Engineering Solution of a Basic Call-Center Model
Engineering Solution of a Basic Call-Center Model
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基本呼叫中心模型的工程解决方案
DOI：
10.1287/mnsc.1040.0302
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
W. Whitt
针对具有泊松到达过程、独立同分布（IID）服务时间、5台服务器、r个额外等待空间和IID客户放弃时间的基本呼叫中心排队模型m /GI/s/r+GI，提出了一种快速计算所有标准稳态性能指标的近似算法。对呼叫中心的实证研究表明，服务时间和放弃时间的分布往往不是接近指数的，因此有必要超越马尔可夫模型M/M/s/r+M的特殊情况，但一般的服务时间和放弃时间分布使得现实模型很难直接分析。该算法基于适当的MarkovianM/M/s/r+M(n)队列模型的近似，其中em (n)表示状态相关的放弃率。在做了额外的近似之后，稳态等待时间分布通过它们的拉普拉斯变换来表征。然后通过数值反变换计算近似分布。仿真实验表明，该近似具有较高的精度。整体算法可用于确定所需的人员配备水平，例如，需要保证的最小服务器数量，首先，放弃率低于任何指定的目标值，其次，在给定客户最终将得到服务的情况下，在指定的截止日期内为到达的客户提供服务的条件概率至少是指定的目标值。
An algorithm is developed to rapidly compute approximations for all the standard steady-state performance measures in the basic call-center queueing modelM/GI/s/r+GI, which has a Poisson arrival process, independent and identically distributed (IID) service times with a general distribution,s servers,r extra waiting spaces and IID customer abandonment times with a general distribution. Empirical studies of call centers indicate that the service-time and abandon-time distributions often are not nearly exponential, so that it is important to go beyond the MarkovianM/M/s/r+M special case, but the general service-time and abandon-time distributions make the realistic model very difficult to analyze directly. The proposed algorithm is based on an approximation by an appropriate MarkovianM/M/s/r+M(n) queueing model, whereM(n) denotes state-dependent abandonment rates. After making an additional approximation, steady-state waiting-time distributions are characterized via their Laplace transforms. Then the approximate distributions are computed by numerically inverting the transforms. Simulation experiments show that the approximation is quite accurate. The overall algorithm can be applied to determine desired staffing levels, e.g., the minimum number of servers needed to guarantee that, first, the abandonment rate is below any specified target value and, second, that the conditional probability that an arriving customer will be served within a specified deadline, given that the customer eventually will be served, is at least a specified target value.