Gt / H2* / st +GI队列模型等待时间的高负荷极限
Heavy-Traffic Limits for Waiting Times in the Gt / H2* / st +GI Queuing Model
摘要: 考虑的队列模型为具有随时间变化的到达率和服务台个数,服从H2*服务时间分布,顾客放弃服从一般的概率分布。通过分析Gt / H2* / st +GI队列模型的一个序列,对队首等待时间进行表示,建立队首等待时间的泛函弱大数定律,并给出证明。
Abstract: This article considered the queuing model, having time-varying arrival rate and staffing, H2* ser-vice times and customer abandonment according to a general probability distribution, analyzed a sequence of Gt / H2* / st +GI queue model, expressed the head of line (HOL) waiting time and ob-tained the Functional weak law of large numbers of HOL waiting time, and proved it.
文章引用:牛鑫, 刘建民, 王青青. Gt / H2* / st +GI队列模型等待时间的高负荷极限[J]. 理论数学, 2019, 9(9): 1094-1101. https://doi.org/10.12677/PM.2019.99134

参考文献

[1] Liu, Y. and Whitt, W. (2014) Many-Server Heavy-Traffic Limit for Queues with Time-Varying Parameters. Annals of Applied Probability, 24, 378-421. [Google Scholar] [CrossRef
[2] Whitt, W. (2005) Heavy-Traffic Limits for the Queue. Mathematics of Operations Research, 30, 1-27. [Google Scholar] [CrossRef
[3] Pang, G. and Whitt, W. (2010) Two-Parameter Heavy-Traffic Limits for Infinite-Server Queues. Queueing Systems, 65, 325-364. [Google Scholar] [CrossRef
[4] Liu, Y. and Whitt, W. (2012) The Many-Server Fluid Queue. Queueing Systems, 71, 405-444. [Google Scholar] [CrossRef
[5] Liu, Y. and Whitt, W. (2012) A Many-Server Fluid Limit for the Queueing Model Experiencing Periods of Overloading. Operations Research Letters, 40, 307-312. [Google Scholar] [CrossRef
[6] Talreja, R. and Whitt, W. (2009) Heavy-Traffic Limits for Waiting Times in Many-Server Queues with Abandonment. Annals of Applied Probability, 19, 2137-2175. [Google Scholar] [CrossRef
[7] 刘建民. 高负荷下带有放弃的 队列[J]. 工程数学学报, 2008, 25(2): 245-252.
[8] Whitt, W. (2004) A Diffusion Approximation for the Queue. Operations Research, 52, 922-941. [Google Scholar] [CrossRef
[9] 解瑞金. 高负荷下带有放弃的排队系统的等待时间[D]: [硕士学位论文]. 西安: 长安大学, 2010.
[10] Halfin, S. and Whitt, W. (1981) Heavy-Traffic Limits for Queues with Many Exponential Servers. http://www.columbia.edu/~ww2040/allpapers.html [Google Scholar] [CrossRef
[11] Puhalskii, A.A. (2013) On the Queue in Heavy Traffic. Mathematical Methods of Operations Research, 78, 119-148. [Google Scholar] [CrossRef
[12] Whitt, W. (2002) Stochastic-Process Limits. Springer, New York. [Google Scholar] [CrossRef
[13] Billingsley, P. (1999) Convergence of Probability Measures. 2nd Edition, Wiley, New York. [Google Scholar] [CrossRef