一对多交互式在线客户服务排队模型

以聊天工具为基础的在线客服大量取代了电话形式的传统客服。与电话客服不同，一个在线客服人员能同时为多个顾客提供交互式的服务，而传统的排队公式都是以一对一服务为基础推导的，无法直接用来计算在线客服的排队指标。分析了一对多交互模式下的排队特点，提出了该模式下的服务水平指标，构建了包含顾客层和消息层的双层排队模型，推导了系统平均客户数量、平均服务时间、平均等待回复时间等指标公式，最后进行了公式解析值的仿真验证。仿真结果表明，顾客平均服务时间和消息平均等待时间等指标能有效描述服务系统的排队状况，而本文提出的双层排队模型能准确计算一对多服务模式下的排队指标。

A Queueing Model of 1-N Interactive Service Mode in Online Customer Service

Using the instant messaging software, online customer service is widely applied in e-commerce, banking, and other commercial fields. Different from that of telephone-based customer service, an online service agent can use the chat software to serve several customers at the same time, which is named as the 1-N service mode. The basic queueing formulas are no longer suitable in such mode. First, the characters of the online customer service were extracted. Besides, based on the newly introduced service performance metrics, a 2-layer queueing model was proposed. Moreover, the functions for the number of customers, average total time in system, and average waiting time were formulated. Furthermore, the analytical formulas were proved by a simulation experiment, in which the 3 key metrics calculated by the proposed model can be approximately matched with simulation results.