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https://nccur.lib.nccu.edu.tw/handle/140.119/127725
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| Title: | 即時雙線服務系統之等候模型
Modeling on a real-time two-tier service system |
| Authors: | 黃賴均
Huang, Lai-Chun |
| Contributors: | 陸行
Luh, Hsing
黃賴均
Huang, Lai-Chun |
| Keywords: | 即時信息
雙線服務系統
類生死過程
矩陣幾何解法
Real-time information
Two-tier service system
QBD process
Matrix geometric method |
| Date: | 2019 |
| Issue Date: | 2019-12-06 09:20:54 (UTC+8) |
| Abstract: | 等待時間一直是服務品質的重要指標，例如減少在醫療保健，公共服務和各種重點服務(VIP)系統的等待時間。本論文考慮由兩個不同的服務站組成的雙線服務系統，包含一個免費服務站，和一個付費服務站，每個服務站都有隊列和服務提供者，據此建立數學等候模型。 兩個服務站提供相同的服務內容。 假設其中付費服務站的隊列具有長度限制，該服務站為了減少客戶等待時間維持服務質量而採取溢價服務。 溢價服務意指系統通過收取額外費用提供另一服務選擇的機制。
由於有一些客戶會根據自己的時間價值做出決策，我們在這種雙線服務系統中研究隊列長度信息對顧客行為的影響，
我們發現向客戶提供即時隊列長度信息可以顯著地減少總等待成本。此外，從最小化所有客戶的總等待成本和最大化付費服務提供者的利潤的角度，我們利用數學模型分析提供即時隊列長度信息與否之影響。
在論文中，我們展示此模型能夠反映減輕客戶等待之負擔的信息效應，同時也揭示價格策略和服務保障對雙線服務系統服務指標的影響。
Waiting time has been an unavoidable concern for service such as healthcare, public provision and VIP systems of various services. We address this issue for considering a two-tier service system which is composed of two different service stations: a gratis station and a toll station. Each service station is set up by a queue and a service provider. The service providers of service stations provide the same service. In the thesis, we study a queueing model that one of the service stations charges a premium in order to guarantee a maximum expected waiting time and the queue of this service station has a length limit.
We study the effects of the queue length information on the performance of such a two-tier service system with customers who make decisions based on their own time value.
We show that offering the real-time queue length information to customers can effectively enhance the performances of both services in the system.
Furthermore, for both with and without real-time queue length information scenarios, we analyze the problem from two perspectives. There are the perspectives of minimizing the expected social waiting cost for customers and maximizing the expected profit for the manager.
We show that this model can obviously reflect the information effects of alleviating the burden of waiting for customers, and it also reveals the impact of service guarantee and price discrimination on the performance of the two-tier service system. |
| Reference: | [1] M. Armony and C. Maglaras. Contact centers with a callback option and realtime delay information. Operations Research, 52(4):527–545, 2004.
[2] M. Armony and C. Maglaras. On customer contact centers with a callback option:Customer decisions, routing rules, and system design. Operations Research, 52(2):271–292, 2004.
[3] S. Asmussen. Random walks. Applied Probability and Queues, 51:220–243, 2003.
[4] D. Bini and B. Meini. On the solution of a nonlinear matrix equation arising in queueing problems. Matrix Analysis and Applications, 17(4):906–926, 1996.
[5] H. Chen, Qian, Q., and A. Zhang. Would allowing privately funded health care reduce public waiting time? theory and empirical evidence from canadian joint replacement surgery data. Production and Operations Management, 24(4):605–618, 2015.
[6] Wikipedia contributors. Exponential distribution. https://en.wikipedia.org/wiki/Exponential_distribution, 2002. Online; accessed 1October2019.
[7] Wikipedia contributors. Newton’s method. https://en.wikipedia.org/wiki/Newton%27s_method, 2002. Online; accessed 4September2019.
[8] Wikipedia contributors. Pareto distribution. https://en.wikipedia.org/wiki/Pareto_distribution, 2002. Online; accessed 25September2019.
[9] Wikipedia contributors. Uniform distribution (continuous). https://en.wikipedia.org/wiki/Uniform_distribution_(continuous), 2005. Online; accessed 27July2019.
[10] N. M. Edelson and D. K. Hilderbrand. Congestion tolls for poisson queuing processes. Journal of the Econometric Society, 43(1):81–92, 1975.
[11] S. H. Fredrick and J. L. Gerald. Introduction to Operation Research. McGrawHill Education, 1995.
[12] S. Gavirneni and V. G. Kulkarni. Selfselecting priority queues with burr distributed waiting costs. Production and Operations Management, 25(6):979–992, 2016.
[13] L Green and S. Savin. Reducing delays for medical appointments: a queueing approach. Operations Research, 56:1526–1538, 2008.
[14] D. Gross and C. M. Harris. Fundamentals of Queueing Theory, 3rd ed. John Wiley & Sons, 1998.
[15] P. Guo and Z. G. Zhang. Strategic queueing behavior and its impact on system performance in service systems with the congestionbased staffing policy. Manufacturing and Service Operations Management, 15(1):118–131, 2015.
[16] P. Guo and P. Zipkin. Analysis and comparison of queues with different levels of delay information. Management Science, 53(6):962–970, 2007.
[17] R. Hassin and M. Haviv. To Queue or not to Queue: Equilibrium Behavior in Queueing Systems., volume 59. Springer Science and Business Media, 2003.
[18] Z. Hua, W. Chen, and Z. G. Zhang. Competition and coordination in two‐tier public service systems under government fiscal policy. Production and Operations Management, 25(8): 1430–1448, 2016.
