Abstract: With the rapid development of mobile internet and instant messaging technology, the new online customer service center has gradually replaced the traditional call center and become the mainstream of customer service center in recent years. The biggest difference with traditional call center is that one agent can serve more than one customer at the same time. The maximum number of customers an agent can serve at the same time, named as service scale, directly affects the efficiency of the online customer service center. When the number increases, the agent needs to be frequently switched between several customers, which will reduce the quality and efficiency of the agent and cause customers to give up while waiting for the reply of the customer service. While the number decreases, more customers are forced to wait for the service, which will lead to a higher rate of customer abandonment and a lower rate of agent utilization. Therefore, when setting the number of customers that can be served at the same time, we should not only consider its impact on the average waiting time of customers in the system, but also consider its impact on the abandonment rate of customers. How to set the upper limit of the number of people that online customer service can serve at the same time is a new but important problem in online customer service center compared with traditional call center.
The basic “one-to-one” queuing model which one customer serves only one customer at the same time, is not directly applicable to the situation of an online call center where one customer can chat with more than one customer at the same time. In order to analyze how to set the upper limit of customers that can be served at the same time, this paper establishes a two-layer queuing model to calculate the average stay time and abandonment rate of customers and other basic queuing indicators in the queuing system. This paper analyzes the characteristics of online customer service mode, divides its one-to-many service process into two one-to-one service processes, and establishes a two-layer queuing model,which is message layer and customer layer by birth-and-death analysis. According to this model, the average stay time and abandonment rate of customers in the system can be calculated directly by giving the customer arrival rate, customer patience time, the number of customer consultation frequency and the average time spent by customers and customer service to prepare each message. In the two-layer queuing model, the abandonment behavior of customers in the process of waiting for customer service access system is specially considered. According to this model, the average stay time of customers and the abandonment rate of customers in the process of waiting for customer service access can be calculated. In the numerical experiment, first of all, a Flexsim simulation model is built to verify the correctness of the two-layer queuing model. And furthermore, the sensitivity analysis is made when the average customer arrival rate, average customer patience time, customer switching cost, the average time of customer reply message and other relevant parameters change are comprehensively completed.
The research in this paper has a strong practical guiding meaning. Enterprises can choose an appropriate model according to their own conditions to calculate the average stay time and abandonment rate of customers in the system by providing basic parameters such as the arrival rate of customers, the number of customer consultation messages, the value of customer patience, the average time for customers and agents to prepare each message. And we take this as the basis for setting the optimal number of online customer service. When the external parameters change within a certain range, the enterprise does not need to spend extra costs. It only needs to adjust the upper limit of the number of online customer service, so as to optimize the average stay time and abandonment rate of customers in the system, which is of great significance for the cost-oriented online customer service enterprise operation. For online customer service enterprises with sufficient funds, the upper limit of the number of online customer service can be adjusted with increasing the number of online customer service agents. The research of this paper also has a strong theoretical significance. It not only provides a referential idea for the establishment of the one-to-many queuing model of online customer service considering the abandonment of customers, but also provides a basic model for the calculation of human demand and the research of load distribution in the process of the expansion of single-agent online customer service center to multi-agent online customer service center.

Key words: online customer service, many customers simultaneous service, optimal service scale, customer abandonment

摘要： 在线客服已成为当前客户服务中心的主要形式,其与传统的电话服务最大的不同是一位客服可同时为多位顾客服务。客服同时服务的人数直接影响着客服中心的服务效率:同时服务的人数较多,顾客虽然可以较早得进入咨询队列,但客服需要在多个不同的咨询主体之间频繁切换,会降低客服的服务效率;同时服务的人数较少,造成更多顾客等待服务开始,导致顾客的放弃率升高,降低客服中心的服务水平与质量。因此,在考虑顾客放弃行为的情况下,通过建立双层排队模型探究顾客平均逗留时间、顾客放弃率与同时服务人数之间的关系以确定最优服务人数,通过数值仿真验证了模型的准确性并进一步完成了相关参数变化时的敏感性分析。

关键词: 在线客服, 一对多服务, 最优服务人数, 顾客放弃