; 108; 157-192. [5] Choi B.D., Chang Y., Single server retrial queues with priority calls. Mathematical and Computer Modeling. 1999; 30(3); 7-32. [6] Choi B.D., Melikov A., Amir velibekov., A simple numerical approximation of joint probabilities of calls in service and calls in the retrial group in a picocell. Appl. Comput. Math. 7(2008); no.1; 21-30. [7] Korolyuk, V.S., Korolyuk, V.V., Stochastic models of systems. Kluwer Academic Pluishers, Boston, 2009. 50 [8] Liang, C.C., Hsu, P.Y., Leu, J.D., Luh, H., An effective approach for content delivery in an evolving intranet environment- a case study of the largest telecom company in Taiwan. Lect Notes Comp Sci. 2005; 3806: 740-49. [9] Liang, C.C., Wang, C.H., Luh, H., Hsu, P.Y., Disaster Avoidance Mechanism for Content-Delivering. Service, Copmputer and Oper Res. 2009; 36(1): 27-39. [10] Mushko V.V., Klimenok V.I., Ramakrishnan K.O., Krishnamoorthy A, Dudin A.N., Multiserver queue with addressed retrials. Annals of Operations Reserch. 2006; 141(1); 283-301. [11] Matlab 7. The MathWorks, Inc.. 2009. [12] Servi L.D., Algorithmic solutions to two-dimensional birth-death processes with application to capacity planning. Telecommunication Systems. 2002; 21(2-4); 205-212. [13] Ross S., A First Course in Probability. Sixth edition, by Prentice-Hall, Inc.. 2002. [14] Taha H.A., Operations Research an introduction. Seventh edition, by Pearson Education, Inc.. 2003. [15] Takayuki O., Analysis of a QBD process that depends on backgroumd QBD processes. Septemer, CMU-CS-04-163. 2004. zh_TW
