We study flow of substance in a channel of network which consists of nodes of network and edges which connect these nodes and form ways for motion of substance. The channel can have arbitrary number of arms and each arm can contain arbitrary number of nodes. The flow of substance is modeled by a system of ordinary differential equations. We discuss first a model for a channel which arms contain infinite number of nodes each. For stationary regime of motion of substance in such a channel we obtain probability distributions connected to distribution of substance in any of channel’s arms and in entire channel. Obtained distributions are not discussed by other authors and can be connected to Waring distribution. Next, we discuss a model for flow of substance in a channel which arms contain finite number of nodes each. We obtain probability distributions connected to distribution of substance in the nodes of the channel for stationary regime of flow of substance. These distributions are also new and we calculate corresponding information measure and Shannon information measure for studied kind of flow of substance.

中文翻译：

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包含任意臂数的网络通道中物质稳定流动的统计特性

我们研究物质在网络通道中的流动，该通道由网络节点和连接这些节点并形成物质运动方式的边组成。通道可以有任意数量的臂，每个臂可以包含任意数量的节点。物质的流动由常微分方程组建模。我们首先讨论一个通道模型，每个通道包含无限数量的节点。对于这种通道中物质运动的静止状态，我们获得了与物质在任何通道臂和整个通道中的分布相关的概率分布。其他作者不讨论获得的发行版，可以连接到 Waring 发行版。接下来，我们讨论通道中物质流动的模型，该通道每个臂包含有限数量的节点。我们获得了与物质在通道节点中的分布相关的概率分布，用于物质流动的静止状态。这些分布也是新的，我们为所研究的物质流计算了相应的信息测度和香农信息测度。