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題名 重試等候系統的通用解法
A Generalized Method for Retrial Queueing Systems
作者 葉新富
Yeh, Hsin-Fu
貢獻者 陸行
Luh, Hsing
葉新富
Yeh, Hsin-Fu
關鍵詞 重試等候系統
截斷方法
馬可夫過程
Retrial system
LDQBDs
Truncated methods
Markov processes
日期 2022
上傳時間 1-Apr-2022 15:04:08 (UTC+8)
摘要 我們為不耐煩顧客之重試等候系統的平穩機率提供一個新的上界。如
果模型滿足某些條件，則會給出更好的上界。以此上界，我們可以用有限
矩陣計算平穩機率，並用數值實驗驗證論文中提出的定理。此外，我們提
出了該定理的進一步推廣形式，任何滿足條件的模型都可以應用這個定理。
We present a new upper bound of the stationary probability of retrial queueing systems with impatient customers. If the model satisfies some conditions, it gives a better upper bound. Furthermore, we can calculate the stationary probability with a finite matrix. Numerical experiments to verify the theorems are presented in the thesis. In addition, we propose a further generalization form of the theorem. Any model satisfying the condition could apply this theorem.
參考文獻 [1] V.V. Anisimov and J.R. Artalejo. Approximation of multiserver retrial queues by means
of generalized truncated models. Top, 10(1):51–66, 2002.
[2] J.R. Artalejo. A classified bibliography of research on retrial queues: progress in 1990–
1999. Top, 7(2):187–211, 1999.
[3] J.R. Artalejo and M. Pozo. Numerical calculation of the stationary distribution of the main
multiserver retrial queue. Annals of Operations Research, 116(1):41–56, 2002.
[4] H. Baumann and W. Sandmann. Numerical solution of level dependent quasi-birth-anddeath processes. Procedia Computer Science, 1(1):1561–1569, 2010.
[5] A. Gómez-Corral. A bibliographical guide to the analysis of retrial queues through matrix
analytic techniques. Annals of Operations Research, 141(1):163–191, 2006.
[6] B.K. Kumar, R.N. Krishnan, R. Sankar, and R. Rukmani. Analysis of dynamic service
system between regular and retrial queues with impatient customers. Journal of Industrial
& Management Optimization, 18(1):267, 2022.
[7] G. Latouche, V. Ramaswami, and Society for Industrial and Applied Mathematics.
Introduction to matrix analytic methods in stochastic modeling. Society for Industrial
and Applied Mathematics, 1999.
[8] J. Liu and J.T. Wang. Strategic joining rules in a single server markovian queue with
bernoulli vacation. Operational Research, 17(2):413–434, 2017.
[9] H.P. Luh and P.C. Song. Matrix analytic solutions for m/m/s retrial queues with impatient
customers. In International Conference on Queueing Theory and Network Applications,
pages 16–33. Springer, 2019.
[10] M.F. Neuts. Matrix-geometric solutions in stochastic models. Johns Hopkins series in the
mathematical sciences. Johns Hopkins University Press, Baltimore, MD, July 1981.
[11] E. Onur, H. Deliç, C. Ersoy, and M. Çaǧlayan. Measurement-based replanning of cell
capacities in gsm networks. Computer Networks, 39(6):749–767, 2002.
[12] V. Ramaswami and P.G. Taylor. Some properties of the rate perators in level dependent
quasi-birth-and-death processes with countable number of phases. Stochastic Models,
12(1):143–164, 1996.
[13] A. Remke, B.R. Haverkort, and L. Cloth. Uniformization with representatives:
comprehensive transient analysis of infinite-state qbds. In Proceeding from the 2006
workshop on Tools for solving structured Markov chains, pages 7–es, 2006.
[14] J.F. Shortle, J.M. Thompson, D. Gross, and C.M. Harris. Fundamentals of queueing theory,
volume 399. John Wiley & Sons, 2018.
[15] P.D. Tuan, M. Hiroyuki, K. Shoji, and T. Yutaka. 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, 2010.
[16] K.Z. Wang, N. Li, and Z.B. Jiang. Queueing system with impatient customers: A review.
In Proceedings of 2010 IEEE international conference on service operations and logistics,
and informatics, pages 82–87. IEEE, 2010.
