Calculating Expected Incomes in Open Markov Networks with Requests of Different Classes and Different Peculiarities

机译:计算Open Markov网络中的预期收入,具有不同类别和不同特点的要求

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A system of difference-differential equations for the expected incomes of open Markov queueing networks with different peculiarities is considered. The number of network states and also the number of equations in this system are both infinite. The incoming flows of requests are elementary and independent while their service times have exponential distributions. The incomes from transitions between different states of the network are deterministic functions that depend on its states; the incomes gained by the queuing server systems per unit time under the invariable states also depend on these states only. The system of the difference-differential equations is solved using the modified method of successive approximations combined with the series method. An example of a Markov G-network with signals and the group elimination of positive requests is studied. As demonstrated below, the expected incomes can be increasing and decreasing time-varying functions; can take positive and negative values.
机译:考虑了用于具有不同特异性的开放马尔可夫排队网络的预期收入的差分方程。网络状态的数量以及该系统中的等式数都是无限的。请求的传入流程是基本的,而独立的,而他们的服务时间具有指数分布。从网络的不同状态之间的转换中的收入是依赖于其状态的确定性函数;在不变状态下每单位时间的排队服务器系统获得的收入也仅取决于这些状态。使用与串联方法组合的连续近似的修改方法解决了差分方程的系统。研究了具有信号的Markov G网络的示例和集体消除正面请求。如下面所示,预期收入可以增加和减少时变函数;可以采取正面和负值。



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