Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?
Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes?
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DOI：
10.1287/msom.2014.0490
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发表时间：
2014-06-01
影响因子：
6.3
通讯作者：
Whitt, Ward
中科院分区：
文献类型：
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作者：
Kim, Song-Hee;Whitt, Ward
呼叫中心和医院等服务系统通常具有随时间强烈变化的到达情况。对于这种到达过程，一个自然的模型是非齐次泊松过程（NHPP），但应该通过对到达数据应用适当的统计检验来进行测试。假设NHPP的速率可被视为近似分段常数，则可以通过结合来自不同子区间的数据，并利用经典的条件均匀性质，应用泊松过程（PP）的柯尔莫哥洛夫 - 斯米尔诺夫（KS）统计检验来测试NHPP。在本文中，我们将KS检验应用于银行呼叫中心和医院急诊科的到达数据，并表明它们与NHPP性质相符，但前提是要仔细分析这些数据。最初的测试拒绝了NHPP零假设，因为它没有考虑到达数据的三个常见特征：（i）数据取整，例如到秒；（ii）选择速率变化过大的子区间；（iii）由于将来自一周中固定某天的固定时段且在多周内到达率不同的数据进行合并而导致的过度离散。在本文中，我们研究如何解决这三个问题中的每一个。
Service systems such as call centers and hospitals typically have strongly time-varying arrivals. A natural model for such an arrival process is a nonhomogeneous Poisson process (NHPP), but that should be tested by applying appropriate statistical tests to arrival data. Assuming that the NHPP has a rate that can be regarded as approximately piecewise-constant, a Kolmogorov-Smirnov (KS) statistical test of a Poisson process (PP) can be applied to test for a NHPP by combining data from separate subintervals, exploiting the classical conditional-uniform property. In this paper, we apply KS tests to banking call center and hospital emergency department arrival data and show that they are consistent with the NHPP property, but only if that data is analyzed carefully. Initial testing rejected the NHPP null hypothesis because it failed to account for three common features of arrival data: (i) data rounding, e.g., to seconds; (ii) choosing subintervals over which the rate varies too much; and (iii) overdispersion caused by combining data from fixed hours on a fixed day of the week over multiple weeks that do not have the same arrival rate. In this paper, we investigate how to address each of these three problems.