Markovian arrival process (MAP) is a popular tool for modeling arrival processes of stochastic systems such as queueing systems, reliability systems and telecommunications networks. In this paper we show how properties of Markovian Arrival Processes can be derived from the general theory of Markov processes with a homogeneous second component. We also present a series of results on queueing systems with MAP arrivals which were published in RUDN University before 1990.

中文翻译：

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关于到达过程的马尔可夫建模

马尔可夫到达过程 (MAP) 是一种流行的工具，用于对随机系统（例如排队系统、可靠性系统和电信网络）的到达过程进行建模。在本文中，我们展示了如何从具有齐次第二分量的马尔可夫过程的一般理论推导出马尔可夫到达过程的性质。我们还展示了 1990 年之前在 RUDN 大学发表的具有 MAP 到达的排队系统的一系列结果。