Rate conservation laws: A survey
Rate conservation laws: A survey
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速率守恒定律：一项调查
DOI：
10.1007/bf01189231
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发表时间：
1994
期刊：
影响因子：
1.2
通讯作者：
M. Miyazawa
中科院分区：
文献类型：
--
作者：
M. Miyazawa
我们调查了速率保护定律，简短的RCL，在队列中产生和相关的随机模型。有其他应用程序。 Mecke的固定随机测量公式可以为此目的而制定为RCL。 ，这是普通期望的一定延伸，并得出适用于样本平均结果的RCL。准预测框架。
We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=λG, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=λG can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.