Abstract: To guarantee the market shares and the benefits of enterprises and to restrain the number of lost customers,an M/M/1/∞ queue model with the variable input rate was employed to analyze the service system with customer impatience.Some important system characteristics such as the captains,the system busy idle rate,the customer loss and the expected waiting time were obtained.Thus a cost model was constructed by considering the fixed costs such as equipment investment and space,and the potential costs such as customer waiting time and lost customers.The optimal service capacity was solved by Newton iteration method,and a parameter analysis was also made.A case study was used to compare the solutions obtained by the present method and the general method respectively,and the necessity and the effectiveness of considering the customer patience in the optimization design of the service capacity of such a system was verified.

Key words: impatient customers, variable input rate, M/M/1/∞, optimal design

摘要： 为保障企业的市场和收益,减少顾客流失,采用输入率可变的M/M/1/∞排队模型对具有无耐性顾客的服务系统进行拟合,得到队长、系统忙闲率、顾客损失、等待时间期望等系统指标。综合考虑包括设备投入、空间占用等固定成本和顾客等待、顾客流失等潜在成本,建立成本费用模型,用牛顿迭代法求解系统的最优服务能力,并进行参数分析。通过一个实例分析对比了所提最优设计和普通设计的优化结果,证明了在此类系统服务能力优化设计中考虑顾客耐性的必要性和有效性。

关键词: 无耐性顾客, 输入率可变, M/M/1/&infin, 优化设计