A New Approach for Modeling Local Selective Connectivity and Maintaining Isolated Regions in Ad Hoc Networks

Abstract

The major prerequisites for successful wireless ad hoc networking are an almost homogeneous distribution of a non-trivial number of nodes and the determination of an almost ideal selective connectivity of these nodes in the network. To give a basic characterization of network connectivity, an ad hoc network model based on planar graphs is introduced. According to this underlying mathematical network description, the features of homogeneous connectivity for ad hoc networks are defined. The network model definitions of a connected, a simple connected, a strict connected, a multiple connected and a strong connected network have an iterative foundation on the meta set of the formal network description and the fulfilled local connectivity requirements. The degree of connectivity of each node and the intensity of connectivity of the network itself is maintained by the multiple paths existing at a time. Due to a specific physical layer ratio of wireless capacity utilization and the average number of independent paths, a condition of isolation provides the opportunity to maintain isolated areas in any given ad hoc network distribution. To support identified isolated regions is a main goal of a hybrid transfer network. According to the common underlying mathematical model of ad hoc networks introduced, a selective network model is defined to analyze local node connectivity. Based on a system architecture with a predetermined number of independent and simultaneous links of each network node, the different optimization degrees of the selection of neighbors are presented. A higher relaying efficiency gives the main opportunity for an ad hoc net to be an essential part of a future networking system. The efficiency of a selective network topology is compared to pure range controlled topology.