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題名 關於具有優先順序但無耐心等候之多服務員排隊模型
On Two Priority Multi-Server Queues with Impatient Customers
作者 李泓緯
貢獻者 陸行
李泓緯
關鍵詞 多服務員等候系統
無耐心排隊
非搶占優先服務策略
日期 2016
上傳時間 21-Jul-2016 10:01:45 (UTC+8)
摘要 我們考慮多服務員的排隊系統，其中包含兩種沒耐心的顧客群，分別是
高優先級和低優先級的顧客。顧客的到來滿足布阿松過程，顧客群有一個滿
足指數分配的耐心程度，在超出這段時間後，會離開系統。在本文中，服
務時間服從指數分配。所有的顧客和服務類型分為先來先服務（First Come First Served, FCFS）和後來先服務（Last Come First Served, LCFS）兩種。藉由隨機變數的拉普拉斯轉換和矩陣幾何方法配合截取法，得到一個近似值的機率分配。我們會計算兩顧客群等候時間的期望值。並且對於較重要的高優先級顧客，計算他們有給定條件的期望值。
參考文獻 [1] F. Baccelli and G. Hebuterne. On queues with impatient customers. 1981.
[2] A. Brandt and M. Brandt. On the m (n)/m (n)/s queue with impatient calls. Performance
Evaluation, 35(1):1–18, 1999.
[3] B. D. Choi, B. Kim, and J. Chung. M/m/1 queue with impatient customers of higher
priority. Queueing Systems, 38(1):49–66, 2001.
[4] O. Garnett, A. Mandelbaum, and M. Reiman. Designing a call center with impatient customers.
Manufacturing & Service Operations Management, 4(3):208–227, 2002.
[5] F. Iravani and B. Balcıog̃lu. On priority queues with impatient customers. Queueing
Systems, 58(4):239–260, 2008.
[6] D. L. Jagerman. Difference equations with applications to queues. CRC Press, 2000.
[7] O. Jouini and A. Roubos. On multiple priority multi-server queues with impatience. Journal
of the Operational Research Society, 65(5):616–632, 2013.
[8] O. Jouini, Z. Aksin, and Y. Dallery. Call centers with delay information: Models and
insights. Manufacturing & Service Operations Management, 13(4):534–548, 2011.
[9] E. P. Kao and S. D. Wilson. Analysis of nonpreemptive priority queues with multiple
servers and two priority classes. European Journal of Operational Research, 118(1):181–
193, 1999.
[10] O. Kella and U. Yechiali. Waiting times in the non-preemptive priority m/m/c queue.
Stochastic Models, 1(2):257–262, 1985.
[11] T. Phung-Duc and K. Kawanishi. Multiserver retrial queues with after-call work. Numerical
Algebra, Control and Optimization, 1(4):639–656, 2011.
[12] T. Phung-Duc, H. Masuyama, S. Kasahara, and Y. Takahashi. A simple algorithm for the
rate matrices of level-dependent qbd processes. In Proceedings of the 5th international
conference on queueing theory and network applications, pages 46–52. ACM, 2010.
[13] T. Phung-Duc, H. Masuyama, S. Kasahara, and Y. Takahashi. A matrix continued fraction
approach to multiserver retrial queues. Annals of Operations Research, 202(1):161–183,
2013.
[14] V. Sarhangian and B. Balciog̃lu. Waiting time analysis of multi-class queues with impatient
customers. Probability in the Engineering and Informational Sciences, 27(03):333–352,
2013.
[15] A. Sleptchenko. Multi-class, multi-server queues with non-preemptive priorities. Eurandom,
2003.
[16] Q. Wang. Modeling and analysis of high risk patient queues. European Journal of Operational
Research, 155(2):502–515, 2004.
[17] S. Zeltyn, Z. Feldman, and S. Wasserkrug. Waiting and sojourn times in a multi-server
queue with mixed priorities. Queueing Systems, 61(4):305–328, 2009.
