On the Use of Graphs for Node Connectivity in Wireless Sensor Networks for Hostile Environments

Abstract

Wireless sensor networks (WSNs) have been extensively studied in the literature. However, in hostile environments where node connectivity is severely compromised, the system performance can be greatly affected. In this work, we consider such a hostile environment where sensor nodes cannot directly communicate to some neighboring nodes. Building on this, we propose a distributed data gathering scheme where data packets are stored in different nodes throughout the network instead to considering a single sink node. As such, if nodes are destroyed or damaged, some information can still be retrieved. To evaluate the performance of the system, we consider the properties of different graphs that describe the connections among nodes. It is shown that the degree distribution of the graph has an important impact on the performance of the system. A teletraffic analysis is developed to study the average buffer size and average packet delay. To this end, we propose a reference node approach, which entails an approximation for the mathematical modeling of these networks that effectively simplifies the analysis and approximates the overall performance of the system.

On Average Distance of Neighborhood Graphs and Its Applications

“…In graph theory, distance measures play an important role, in particular diameter and radius are two fundamental graph invariants. Their most important applications are in the analysis of networks, in particular social and economic networks [1], Information and Technological networks [2][3][4], Biological networks [5], Transportation networks [6][7][8], and facility location problems [9,10]. The other important graph invariant is average distance.…”

“…However, in a metabolic network, the efficiency of mass transfer can be judged by studying its average path length [11]. On the other hand, a power grid network can have less loss of energy transfer if its average path length is minimized [2,4].…”