We consider random-access networks where nodes represent servers with a queue and can be either active or inactive. A node deactivates at unit rate, while it activates at a rate that depends on its queue length, provided none of its neighbors is active. We consider arbitrary bipartite graphs in the limit as the initial queue lengths become large and identify the transition time between the two states where one half of the network is active and the other half is inactive. The transition path is decomposed into a succession of transitions on complete bipartite subgraphs. We formulate a randomized greedy algorithm that takes the graph as input and gives as output the set of transition paths the network is most likely to follow. Along each path we determine the mean transition time and its law on the scale of its mean. Depending on the activation rates, we identify three regimes of behavior.

中文翻译：

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具有二分干扰图的无线随机接入网络

我们考虑随机访问网络，其中节点代表带有队列的服务器，并且可以是活动的或非活动的。节点以单位速率停用，而它以取决于其队列长度的速率激活，前提是其邻居均不处于活动状态。当初始队列长度变大时，我们考虑极限内的任意二部图，并确定网络一半处于活动状态而另一半处于不活动状态的两种状态之间的转换时间。转移路径被分解为完整二部子图上的一系列转移。我们制定了一种随机贪婪算法，该算法将图作为输入，并给出网络最有可能遵循的一组转换路径作为输出。沿着每条路径，我们确定平均过渡时间及其均值范围内的规律。根据激活率，我们确定了三种行为模式。