Statistical characterization of multicast performance in dense wireless networks

Multicast is a fundamental service in several scenarios involving wireless multihop communications, such as in ad hoc and sensor networks. Accordingly, appropriate solutions are required that achieve resource efficiency and scalability. It is possible to state the problem of optimal multicast in dense wireless networks in the terms of the Euclidean Steiner Tree problem. This has been thoroughly studied in the past as it can be applied in several engineering scenarios. However, it is well known that the Euclidean Steiner Tree problem is NP hard and even heuristics and approximation algorithms proposed in the literature cannot be applied in distributed environments like those addressed in this paper. Accordingly, solutions should be considered in which any intermediate node in the multicast tree is responsible of building a small part of the tree itself. In this paper, a geographical multicast protocol is considered in which each intermediate node decides the direction or the directions (if it identifies the need for a fork in the tree) along which the packet should be forwarded. The main contribution of this paper is to study and characterize the statistical properties of the multicast trees that can be obtained with such distributed approach. Indeed, simulation results show that the cost of the tree can be represented by a Gaussian random variable in which the average value and the variance comply to well defined laws.