水平穿越法在带有不耐烦顾客的呼叫中心中的建模及应用

研究了一种需求服从泊松分布的多座席呼叫中心服务系统的两个问题, 其中考虑了顾客的不耐烦行为. 第一个问题中只有单一排队队列, 顾客进入系统后由于不能立即接受服务或等待时间超过其期望等待时间会选择放弃排队. 第二个问题中有两个排队队列, 主排队队列是顾客呼入队列, 次排队队列是座席提供回拨服务的队列, 且这个队列的顾客来源于由于等待时间超过其期望等待时间放弃排队的主排队队列的顾客. 本文利用水平穿越法得到了稳态时第一个问题的顾客平均等待时间及顾客总的放弃概率及第二个问题中座席繁忙的概率. 该方法不仅具有直观清晰的物理意义, 而且能避免排队系统中冗长的推导过程, 有利于快速简单解决问题. 数值分析表明第一个问题中顾客平均等待时间是座席数的凸函数, 并且顾客的不耐烦程度越高则他们的平均等待时间越短. 同时坐席数的增加在初期能够显著提高接通率, 达到一定数量后效用开始递减. 而且在系统其它参数确定且系统需求流较大情况下, 顾客的放弃率大小对顾客总的放弃概率大小的影响几乎可以忽略.

Modeling and application of level crossing in call centers with impatient customers

This paper discusses about two problems in a multi-sever call center with Poisson arrivals, in which the impatient behavior of customer is also considered. In the first problem, there is only one waiting line, customers may abandon waiting when they cannot receive service immediately or the waiting time is much longer than they expected. In the second problem, two waiting lines are used, the first one called main line is used for call-in customers, and the other named call-back line, which means that the server would call back to the customers, who comes from the main line but abandon waiting for his impatience. With level crossing method in this paper we get the average waiting time and the total abandonment probability of customers in the first problem and the busy servers probability in the second problem in steady state. This method can not only give us an intuitive and clear physical meaning, but also avoid the lengthy and tedious derivation process, this would be much better for solving problems. The numerical analysis for the first problem in this paper shows that the average waiting time is a convex function of the servers number, but this waiting time would become shorter with the increase of impatience of customers. In the mean time, the probability of the successful connection call could be obviously improved at the beginning, and this effect would be decreased after the servers reach a specification number. Moreover, if other parameters in the system are fixed and in the condition that the demand fluid is large enough, the influence of the customer abandonment rate can be even neglected for the total abandonment probability.