Queue length synchronization in a communication network

Traffic flows on networks have been the subject of intensive study [1]. We study this problem in the context of a two dimensional lattice of nodes and hubs. When many messages flow on the lattice, hubs which lie on many message paths tend to get congested. We rank the hubs by their coefficient of betweenness centrality (CBC) [2] which is defined as the number of messages Nk running through a given hub k, to the total number of messages N running simultaneously in the lattice. Hubs with high CBC values serve as potential congestion points in the network. We find that the queue length at the hubs with high CBC tend to synchronize when the network is in the congested phase. Here, the queue length of a hub is defined as as the number of messages which have taken this hub as their temporary target [2]. This congestion can be relieved by the addition of assortative connections [2] to the hubs of high CBC, either randomly or through the gradient mechanism [3].