On minimal representations of Rational Arrival Processes
On minimal representations of Rational Arrival Processes
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DOI：
10.1007/s10479-011-1001-5
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发表时间：
2013
影响因子：
4.8
通讯作者：
P. Buchholz;M. Telek
中科院分区：
文献类型：
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作者：
P. Buchholz;M. Telek
理性到达过程（RAPs）形成了随机过程的一个一般类别，其中包括马尔可夫到达过程（MAPs）作为一个子类。本文研究了RAPs及其不同大小的表示。我们给出了一些不同表示之间的转换方法，并给出了评估最小表示大小的条件。通过使用线性系统理论的一些类似结果，定义了一种最小化方法，该方法允许将RAP（从冗余高维）转换为其最小表示之一。给出了一种计算最小表示的算法。此外，我们将该方法扩展到具有批量到达的RAPs （BRAPs）和具有不同客户类型到达的RAPs （mrap）。
Rational Arrival Processes (RAPs) form a general class of stochastic processes which include Markovian Arrival Processes (MAPs) as a subclass. In this paper we study RAPs and their representations of different sizes. We show some transformation methods between different representations and present conditions to evaluate the size of the minimal representation. By using some analogous results from linear systems theory, a minimization approach is defined which allows one to transform a RAP (from a redundant high dimension) into one of its minimal representations. An algorithm for computing a minimal representation is also given. Furthermore, we extend the approach to RAPs with batch arrivals (BRAPs) and to RAPs with arrivals of different customer types (MRAPs).