随机环境中的M/M/n排队系统
M/M/n Queuing System in Random Environment
摘要: 本文给出随机环境中的M/M/n排队系统的定义,随机环境中的M/M/n排队系统的平衡条件 ,L(θ)*Lq(θ)*K(θ)*的表达式及其关系,最后给出X*的转移概率的随机Kolmogorov向前和向后方程。
Abstract: In this paper, we give the definition of M/M/n queuing system in random environment, the equilibrium condition of M/M/n queuing system in random environment , the expressions of L(θ)*, Lq(θ)*, K(θ)* and their relations, finally the random Kolmogorov forward and backward equations of of X* are given.
文章引用:单超超, 池夏夏. 随机环境中的M/M/n排队系统[J]. 应用数学进展, 2021, 10(2): 506-517. https://doi.org/10.12677/AAM.2021.102055

参考文献

[1] Wang, J., Huang, Y. and Do, T.V. (2013) A Single-Server Discrete-Time Queue with Correlated Positive and Negative Customer Arrivals. Applied Mathematical Modeling, 37, 6212-6224. [Google Scholar] [CrossRef
[2] Bae, J. and Kim, S. (2010) The Stationary Workload of the G/M/1 Queue with Impatient Customers. Queuing Systems, 64, 253-265. [Google Scholar] [CrossRef
[3] Taufemback, C. and Silva, S.D. (2012) Queuing Theory Applied to the Optimal Management of Bank Excess Reserves. Physica A, 391, 1381-1387. [Google Scholar] [CrossRef
[4] Laxmi, P.V. and Jyothsna, K. (2015) Balking and Renerging Mutiple Working Vacations Queue with Heterogeneous Severs. Journal of Mathematical Modeling and Algorithms in Operations Research, 14, 267-285. [Google Scholar] [CrossRef
[5] Rajadurai, P., Chandrasekaran, V.M. and Saravanarajan, M.C. (2018) Analysis of an Unreliable Retrial G-Queue with Working Vacations and Vacation Interruption under Bernoulli Schedule. AinShams Engineering Journal, 9, 567-580. [Google Scholar] [CrossRef
[6] Hu, D.H. (2004) The Construction of Markov Processes in Random Environments and the Equivalence Theorems. Science in China (Series A), 47, 481-496. [Google Scholar] [CrossRef
[7] 胡迪鹤. 随机环境中的生灭过程的基本概念及存在性[J]. 武汉大学学报(理学版), 2003, 41(1): 1-5.
[8] 吕平, 杨广宇, 胡迪鹤. 随机环境中分枝q-过程[J]. 应用数学学报,2009, 32(5): 799-809.
[9] 单超超, 吕平. 随机环境中的泊松过程[J]. 杭州师范大学学报(自然科学版), 2020. (待发表)
[10] 高振龙, 胡迪鹤, 王伟刚. 随机环境中双移民生灭过程的极限性质[J]. 武汉大学学报(理学版), 2007, 53(1): 21-25.
[11] 孙荣恒, 李建平. 排队论基础[M]. 北京: 科学出版社, 2002.
[12] 胡迪鹤. 随机环境中的马尔可夫过程[M]. 北京: 高等教育出版社, 2011.