The importance of fundamental research on network topologies is widely acknowledged. This study aims to elucidate the effect of congestion avoidance of agents given congestion information on optimizing traffic in a network topology. We investigated stochastic traffic networks in a star topology with a central node connected to isolated secondary nodes with different preferences. Each agent at the central node selects a secondary node by referring to the declining preferences based on the congestion rate of the secondary nodes. We examined two scenarios: 1) Each agent can repeatedly visit the central and secondary nodes. 2) Each agent can access each secondary node only once. For 1), we investigated the uniformity of the agent distribution in a stationary state, and for 2), we measured the travel time for all agents visiting all nodes. When agents repeatedly visit central and other nodes, the uniformity of agent distribution has been found to show three types of nonlinear dependence on the increase in nodes. We found that multivariate statistics describe these characteristic dependences well, suggesting that the balance between the equalization of network usage by avoiding congestion and the covariance caused by mutual referral to congestion information determines the uniformity. We discovered that congestion-avoidance linearizes the travel time, which increases exponentially with the number of nodes, notwithstanding the degree of reference to the congestion information. Consequently, we successfully described the optimization effect of congestion-avoidance on the collective dynamics of agents in star topologies. Our findings are useful in many areas of network science.

中文翻译：

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由于拥塞信息提供而避免拥塞对优化内生星形网络拓扑上的代理动态的影响

网络拓扑基础研究的重要性已得到广泛认可。本研究旨在阐明给定拥塞信息的代理的拥塞避免对优化网络拓扑中的流量的影响。我们研究了星形拓扑中的随机交通网络，其中一个中心节点连接到具有不同偏好的隔离辅助节点。中心节点的每个代理根据辅助节点的拥塞率参考下降的偏好选择一个辅助节点。我们检查了两种情况：1）每个代理可以重复访问中心节点和辅助节点。2) 每个代理只能访问每个辅助节点一次。对于 1)，我们研究了静止状态下代理分布的均匀性，对于 2)，我们测量了访问所有节点的所有代理的旅行时间。当智能体反复访问中心和其他节点时，发现智能体分布的均匀性表现出三种非线性依赖于节点的增加。我们发现多元统计很好地描述了这些特征依赖关系，这表明通过避免拥塞来均衡网络使用与相互引用拥塞信息引起的协方差之间的平衡决定了一致性。我们发现拥塞避免使旅行时间线性化，尽管对拥塞信息的参考程度随着节点数量的增加呈指数增长。因此，我们成功地描述了拥塞避免对星形拓扑中代理的集体动态的优化效果。我们的发现在网络科学的许多领域都很有用。