通信网络中的消息传送
Message Transfer in a Communication Network
摘要：
我们研究的$2-d$通信网络中的定期节点和随机分布的集线器的消息传递。我们研究了格上的单消息传递和多消息传递。在固定间隔的源和目标对之间行进的单个消息的平均行进时间示出了作为具有特征幂律尾部的枢纽密度的函数的$q-$指数行为，表明作为枢纽密度的函数的平均行进时间的快速下降。这种幂律尾出现的结果，在高枢纽密度的旅行时间的对数正态分布。当许多消息在网格上传输时，可以看到拥塞-去拥塞过渡。拥塞阶段的消息等待时间呈高斯分布，而非拥塞阶段的消息等待时间呈对数正态分布。因此，拥塞或去拥塞行为在等待时间分布的行为中被加密。
英文摘要：
We study message transfer in a $2-d$ communication network of regular nodes and randomly distributed hubs. We study both single message transfer and multiple message transfer on the lattice. The average travel time for single messages travelling between source and target pairs of fixed separations shows $q-$exponential behaviour as a function of hub density with a characteristic power-law tail, indicating a rapid drop in the average travel time as a function of hub density. This power-law tail arises as a consequence of the log-normal distribution of travel times seen at high hub densities. When many messages travel on the lattice, a congestion-decongestion transition can be seen. The waiting times of messages in the congested phase show a Gaussian distribution, whereas the decongested phase shows a log-normal distribution. Thus, the congested or decongested behaviour is encrypted in the behaviour of the waiting time distributions.
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