Analyzing the Connectivity of the Wireless Sensor Networks

Wireless Sensor Networks (WSNs) are utilized to communicate the collected information wirelessly. A wireless network can be represented as a graph composed of nodes and links. Such graph is known as connected graph if it has at least one path from any node to any other nodes, otherwise it will be indicated as a disconnected graph. A graph is considered a connected graph if for any two vertices x1 and x2 belong to a graph, there is a path whose ends at x1 and x2. The connectivity problems in WSNs are representing a crucial issue in all the WSNs applications. The network connectivity is an indication for a connected graph, it can be lost by removing certain number of the nodes from the network. This number of nodes can be used as one of the network connectivity threshold values. Sensors in a WSN can communicate and exchange information with neighbors based on their communication radius. This paper is to model the connectivity and the connectivity probability problems in WSNs. The effects of varying the number of the deployed sensors and their communication radius (range) on the network connectivity are analyzed and evaluated. To evaluate the developed model in this study, different rates are used in transmitting messages during the proposed WSNs. These rates are implemented as random values with different rates to model the connectivity probability. The number of the generated messages are created based on a Poisson distribution with different means. The connectivity probability is estimated based on the binomial probability distribution. Another approach is used to estimate the network connectivity based on an exact sent message rate. Different network performance metrics are calculated to evaluate the network behaviors.