关键词: 无耐性顾客, 输入率可变, M/M/1/&infin, 优化设计

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