Scheduling Method for Multi-channel Wireless Networks Based on Optimization of Age of Information
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摘要: 信息年龄(AoI)是近年来针对时间敏感类应用所提出的一种描述数据交付及时性的度量标准，它是从网络中目标节点的角度出发，衡量其最新收到的数据包的新鲜程度。在信道资源受限的多信道无线网络场景中，基于信息年龄的链路调度问题需要考虑信道资源和链路冲突的约束。针对上述问题，该文提出一种逐时隙调度链路进行数据传输的调度方法，以最小化网络的平均信息年龄。该文首先将信息年龄的优化问题转化为李雅普诺夫优化问题，然后将冲突约束下的多信道分配问题转换为二分图匹配问题并采用Kuhn-Munkres(KM)算法进行求解，进而得到约束条件下的链路调度方法。仿真结果表明，所提方法有效地优化了网络中的平均信息年龄，提升了网络数据的新鲜度。Abstract: Age of Information (AoI) is a novel metric that describes the timeliness of data delivery for time-sensitive applications, which measures the freshness of the most recently received packet from the perspective of destination node. In the multi-channel wireless network scenario with limited channel resources, the constraints of channel resources and link conflicts should be considered in the link scheduling with respect to AoI. To address this issue, in this paper, a time slot based scheduling method for data transmission to minimize the average AoI in the network is proposed. In this method, the optimization problem of AoI is first formulated into a Lyapunov optimization problem. Then the multi-channel conflict problem is converted to find the maximum matching policy of bipartite graph, which is solved by Kuhn-Munkres (KM) algorithm. Thus, a scheduling policy under constraints is obtained. The simulation results demonstrate that the proposed method optimizes effectively the average AoI and improves the freshness of data in the network.
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表 1 KM匹配算法执行过程
KM匹配算法求解带权二分图的最大权匹配 步骤 1 构建二分图$G$的点集为信道的点集$\{ {x_1},\;{x_2},\;\cdots,\;{x_M}\} $，目标节点的点集$\{ {y_1},\;{y_2},\;\cdots,\;{y_a}\} $。定义信道${x_j}$和目标节点${y_b}$的边权为
$w({x_j},\;{y_b}) = \max \;\{ - {W_{i,j} }|i \in ({y_{b - 1} } + 1,\;{y_{b - 1} } + 2,\;\cdots,\;{y_b})\}$。步骤 2 定义信道点集和目标节点的点集的顶标值，对于信道${x_j}$的顶标值为$L({x_j}) = \max \;\{ w({x_j},\;{y_b})|b \in (1,\;2,\;\cdots,\;a)\} $，即为信道${x_j}$在所
有目标节点下最大的边权值；初始化信道点集的顶标值，对于信道${y_b}$的顶标值$L({y_b}) = 0$。步骤 3 构建相等子图${G_e}$，用来保留二分图$G$中所有的点集和顶标值。 步骤 4 ${\rm{for}} \;j = 1,\;2,\;\cdots,\;M$ 在相等子图${G_e}$中添加满足匹配条件$L({x_j}) + L({y_b}) = w({x_j},{y_b})$的边，使用匈牙利算法在${G_e}$中寻找其最优匹配[19]。若未找到其最优匹配，
则根据匈牙利算法中形成的交错树，该交错树为匈牙利算法中所访问的目标节点与信道间形成的点集，取相等子图点集中所有信道节点
$x_j^{'}$被访问到而目标节点$y_b^{'}$没被访问到的边，求解交错树中的各松弛量$L(x_j^{'}) + L(y_b^{'}) - w(x_j^{'},y_b^{'})$的最小值$q$，将交错树中所有信道顶标减
小$q$，目标节点顶标增加$q$，再重新匹配该信道。end for 
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