呼叫中心提示时间与顾客耐心的主从博弈模型

Stackelberg game model for call centers with delay information

研究呼叫中心与顾客之间的提示排队时间确定与顾客耐心度选择问题.针对一类M/M/N+M呼叫中心排队模型,研究了排队时间提示对顾客耐心心理与放弃行为的影响,并建立了基于呼叫中心和顾客效用函数的非合作Stackelberg博弈模型,目标是求呼叫中心和顾客效用值最大的最优策略.采用排队论分析了呼叫中心的排队过程,给出了二分法和不动点结合的系统性能指标求解算法.最后,通过数值实验,分析了提示时间可靠性和顾客耐心变化率对性能指标影响规律,对比了不同博弈策略下的呼叫中心和顾客的效用值实验结果表明了方法的合理性和有效性.

This paper studies a decision problem on waiting delay time and patience time by a call center and customers, respectively. Firstly, for a M/M/N＋M call center queue model, a non-cooperative Stackelberg game model is formulated to maximize the value of the utility function based on the impact of delay time on the customers＇ impatience psychology. Secondly, the performance of the queuing process is obtained by the combination of the bisection algorithm and the fixed point algorithm after the process analysis with queue theory. Finally, the impact of the delay time reliability and the patient change rate on the system performance is analyzed with the numerical results. Moreover, this paper compares the value of the utility function of the call center and the customers under different game strategies and effectiveness of the method. The experimental results illustrate the reasonability