描述 碩士
國立政治大學
應用數學系
102751002
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0102751002
資料類型 thesis
dc.contributor.advisor 陸行zh_TW
dc.contributor.author (Authors) 李泓緯zh_TW
dc.creator (作者) 李泓緯zh_TW
dc.date (日期) 2016en_US
dc.date.accessioned 21-Jul-2016 10:01:45 (UTC+8)-
dc.date.available 21-Jul-2016 10:01:45 (UTC+8)-
dc.date.issued (上傳時間) 21-Jul-2016 10:01:45 (UTC+8)-
dc.identifier (Other Identifiers) G0102751002en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/99414-
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) 102751002zh_TW
dc.description.abstract (摘要) 我們考慮多服務員的排隊系統，其中包含兩種沒耐心的顧客群，分別是
高優先級和低優先級的顧客。顧客的到來滿足布阿松過程，顧客群有一個滿
足指數分配的耐心程度，在超出這段時間後，會離開系統。在本文中，服
務時間服從指數分配。所有的顧客和服務類型分為先來先服務（First Come First Served, FCFS）和後來先服務（Last Come First Served, LCFS）兩種。藉由隨機變數的拉普拉斯轉換和矩陣幾何方法配合截取法，得到一個近似值的機率分配。我們會計算兩顧客群等候時間的期望值。並且對於較重要的高優先級顧客，計算他們有給定條件的期望值。		zh_TW
dc.description.tableofcontents Abstract i
中文摘要ii
Contents iii
List of Figures v
List of Tables vi
1 Introduction 1
2 Preliminaries 4
2.1 Modeling 4
2.2 Notation 5
2.3 Expected waiting time 6
3 The probability of numbers of customers in the queues 8
3.1 Analysis of high-priority customers 9
3.2 Analysis of low-priority customers 11
3.2.1 Truncation point 15
3.2.2 Matrix-product rate 16
3.3 Method to compute the probability of all servers idle 17
4 Analysis of Queueing Delays 21
4.1 Analysis of ModelFCFS 22
4.2 Analysis of ModelLCFS 24
5 Numerical results 28
5.1 Comparison the probability of all servers idle 28
5.2 Comparison between FCFS and LCFS 32
6 Conclusion 37
Appendix
A The probability of all server idles and LST of the virtual waiting time 38
B Computation of R(n) 41
Bibliography 42		zh_TW
dc.format.extent 388142 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0102751002en_US
dc.subject (關鍵詞) 多服務員等候系統zh_TW
dc.subject (關鍵詞) 無耐心排隊zh_TW
dc.subject (關鍵詞) 非搶占優先服務策略zh_TW
dc.title (題名) 關於具有優先順序但無耐心等候之多服務員排隊模型zh_TW
dc.title (題名) On Two Priority Multi-Server Queues with Impatient Customersen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] F. Baccelli and G. Hebuterne. On queues with impatient customers. 1981.
[2] A. Brandt and M. Brandt. On the m (n)/m (n)/s queue with impatient calls. Performance
Evaluation, 35(1):1–18, 1999.
[3] B. D. Choi, B. Kim, and J. Chung. M/m/1 queue with impatient customers of higher
priority. Queueing Systems, 38(1):49–66, 2001.
[4] O. Garnett, A. Mandelbaum, and M. Reiman. Designing a call center with impatient customers.
Manufacturing & Service Operations Management, 4(3):208–227, 2002.
[5] F. Iravani and B. Balcıog̃lu. On priority queues with impatient customers. Queueing
Systems, 58(4):239–260, 2008.
[6] D. L. Jagerman. Difference equations with applications to queues. CRC Press, 2000.
[7] O. Jouini and A. Roubos. On multiple priority multi-server queues with impatience. Journal
of the Operational Research Society, 65(5):616–632, 2013.
[8] O. Jouini, Z. Aksin, and Y. Dallery. Call centers with delay information: Models and
insights. Manufacturing & Service Operations Management, 13(4):534–548, 2011.
[9] E. P. Kao and S. D. Wilson. Analysis of nonpreemptive priority queues with multiple
servers and two priority classes. European Journal of Operational Research, 118(1):181–
193, 1999.
[10] O. Kella and U. Yechiali. Waiting times in the non-preemptive priority m/m/c queue.
Stochastic Models, 1(2):257–262, 1985.
[11] T. Phung-Duc and K. Kawanishi. Multiserver retrial queues with after-call work. Numerical
Algebra, Control and Optimization, 1(4):639–656, 2011.
[12] T. Phung-Duc, H. Masuyama, S. Kasahara, and Y. Takahashi. A simple algorithm for the
rate matrices of level-dependent qbd processes. In Proceedings of the 5th international
conference on queueing theory and network applications, pages 46–52. ACM, 2010.
[13] T. Phung-Duc, H. Masuyama, S. Kasahara, and Y. Takahashi. A matrix continued fraction
approach to multiserver retrial queues. Annals of Operations Research, 202(1):161–183,
2013.
[14] V. Sarhangian and B. Balciog̃lu. Waiting time analysis of multi-class queues with impatient
customers. Probability in the Engineering and Informational Sciences, 27(03):333–352,
2013.
[15] A. Sleptchenko. Multi-class, multi-server queues with non-preemptive priorities. Eurandom,
2003.
[16] Q. Wang. Modeling and analysis of high risk patient queues. European Journal of Operational
Research, 155(2):502–515, 2004.
[17] S. Zeltyn, Z. Feldman, and S. Wasserkrug. Waiting and sojourn times in a multi-server
queue with mixed priorities. Queueing Systems, 61(4):305–328, 2009.		zh_TW