具有二部干扰图的无线随机接入网络
Wireless random-access networks with bipartite interference graphs
AI总结：
研究具有二部干扰图的无线随机接入网络在大初始队列长度极限下的状态转换时间，提出随机化贪婪算法计算最可能转换路径及均值尺度上的转换时间分布，并识别三种行为状态。
摘要：
我们考虑随机接入网络，其中节点代表带有队列的服务器，并且可以处于活动或非活动状态。节点以单位速率失活，而只要其邻居中没有节点处于活动状态，它就以取决于其队列长度的速率激活。我们考虑任意二部图，在初始队列长度变得很大的极限下，识别网络一半处于活动状态而另一半处于非活动状态这两种状态之间的转换时间。转换路径被分解为在完全二部子图上的一系列转换。我们提出了一种随机化贪婪算法，该算法以图为输入，输出网络最可能遵循的转换路径集合。沿着每条路径，我们确定了平均转换时间及其在均值尺度上的分布律。根据激活速率的不同，我们识别出三种行为状态。
英文摘要：
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.
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