[19] H. Jiang, Pang Z., and S. Savin. Performancebased contracts for outpatient medical services. Manufacturing and Service Operations Management, 14(4):654–669, 2012.
[20] M. Johar and E. Savage. Do private patients have shorter waiting times for elective surgery? evidence from new south wales public hospitals. Economic Papers: A Journal of Applied Economics and Policy, 29(2):128–142, 2010.
[21] S. Kapodistria and Z. Palmowski. Matrix geometric approach for random walks: Stability condition and equilibrium distribution. Stochastic Models, 33(4):572–597, 2017.
[22] L. Kleinrock. Optimum bribing for queue position. Operations Research, 15(2):304–318, 1967.
[23] G. Latouche and V. Ramaswami. Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM, 1999.
[24] H. P. Luh and P. C. Song. Matrix analytic solutions for m/m/s retrial queues with impatient customers. International Conference on Queueing Theory and Network Applications, 11688:16–33, 2019.
[25] MathWorks MATLAB. Matlab r2018b. The MathWorks: Natick, MA, USA, 2018.
[26] H. Mendelson and S. Whang. Optimal incentivecompatible priority pricing for the m/m/1 queue. Operations Research, 38(5):870–883, 1990.
[27] R. T. Meulen and F. Jotterand. Individual responsibility and solidarity in european healthcare: further down the road to twotier system of health care. Journal of Medicine and Philosophy, 33(3):191–197, 2008.
[28] P. Naor. The regulation of queue size by levying tolls. Econometrica, 37(1):15 – 23, 1969.
[29] H. Nazerzadeh and R. S. Randhawa. Asymptotic optimality of two service grades for customer differentiation in queueing systems. working paper, University of Southern California, 2014.
[30] M. F. Neuts. Matrixgeometric Solutions in Stochastic Models: An Algorithmic Approach. Courier Corporation, 1994.
[31] E.L. Plambeck. Optimal leadtime differentiation via diffusion approximations. Operations Research, 52(2):213–228, 2004.
[32] Q. Qian, Guo P., and Lindsey R. Comparison of subsidy schemes for reducing waiting times in healthcare systems. Production and Operations Management, 26(11):2033–2049,
2017.
[33] R. Schroeter. The costs of concealing the customer queue. working paper, Bureau of Business and Economic Research, Arizona State, 1982.
[34] S. Stidham Jr. Optimal Design of Queueing Systems. Chapman and Hall, 2009.
[35] Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí. Scatter search and local nlp solvers: A multistart framework for global optimization. INFORMS Journal on Computing, 19(3):328 – 340, 2007.
[36] G. Wan and Q. Wang. Two‐tier healthcare service systems and cost of waiting for patients. Applied Stochastic Models in Business and Industry, 33(2):167–183, 2017.
[37] G. Z. Zhang and H. P. Luh. Information effects on performance of twotier service systems with strategic customers. working paper, 2013k. Optimum bribing for queue position. Operations Research, 15(2):304–318, 1967.
[23] G. Latouche and V. Ramaswami. Introduction to Matrix Analytic Methods in Stochastic Modeling. SIAM, 1999.
[24] H. P. Luh and P. C. Song. Matrix analytic solutions for m/m/s retrial queues with impatient customers. International Conference on Queueing Theory and Network Applications, 11688:16–33, 2019.
[25] MathWorks MATLAB. Matlab r2018b. The MathWorks: Natick, MA, USA, 2018.
[26] H. Mendelson and S. Whang. Optimal incentivecompatible priority pricing for the m/m/1 queue. Operations Research, 38(5):870–883, 1990.
[27] R. T. Meulen and F. Jotterand. Individual responsibility and solidarity in european healthcare: further down the road to twotier system of health care. Journal of Medicine and Philosophy, 33(3):191–197, 2008.
[28] P. Naor. The regulation of queue size by levying tolls. Econometrica, 37(1):15 – 23, 1969.
[29] H. Nazerzadeh and R. S. Randhawa. Asymptotic optimality of two service grades for customer differentiation in queueing systems. working paper, University of Southern California, 2014.
[30] M. F. Neuts. Matrixgeometric Solutions in Stochastic Models: An Algorithmic Approach. Courier Corporation, 1994.
[31] E.L. Plambeck. Optimal leadtime differentiation via diffusion approximations. Operations Research, 52(2):213–228, 2004.
[32] Q. Qian, Guo P., and Lindsey R. Comparison of subsidy schemes for reducing waiting times in healthcare systems. Production and Operations Management, 26(11):2033–2049, 2017.
[33] R. Schroeter. The costs of concealing the customer queue. working paper, Bureau of Business and Economic Research, Arizona State, 1982.
[34] S. Stidham Jr. Optimal Design of Queueing Systems. Chapman and Hall, 2009.
[35] Z. Ugray, L. Lasdon, J. Plummer, F. Glover, J. Kelly, and R. Martí. Scatter search and local nlp solvers: A multistart framework for global optimization. INFORMS Journal on Computing, 19(3):328 – 340, 2007.
[36] G. Wan and Q. Wang. Two‐tier healthcare service systems and cost of waiting for patients. Applied Stochastic Models in Business and Industry, 33(2):167–183, 2017.
[37] G. Z. Zhang and H. P. Luh. Information effects on performance of twotier service systems with strategic customers. working paper, 2013 |
| Description: | 碩士
國立政治大學
應用數學系
105751017 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0105751017 |
| Data Type: | thesis |
| DOI: | 10.6814/NCCU201901241 |
| Appears in Collections: | [應用數學系] 學位論文
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