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 Title: 重試等候系統的通用解法A Generalized Method for Retrial Queueing Systems Authors: 葉新富Yeh, Hsin-Fu Contributors: 陸行Luh, Hsing葉新富Yeh, Hsin-Fu Keywords: 重試等候系統截斷方法馬可夫過程Retrial systemLDQBDsTruncated methodsMarkov processes Date: 2022 Issue Date: 2022-04-01 15:04:08 (UTC+8) Abstract: 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. Reference: [1] V.V. Anisimov and J.R. Artalejo. Approximation of multiserver retrial queues by meansof 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 mainmultiserver 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 matrixanalytic 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 servicesystem 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 Industrialand Applied Mathematics, 1999.[8] J. Liu and J.T. Wang. Strategic joining rules in a single server markovian queue withbernoulli 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 impatientcustomers. 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 themathematical sciences. Johns Hopkins University Press, Baltimore, MD, July 1981.[11] E. Onur, H. Deliç, C. Ersoy, and M. Çaǧlayan. Measurement-based replanning of cellcapacities 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 dependentquasi-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 2006workshop 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 matricesof level-dependent qbd processes. In Proceedings of the 5th international conference onqueueing 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. AppliedMathematical Modelling, 33(6):2596–2606, 2009 Description: 碩士國立政治大學應用數學系108751006 Source URI: http://thesis.lib.nccu.edu.tw/record/#G0108751006 Data Type: thesis Appears in Collections: [應用數學系] 學位論文

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