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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\n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\n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\n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\nof generalized truncated models. Top, 10(1):51–66, 2002.\n[2] J.R. Artalejo. A classified bibliography of research on retrial queues: progress in 1990–\n1999. Top, 7(2):187–211, 1999.\n[3] J.R. Artalejo and M. Pozo. Numerical calculation of the stationary distribution of the main\nmultiserver retrial queue. Annals of Operations Research, 116(1):41–56, 2002.\n[4] H. Baumann and W. Sandmann. Numerical solution of level dependent quasi-birth-anddeath processes. Procedia Computer Science, 1(1):1561–1569, 2010.\n[5] A. Gómez-Corral. A bibliographical guide to the analysis of retrial queues through matrix\nanalytic techniques. Annals of Operations Research, 141(1):163–191, 2006.\n[6] B.K. Kumar, R.N. Krishnan, R. Sankar, and R. Rukmani. Analysis of dynamic service\nsystem between regular and retrial queues with impatient customers. Journal of Industrial\n& Management Optimization, 18(1):267, 2022.\n[7] G. Latouche, V. Ramaswami, and Society for Industrial and Applied Mathematics.\nIntroduction to matrix analytic methods in stochastic modeling. Society for Industrial\nand Applied Mathematics, 1999.\n[8] J. Liu and J.T. Wang. Strategic joining rules in a single server markovian queue with\nbernoulli vacation. Operational Research, 17(2):413–434, 2017.\n[9] H.P. Luh and P.C. Song. Matrix analytic solutions for m/m/s retrial queues with impatient\ncustomers. In International Conference on Queueing Theory and Network Applications,\npages 16–33. Springer, 2019.\n[10] M.F. Neuts. Matrix-geometric solutions in stochastic models. Johns Hopkins series in the\nmathematical sciences. Johns Hopkins University Press, Baltimore, MD, July 1981.\n[11] E. Onur, H. Deliç, C. Ersoy, and M. Çaǧlayan. Measurement-based replanning of cell\ncapacities in gsm networks. Computer Networks, 39(6):749–767, 2002.\n[12] V. Ramaswami and P.G. Taylor. Some properties of the rate perators in level dependent\nquasi-birth-and-death processes with countable number of phases. Stochastic Models,\n12(1):143–164, 1996.\n[13] A. Remke, B.R. Haverkort, and L. Cloth. Uniformization with representatives:\ncomprehensive transient analysis of infinite-state qbds. In Proceeding from the 2006\nworkshop on Tools for solving structured Markov chains, pages 7–es, 2006.\n[14] J.F. Shortle, J.M. Thompson, D. Gross, and C.M. Harris. Fundamentals of queueing theory,\nvolume 399. John Wiley & Sons, 2018.\n[15] P.D. Tuan, M. Hiroyuki, K. Shoji, and T. Yutaka. A simple algorithm for the rate matrices\nof level-dependent qbd processes. In Proceedings of the 5th international conference on\nqueueing theory and network applications, pages 46–52, 2010.\n[16] K.Z. Wang, N. Li, and Z.B. Jiang. Queueing system with impatient customers: A review.\nIn Proceedings of 2010 IEEE international conference on service operations and logistics,\nand informatics, pages 82–87. IEEE, 2010.\n[17] W.S. Yang and S.C. Taek. M/M/s queue with impatient customers and retrials. Applied\nMathematical 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, Hsing en_US dc.contributor.author (Authors) 葉新富 zh_TW dc.contributor.author (Authors) Yeh, Hsin-Fu en_US dc.creator (作者) 葉新富 zh_TW dc.creator (作者) Yeh, Hsin-Fu en_US dc.date (日期) 2022 en_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) G0108751006 en_US dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=158863 - 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) 108751006 zh_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\n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\n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\n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\nAbstract ii\nContents iii\nList of