摘要
陆传赉在文献[1]中研究了当系统中的队长为r时,新来的顾客以概率αr=1/(r+1)或αr=1/(r+1)-1/(r+2)加入系统,即输入率为λr=λαr,服务率为μ的可变输入率的M/M/1排队模型;以及当排队等待的队长为r时,不耐烦顾客离开队伍的强度为Δr=rδ(δ≥0)的具有不耐烦顾客的M/M/n排队模型;并得到了这两个系统的平稳分布以及主要指标。本文推广了文献[1]的上述两个模型;把具有不耐烦顾客的M/M/n排队模型和可变输入率的M/M/n的排队模型进行了结合研究,即讨论了输入率可变同时具有不耐烦顾客的情况;考虑了输入率λr和服务率μr都随队长r变化的情况,即λr=λαr=λ/1+r,r=0,1,2,…μr=rμ,0≤r≤n nμ+Δr-n,r>n,建立了输入率可变且具有不耐烦顾客的M/M/n排队模型,得到了模型的平稳分布以及各种指标,并举例说明了该模型在实际问题中的应用。
Lu Chuan-lai studied the M/M/1 queuing system with variable input rate when the new customer joined the system with the probability αr=1/（r＋1）or αr=1/（r＋1）-1/（r＋2）.Namely the input rate is λr=λαr,and the service rate u is a constant when the queue length is r in the literature[1].And studied the M/M/n queuing system of impatient customers which the customers leave the intensity of troops is Δr=rδ（δ≥0）.And the stable distribution and key indicators of the system is receied.In this paper,we generalize the above two models in [1].This article is puts the queuing model with impatient customers and variable input rate combined queuing model.Namely this article studes the M/M/n queuing system with variable input rate and impatient customers.We consider the situation which input rate and service rate with the change of captain r.That is {λr=λαr=λ/1＋r r=0,1,2,…μr={rμ,0≤r≤n nμ＋Δr-n,rn.I established a queuing model with variable input rate of impatient customers and obtained the stable distribution and key indicators of the system.The article also illustrates the application of this model in practical problems.
出处
《重庆师范大学学报（自然科学版）》
CAS
2011年第3期49-52,共4页
Journal of Chongqing Normal University:Natural Science
