In this paper, we study the \(M_n/M_n/c/(K_1+K_2)+M_n\) system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join the online or the offline/callback queue or simply balk. Customers waiting in the online queue are impatient and if their patience expires, they may choose to join the callback queue instead of abandoning the system for good. Customers in the callback queue are assumed to be patient. Customers are served following a threshold policy: when the number of customers in the callback queue surpasses a threshold level, the next customer to serve is picked from here. Otherwise, only after a predetermined number of agents are reserved for future arrivals, customers remaining in the callback queue can be served. We conduct an exact analysis of this system and obtain its steady-state performance measures. The times spent in both queues are expressed as Phase-type distributions. With numerical examples, we present how the policy responds when shorter callback times are promised or customer characteristics vary.

在本文中，我们研究\（M_n / M_n / c /（K_1 + K_2）+ M_n \）具有两个有限大小队列的系统，其中基础指数随机变量具有与状态相关的速率。当所有服务器都处于繁忙状态时，客户可以在到达时加入在线或离线/回调队列，或者干脆放弃。在在线队列中等待的客户没有耐心，如果他们的耐心到期了，他们可以选择加入回调队列，而不是永久放弃系统。假定回调队列中的客户耐心等待。根据阈值策略为客户提供服务：当回调队列中的客户数量超过阈值级别时，将从此处选择下一个要服务的客户。否则，只有在预定数量的座席被保留以用于将来的到达之后，才可以为保留在回调队列中的客户提供服务。我们对该系统进行精确分析，并获得其稳态性能指标。在两个队列中花费的时间表示为阶段类型分布。通过数字示例，我们介绍了在承诺较短的回调时间或客户特征发生变化时策略如何响应。