全文总字数：3290字
1. 毕业设计（论文）的内容和要求
M/M/1是最为经典的排队系统，到达顾客的时间间隔与接受服务所需要的时长均服从参数恒定的指数分布。
然而在实际应用场景下，这两个参数都有可能随环境而发生变化，譬如顾客到达可能存在高峰期和平峰期，也即模型具有不同的随机环境。
本文将研究带有三种随机环境的M/M/1排队系统，应用矩阵几何解的方法，得到系统的稳态分布，从而进一步得到系统的各个性能指标, 如：每个顾客的平均等待时间、系统的平均队长等。
2. 实验内容和要求
matlab编程画图：1、输入率对系统平均队长的影响；2、输入率对顾客平均等待时间的影响；
3. 参考文献
【1】N. T. Thomopoulos (2012) Fundamentals of Queuing Systems. Springer, New York.【2】Neuts M F (1981) Matrix-Geometric Solutions in Stochastic Models: Algorithmic Approach. Johns Hopkins University Press, Baltimore【3】 Latouche G and Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modeling. ASA-SIAM Series on Statistics and Applied Probability. Philadelphia【4】Haverkort B and Ost A (1997) Steady state analysis of infinite stochastic petri nets: a comparing between the spectral expansion and the matrix geometric method, 7th InternationalWorkshop on petri Nets and Performance models. 335-346【5】Mitrani I and Chakka R (1995) Spectral expansion solution for a class of Markov models:application and comparison with the matrix-geometric method. Perform Eval 23(3):241-260【6】Dobbie, J. M. (1961). Letter to the editor-a doubled-ended queuing problem of Kendall.Operations Research, 9(5), 755757.【7】Edelson, N. M., Hilderbrand, D. K. (1975). Congestion tolls for Poisson queuing pro-cesses. Econometrica: Journal of the Econometric Society, 43(1), 8192.【8】Giveen, S. M. (1963). A taxicab problem with time-dependent arrival rates. SIAM Review,5(2), 119127.【9】Guo, P., Hassin, R. (2011). Strategic behavior and social optimization in Markovianvacation queues. Operations Research, 59, 986997.【10】Gurvich, I., Ward, A. (2014). On the dynamic control of matching queues. StochasticSystems, 4(2), 479523.【11】Hassin, R., Haviv, M. (2003). To queue or not to queue: Equilibrium behavior in queueing systems. Springer Science Business Media.【12】Jain, H. C. (1962). A double-ended queueing system. Defence Science Journal, 12(4),327332.【13】Kashyap, B. R. K. (1966). The double-ended queue with bulk service and limited waitingspace. Operations Research, 14(5), 822834.【14】Kashyap, B. R. K. (1967). Further results for the double ended queue. Metrika, 11(1),168186.【15】Kendall, D. (1951). Some problems in the theory of queues. Journal of the Royal Statistical Society, Series B, 13(2), 151185.【16】Kim, W. K., Yoon, K. P., Mendoza, G., Sedaghat, M. (2010). Simulation model for ex-tended double-ended queueing. Computers and Industrial Engineering, 59(2), 209219. Li.【17】Q., Guo, P., Li, C. L., Song, J. S. (2016). Equilibrium joining strategies and optimalcontrol of a make-to-stock queue. Production and Operations Management, 25(9),15131527.【18】Chakka R (1995) Performance and reliability modelling of computing systems using spectralexpansion. Ph.D. Thesis, University of Newcastle upon Tyne, Newcastle upon Tyne
4. 毕业设计（论文）计划
2020年12月15日-2020年12月22日 任务书下达。
2020年12月22日-2021年1月12日 收集资料，熟悉课题，完成开题报告。
2021年2月1日-2021年2月15日 画出系统状态转移图。
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