Abstract

A deterministic dynamical system representing the contour network is considered. The number of contours is two. At each contour there is a segment moving with a constant velocity which is called the cluster, because in the discrete variant of the system it corresponds to the cluster of particles, that is, to the group of particles occupying the adjacent cells and moving simultaneously. The lengths of contours and the lengths of clusters are prescribed. There is a common point named a node. Clusters cannot pass a node simultaneously. A cluster stops and waits for the node to empty if this cluster comes to the node at the instance when another cluster passes through the node. If clusters come to a node simultaneously, then precedence is given to the cluster considered the priority cluster (the priority rule of conflict resolution). The theorems on the average speed of cluster motion are proved taking delays in different types of the system’s behavior into account. It is established that the average speed of motion of each cluster in the system is independent of the cluster position at the initial time instance in contrast to the analogous system with another rule of conflict resolution considered previously, where such dependence appears in the general case. The possible practical interpretation of the studied system is given. The presented system is referred to as the class of dynamical networks introduced and investigated by A.P. Buslaev. The results may be applied to solve questions on the automatization of motion of a continuous mass, simulate the motion of transport, and other areas.

中文翻译：

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具有优先规则的两轮廓线系统中的群集运动解决冲突

摘要

考虑表示轮廓网络的确定性动力学系统。轮廓的数量是两个。在每个轮廓上都有一个以恒定速度运动的段，称为簇，因为在系统的离散变体中，它对应于粒子簇，即对应于占据相邻单元并同时运动的粒子组。规定轮廓的长度和簇的长度。有一个公共点称为节点。群集无法同时通过节点。如果某个群集在另一个群集通过该实例时到达该节点，则该群集将停止并等待该节点清空。如果群集同时到达一个节点，则将优先级给予被视为优先级群集的群集（冲突解决的优先级规则）。证明了群集运动平均速度的定理，其中考虑了不同类型系统行为的延迟。可以确定的是，与之前考虑过另一种解决冲突规则的类似系统不同，系统中每个群集在初始时间实例的平均运动速度独立于群集位置，在一般情况下会出现这种依赖性。给出了对所研究系统的可能的实际解释。提出的系统称为AP Buslaev引入和研究的动态网络类。结果可用于解决有关连续质量运动自动化的问题，模拟运输运动以及其他区域的运动。