In this article, we consider random occupancy models and the related problems based on the methods of generating functions. The waiting time distributions associated with sequential random occupancy models are investigated through the probability generating functions. We provide the effective computational tools for the evaluation of the probability functions by making use of the Bell polynomials. The results presented here provide a wide framework for developing the theory of occupancy models. Finally, we treat several examples in order to demonstrate how our theoretical results are employed for the investigation of the random occupancy models along with numerical results.

中文翻译：

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随机占用模型中的齐次多元分布及其应用

在本文中，我们将基于生成函数的方法考虑随机占用模型和相关问题。通过概率生成函数研究与顺序随机占用模型关联的等待时间分布。通过使用贝尔多项式，我们为评估概率函数提供了有效的计算工具。此处提供的结果为开发占用模型理论提供了广泛的框架。最后，我们将处理几个示例，以证明我们的理论结果以及数值结果如何用于调查随机占用模型。