[17] W.S. Yang and S.C. Taek. M/M/s queue with impatient customers and retrials. Applied
Mathematical Modelling, 33(6):2596–2606, 2009
描述 碩士
國立政治大學
應用數學系
108751006
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108751006
資料類型 thesis
dc.contributor.advisor 陸行zh_TW
dc.contributor.advisor Luh, Hsingen_US
dc.contributor.author (Authors) 葉新富zh_TW
dc.contributor.author (Authors) Yeh, Hsin-Fuen_US
dc.creator (作者) 葉新富zh_TW
dc.creator (作者) Yeh, Hsin-Fuen_US
dc.date (日期) 2022en_US
dc.date.accessioned 1-Apr-2022 15:04:08 (UTC+8)-
dc.date.available 1-Apr-2022 15:04:08 (UTC+8)-
dc.date.issued (上傳時間) 1-Apr-2022 15:04:08 (UTC+8)-
dc.identifier (Other Identifiers) G0108751006en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/139555-
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) 108751006zh_TW
dc.description.abstract (摘要) 我們為不耐煩顧客之重試等候系統的平穩機率提供一個新的上界。如
果模型滿足某些條件，則會給出更好的上界。以此上界，我們可以用有限
矩陣計算平穩機率，並用數值實驗驗證論文中提出的定理。此外，我們提
出了該定理的進一步推廣形式，任何滿足條件的模型都可以應用這個定理。		zh_TW
dc.description.abstract (摘要) We present a new upper bound of the stationary probability of retrial queueing systems with impatient customers. If the model satisfies some conditions, it gives a better upper bound. Furthermore, we can calculate the stationary probability with a finite matrix. Numerical experiments to verify the theorems are presented in the thesis. In addition, we propose a further generalization form of the theorem. Any model satisfying the condition could apply this theorem.en_US
dc.description.tableofcontents 中文摘要 i
Abstract ii
Contents iii
List of Tables v
List of Figures vi
1 Introduction and the System Model 1
2 The Main Theorem 6
3 Model Analysis 10
3.1 Model Analysis 10
3.2 An Additional Main Theorem 18
4 Numerical Results 22
4.1 Computation of Performance Indices 22
4.2 Numerical Experiments 23
5 A Further Generalization 26
5.1 The General Main Theorem 26
5.2 A General Main Theorem 36
6 Conclusions 39
Bibliography 40
A Code in Numerical Examples 42
B Functions Used in Examples 44		zh_TW
dc.format.extent 572974 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108751006en_US
dc.subject (關鍵詞) 重試等候系統zh_TW
dc.subject (關鍵詞) 截斷方法zh_TW
dc.subject (關鍵詞) 馬可夫過程zh_TW
dc.subject (關鍵詞) Retrial systemen_US
dc.subject (關鍵詞) LDQBDsen_US
dc.subject (關鍵詞) Truncated methodsen_US
dc.subject (關鍵詞) Markov processesen_US
dc.title (題名) 重試等候系統的通用解法zh_TW
dc.title (題名) A Generalized Method for Retrial Queueing Systemsen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] V.V. Anisimov and J.R. Artalejo. Approximation of multiserver retrial queues by means
of generalized truncated models. Top, 10(1):51–66, 2002.
[2] J.R. Artalejo. A classified bibliography of research on retrial queues: progress in 1990–
1999. Top, 7(2):187–211, 1999.
[3] J.R. Artalejo and M. Pozo. Numerical calculation of the stationary distribution of the main
multiserver retrial queue. Annals of Operations Research, 116(1):41–56, 2002.
[4] H. Baumann and W. Sandmann. Numerical solution of level dependent quasi-birth-anddeath processes. Procedia Computer Science, 1(1):1561–1569, 2010.
[5] A. Gómez-Corral. A bibliographical guide to the analysis of retrial queues through matrix
analytic techniques. Annals of Operations Research, 141(1):163–191, 2006.
[6] B.K. Kumar, R.N. Krishnan, R. Sankar, and R. Rukmani. Analysis of dynamic service
system between regular and retrial queues with impatient customers. Journal of Industrial
& Management Optimization, 18(1):267, 2022.
[7] G. Latouche, V. Ramaswami, and Society for Industrial and Applied Mathematics.
Introduction to matrix analytic methods in stochastic modeling. Society for Industrial
and Applied Mathematics, 1999.
[8] J. Liu and J.T. Wang. Strategic joining rules in a single server markovian queue with
bernoulli vacation. Operational Research, 17(2):413–434, 2017.
[9] H.P. Luh and P.C. Song. Matrix analytic solutions for m/m/s retrial queues with impatient
customers. In International Conference on Queueing Theory and Network Applications,
pages 16–33. Springer, 2019.
[10] M.F. Neuts. Matrix-geometric solutions in stochastic models. Johns Hopkins series in the
mathematical sciences. Johns Hopkins University Press, Baltimore, MD, July 1981.
[11] E. Onur, H. Deliç, C. Ersoy, and M. Çaǧlayan. Measurement-based replanning of cell
capacities in gsm networks. Computer Networks, 39(6):749–767, 2002.
[12] V. Ramaswami and P.G. Taylor. Some properties of the rate perators in level dependent
quasi-birth-and-death processes with countable number of phases. Stochastic Models,
12(1):143–164, 1996.
[13] A. Remke, B.R. Haverkort, and L. Cloth. Uniformization with representatives:
comprehensive transient analysis of infinite-state qbds. In Proceeding from the 2006
workshop on Tools for solving structured Markov chains, pages 7–es, 2006.
[14] J.F. Shortle, J.M. Thompson, D. Gross, and C.M. Harris. Fundamentals of queueing theory,
volume 399. John Wiley & Sons, 2018.
[15] P.D. Tuan, M. Hiroyuki, K. Shoji, and T. Yutaka. 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, 2010.
[16] K.Z. Wang, N. Li, and Z.B. Jiang. Queueing system with impatient customers: A review.
In Proceedings of 2010 IEEE international conference on service operations and logistics,
and informatics, pages 82–87. IEEE, 2010.
[17] W.S. Yang and S.C. Taek. M/M/s queue with impatient customers and retrials. Applied
Mathematical Modelling, 33(6):2596–2606, 2009		zh_TW
dc.identifier.doi (DOI) 10.6814/NCCU202200361en_US