Approximations for Chat Service Systems Using Many-Server Diffusion Limits
研究了客服聊天系统的排队模型，其中一名客服可同时服务多名顾客，通过证明排队过程在多服务器重流量下的扩散收敛，给出了稳态性能指标的近似公式，数值实验验证了准确性。
We study a queueing model of customer service chat systems. A unique feature of these queueing systems is that a single agent can serve multiple customers simultaneously. We prove the convergence of the queueing process to different diffusion processes in a many-server heavy-traffic regime in three different cases. Using this result, we are able to offer approximations for the steady-state performance measures such as the number of customers in the system, the abandonment probability, and the sojourn time of a customer. Our numerical experiments show that proposed approximations are accurate in various cases.