Distance Distributions in Finite Uniformly Random Networks: Theory and Applications

In wireless networks, the knowledge of nodal distances is essential for performance analysis and protocol design. When determining distance distributions in random networks, the underlying nodal arrangement is almost universally taken to be a stationary Poisson point process. While this may be a good approximation in some cases, there are also certain shortcomings to this model such as the fact that in practical networks, the number of nodes in disjoint areas are not independent. This paper considers a more realistic network model where a known and fixed number of nodes are independently distributed in a given region and characterizes the distribution of the Euclidean internode distances. The key finding is that when the nodes are uniformly randomly placed inside a ball of arbitrary dimensions, the probability density function of the internode distances follows a generalized beta distribution. This result is applied to study wireless network characteristics such as energy consumption,...

• Type: Journal
• Year: 2008
• Where: CORR
• Authors: Sunil Srinivasa, Martin Haenggi
• Keywords: CORR 2008, Education, Nodal Distances, Stationary Poisson Point, Wireless Network