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中文摘要：
为了对呼叫中心（Call Center）的整体性能进行定量优化分析，针对顾客在ACD（Automatic Call Distributor）中排队时会因不耐烦而放弃等待，服务台（Agents）根据顾客等待队长使用可变服务率，同时考虑服务台发生故障对系统的影响，讨论了不耐烦、可变服务率M／M／S／K＋M可修排队人模型．采用矩阵几何方法求解，给出解析解和系统稳态性能指标．结果表明：呼叫中心相关参数给定的条件下可以求出最优服务台数；当等待队长大于零时适当提高服务率可以使系统更优化；为了提高系统性能，可以根据系统中平均故障台数这一指标配备备用服务台；适当增加服务台或者中继线可以提高顾客满意度，减少顾客损失率。
英文摘要：
In order to analyze performance qualities of a call center quantitatively, as such characters that a customer＇s waiting queue will probably be abandoned due to impatience when all the servers are busy, agents change service rate according to the length of waiting queue and the servers can break down at any time. An M/M/S/K ＋ M queueing model in the changeable service rate with impatience and server breakdowns is studied. An analytic solution and some system measures in stability of the model are given. It is pointed out that optimal number of servers can be derived if interrelated parameters are given, customers will be more satisfied if agents or trunks are increased, and the system performance can be improved by using quicker service rate when the length of waiting queue is greater than zero. In addition the spare servers can be provided according the measure of expected value of server breakdowns.
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