Analysis of Shortest Paths and Subscriber Line Lengths in Telecommunication Access Networks

作者：Gloaguen C^*; Fleischer F; Schmidt H; Schmidt V

来源：Networks and Spatial Economics, 2010, 10(1): 15-47.

DOI：10.1007/s11067-007-9021-z

• Telecommunication network modelling
• Stochastic geometry
• Point process
• Palm probability
• Neveu's exchange formula
• Spatial tessellation
• Typical Cox-Voronoi cell
• Access network
• Shortest path
• Subscriber line

We consider random geometric models for telecommunication access networks and analyse their serving zones which can be given, for example, by a class of so-called Cox-Voronoi tessellations (CVTs). Such CVTs are constructed with respect to locations of network components, the nucleii of their induced cells, which are scattered randomly along lines induced by a Poisson line process. In particular, we consider two levels of network components and investigate these hierarchical models with respect to mean shortest path length and mean subscriber line length, respectively. We explain point-process techniques which allow for these characteristics to be computed without simulating the locations of lower-level components. We sustain our results by numerical examples which were obtained through Monte Carlo simulations, where we used simulation algorithms for typical Cox-Voronoi cells derived in a previous paper. Also, briefly, we discuss tests of correctness of the implemented algorithms. Finally, we present a short outlook to possible extensions concerning multi-level models and iterated random tessellations.

• 出版日期2010-3