Tables v\nList of Figures vi\n1 Introduction and the System Model 1\n2 The Main Theorem 6\n3 Model Analysis 10\n3.1 Model Analysis 10\n3.2 An Additional Main Theorem 18\n4 Numerical Results 22\n4.1 Computation of Performance Indices 22\n4.2 Numerical Experiments 23\n5 A Further Generalization 26\n5.1 The General Main Theorem 26\n5.2 A General Main Theorem 36\n6 Conclusions 39\nBibliography 40\nA Code in Numerical Examples 42\nB 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/#G0108751006 en_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 system en_US dc.subject (關鍵詞) LDQBDs en_US dc.subject (關鍵詞) Truncated methods en_US dc.subject (關鍵詞) Markov processes en_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 Systems en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] V.V. Anisimov and J.R. Artalejo. Approximation of multiserver retrial queues by means\nof generalized truncated models. Top, 10(1):51–66, 2002.\n[2] J.R. Artalejo. A classified bibliography of research on retrial queues: progress in 1990–\n1999. Top, 7(2):187–211, 1999.\n[3] J.R. Artalejo and M. Pozo. Numerical calculation of the stationary distribution of the main\nmultiserver retrial queue. Annals of Operations Research, 116(1):41–56, 2002.\n[4] H. Baumann and W. Sandmann. Numerical solution of level dependent quasi-birth-anddeath processes. Procedia Computer Science, 1(1):1561–1569, 2010.\n[5] A. Gómez-Corral. A bibliographical guide to the analysis of retrial queues through matrix\nanalytic techniques. Annals of Operations Research, 141(1):163–191, 2006.\n[6] B.K. Kumar, R.N. Krishnan, R. Sankar, and R. Rukmani. Analysis of dynamic service\nsystem between regular and retrial queues with impatient customers. Journal of Industrial\n& Management Optimization, 18(1):267, 2022.\n[7] G. Latouche, V. Ramaswami, and Society for Industrial and Applied Mathematics.\nIntroduction to matrix analytic methods in stochastic modeling. Society for Industrial\nand Applied Mathematics, 1999.\n[8] J. Liu and J.T. Wang. Strategic joining rules in a single server markovian queue with\nbernoulli vacation. Operational Research, 17(2):413–434, 2017.\n[9] H.P. Luh and P.C. Song. Matrix analytic solutions for m/m/s retrial queues with impatient\ncustomers. In International Conference on Queueing Theory and Network Applications,\npages 16–33. Springer, 2019.\n[10] M.F. Neuts. Matrix-geometric solutions in stochastic models. Johns Hopkins series in the\nmathematical sciences. Johns Hopkins University Press, Baltimore, MD, July 1981.\n[11] E. Onur, H. Deliç, C. Ersoy, and M. Çaǧlayan. Measurement-based replanning of cell\ncapacities in gsm networks. Computer Networks, 39(6):749–767, 2002.\n[12] V. Ramaswami and P.G. Taylor. Some properties of the rate perators in level dependent\nquasi-birth-and-death processes with countable number of phases. Stochastic Models,\n12(1):143–164, 1996.\n[13] A. Remke, B.R. Haverkort, and L. Cloth. Uniformization with representatives:\ncomprehensive transient analysis of infinite-state qbds. In Proceeding from the 2006\nworkshop on Tools for solving structured Markov chains, pages 7–es, 2006.\n[14] J.F. Shortle, J.M. Thompson, D. Gross, and C.M. Harris. Fundamentals of queueing theory,\nvolume 399. John Wiley & Sons, 2018.\n[15] P.D. Tuan, M. Hiroyuki, K. Shoji, and T. Yutaka. A simple algorithm for the rate matrices\nof level-dependent qbd processes. In Proceedings of the 5th international conference on\nqueueing theory and network applications, pages 46–52, 2010.\n[16] K.Z. Wang, N. Li, and Z.B. Jiang. Queueing system with impatient customers: A review.\nIn Proceedings of 2010 IEEE international conference on service operations and logistics,\nand informatics, pages 82–87. IEEE, 2010.\n[17] W.S. Yang and S.C. Taek. M/M/s queue with impatient customers and retrials. Applied\nMathematical Modelling, 33(6):2596–2606, 2009 zh_TW dc.identifier.doi (DOI) 10.6814/NCCU202200361 en_US
