Scaling limits for shortest path lengths along the edges of stationary tessellations
Scaling limits for shortest path lengths along the edges of stationary tessellations
复制标题
沿固定镶嵌边缘的最短路径长度的缩放限制
DOI：
10.1239/aap/1293113145
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发表时间：
2009
影响因子：
1.2
通讯作者：
V. Schmidt
中科院分区：
文献类型：
--
作者：
F. Voss;C. Gloaguen;V. Schmidt
我们考虑空间随机模型，它可以应用于，例如，电信网络与两个层次。特别地，我们考虑集中在随机镶嵌T的边集T（1）上的考克斯过程XL和X H，其中XL和X H的点XL，n和X H，n可以分别描述低层和高层网络组件的位置，T（1）是网络的底层基础设施，例如道路系统、铁路等。此外，每个点XL，用沿T的边沿着到X H的最近点（在欧几里德意义上）的最短路径来标记X L的n。我们调查的典型的最短路径长度C * 的标记点过程，这是一个重要的特性，例如，电信网络的性能分析和规划。特别地，我们证明了当比例因子κ收敛于0或∞时，C * 的分布收敛于简单的参数极限分布。这可以用来近似密度的C * 的解析公式为广泛的κ。
We consider spatial stochastic models, which can be applied to, e.g. telecommunication networks with two hierarchy levels. In particular, we consider Cox processes X L and X H concentrated on the edge set T (1) of a random tessellation T, where the points X L,n and X H,n of X L and X H can describe the locations of low-level and high-level network components, respectively, and T (1) the underlying infrastructure of the network, such as road systems, railways, etc. Furthermore, each point X L,n of X L is marked with the shortest path along the edges of T to the nearest (in the Euclidean sense) point of X H . We investigate the typical shortest path length C * of the resulting marked point process, which is an important characteristic in, e.g. performance analysis and planning of telecommunication networks. In particular, we show that the distribution of C * converges to simple parametric limit distributions if a scaling factor κ converges to 0 or ∞. This can be used to approximate the density of C * by analytical formulae for a wide range of κ.