输入率可变且有差错服务及不耐烦顾客的排队模型分析  

Queuing model with variable input rates,mistake service and impatient customers

作　　者：潘全如[1] 

机构地区：[1]江苏科技大学数理学院,江苏镇江212003

出　　处：《江苏科技大学学报（自然科学版）》2012年第5期514-518,共5页Journal of Jiangsu University of Science and Technology:Natural Science Edition

基　　金：国家自然科学基金资助项目(2010SL135J);江苏省高校自然科学基金资助项目(10KJB110003)

摘　　要：在系统顾客容量不变的情况下,顾客到达系统后是否进入系统接受服务对销售行业影响是巨大的.从排队长度对顾客输入率的影响着手,研究了输入率、服务正确率及不耐烦顾客强度均与队长有关的排队模型,得出了进入系统的顾客流是泊松过程.系统中的顾客数是生灭过程,同时求得了系统的队长平稳分布,因没有进入系统而导致系统损失的概率、因不耐烦而离去的顾客的均值、单位时间内系统服务错误率、因系统容量有限而无法加入队列的损失概率等多项指标,得出了并非输入率越高系统就盈利越多、并非系统服务正确率越低系统就赚得越少等结论.还得到了能使企业利润最大化的系统容量及服务速度,为销售行业提高自己的销售业绩提供了很有价值的参考.The customers do not necessarily get into the system though arriving at it in the case of a fixed custom- er number, which influences sales industry enormously. Focusing on the influence of queue length on input rate, we build up a queuing model with variable input rates, mistake service and impatient customers, and draw the following conclusions： the customers get into the system in Poissonian flow; the number of customers in the sys- tem is a birth-death process. We obtained the stationary queue length distribution of the model, the loss proba- bility for the customers not entering the system while arriving at the system, the mean of the customers who leaves the system due to impatience, the service error rate per unit time and the loss probability for the customers not joining the queue due to the limited capacity of the system and so on. This paper also justifies the falsehood of the following assumptions ： the bigger the input rate is, the more profit business will get ; the bigger the number of impatient customers is, the less profit business will make. We also obtaind the appropriate service speed and ca- pacity a business should keep to make the biggest profit, which provides a valuable reference for the retail indus- try to improve their sales performance.

关 键 词：可变输入率 差错服务 不耐烦顾客 

分 类 号：O226[理学—运筹学与控制论]