论文标题
带有两分的干扰图的无线随机访问网络
Wireless random-access networks with bipartite interference graphs
论文作者
论文摘要
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不活动的。一个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，前提是其邻居没有活跃。当初始队列长度变大，并确定一个网络有效的两个状态和另一半是不活动的两个状态之间的过渡时间，我们考虑了限制的任意两分图。过渡路径被分解为一系列在完整的两部分子图上的转变。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输出，该网络最有可能遵循的过渡路径集。沿着每条路径，我们根据其平均值确定平均过渡时间及其定律。根据激活率，我们确定了三个行为制度。
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.
