Congestion inherently occurs on the Internet due to traffic concentration on certain nodes or links of networks. The traffic concentration is caused by inefficient use of topological information of networks in existing routing protocols, which reduces to inefficient mapping between traffic demands and network resources. Actually, the route with minimum cost, i.e., number of hops, selected as a transmission route by existing routing protocols would pass through specific nodes with common topological characteristics that could contribute to a large improvement in minimizing the cost. However, this would result in traffic concentration on such specific nodes. Therefore, we propose a measure of the distance between two nodes that is suitable for reducing traffic concentration on specific nodes. To consider the topological characteristics of the congestion points of networks, we define node-to-node distance by using a generalized norm, p-norm, of a vector of which elements are degrees of intermediate nodes of the route. Simulation results show that both the maximum Stress Centrality (SC) and the coefficient of variation of the SC are minimized in some network topologies by selecting transmission routes based on the proposed measure of node-to-node distance.

Probability distribution of the node degree has long been regarded as one of the important metrics to characterize the wireless ad hoc networks. However, there is no exact formulation for this probability distribution when shadow fading effects are considered. In this letter, by deriving the conditional probability of the node degree and the joint distribution of the distances between nodes and a randomly selected reference node (RSRN), we show that the probability distribution of the node degree for the wireless ad hoc networks in the shadow fading environments is binomial.