Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process
Choosing arrival process models for service systems: Tests of a nonhomogeneous Poisson process
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选择服务系统的到达过程模型：非齐次泊松过程的测试
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发表时间：
2014
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通讯作者：
W. Whitt
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作者：
W. Whitt
呼叫中心和医院急诊室等服务系统通常具有强烈的时变到达率。因此，非齐次泊松过程（NHPP）是用于排队模型中到达过程以进行性能分析的自然模型。然而，正如布朗等人所强调的，用服务系统数据进行统计检验以确认NHPP确实合适是很重要的。他们在利用条件均匀（CU）性质将NHPP转换为在[0,1]上均匀分布的一系列独立同分布随机变量，然后对数据进行对数变换之后，提出了一种基于柯尔莫哥洛夫 - 斯米尔诺夫（KS）统计量的特定统计检验。我们研究为什么进行最终的数据变换是重要的，并考虑它应该采取什么形式。我们进行了大量的模拟实验来研究这些替代统计检验的功效。我们得出结论，布朗等人的一般方法是出色的，但刘易斯借鉴德宾的方法提出的一种替代数据变换产生了一种对NHPP检验具有始终更大功效的检验。我们还得出结论，在CU变换之后的KS检验，在没有任何额外数据变换的情况下，往往最适合用于针对主要仅通过随机性和时间依赖性而不同于NHPP的替代假设进行检验。© 2014威利期刊公司，《海军研究后勤学》61：66 - 90，2014
Service systems such as call centers and hospital emergency rooms typically have strongly time‐varying arrival rates. Thus, a nonhomogeneous Poisson process (NHPP) is a natural model for the arrival process in a queueing model for performance analysis. Nevertheless, it is important to perform statistical tests with service system data to confirm that an NHPP is actually appropriate, as emphasized by Brown et al. [8]. They suggested a specific statistical test based on the Kolmogorov–Smirnov (KS) statistic after exploiting the conditional‐uniform (CU) property to transform the NHPP into a sequence of i.i.d. random variables uniformly distributed on [0,1] and then performing a logarithmic transformation of the data. We investigate why it is important to perform the final data transformation and consider what form it should take. We conduct extensive simulation experiments to study the power of these alternative statistical tests. We conclude that the general approach of Brown et al. [8] is excellent, but that an alternative data transformation proposed by Lewis [22], drawing upon Durbin [10], produces a test of an NHPP test with consistently greater power. We also conclude that the KS test after the CU transformation, without any additional data transformation, tends to be best to test against alternative hypotheses that primarily differ from an NHPP only through stochastic and time dependence. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 66–90, 2014