论文标题
无线网络中的渐近临界传输半径
Asymptotic Critical Transmission Radii in Wireless Networks over a Convex Region
论文作者
论文摘要
无线临时和传感器网络中的关键传输范围（或半径）已针对各种性能指标进行了广泛研究，例如连通性，覆盖率，功率分配和能源消耗。但是，分布网络的区域通常是正方形或现有作品中的磁盘，这严重限制了现实生活中的应用。在本文中，我们考虑了一个无线节点均匀分布的凸区域（即正方形和磁盘的概括）。我们已经研究了两种类型的关键传播半径，分别根据k连接性和最小顶点程度定义，并确定了其精确的渐近分布。这些使得先前的结果在正方形或磁盘的特殊情况下获得。更重要的是，我们的结果揭示了区域形状如何影响临界传输范围：完全决定了传输范围的是（固定区域）区域的边界的长度。此外，通过等法不平等，仅当区域是磁盘时，最小的临界传输范围是实现的。
Critical transmission ranges (or radii) in wireless ad-hoc and sensor networks have been extensively investigated for various performance metrics such as connectivity, coverage, power assignment and energy consumption. However, the regions on which the networks are distributed are typically either squares or disks in existing works, which seriously limits the usage in real-life applications. In this article, we consider a convex region (i.e., a generalisation of squares and disks) on which wireless nodes are uniformly distributed. We have investigated two types of critical transmission radii, defined in terms of k-connectivity and the minimum vertex degree, respectively, and have also established their precise asymptotic distributions. These make the previous results obtained under the circumstance of squares or disks special cases of this work. More importantly, our results reveal how the region shape impacts on the critical transmission ranges: it is the length of the boundary of the (fixed-area) region that completely determines the transmission ranges. Furthermore, by isodiametric inequality, the smallest critical transmission ranges are achieved when regions are disks only.
