The communications industry anticipates that Wireless Sensor Networks (WSNs) are the emerging technology to greatly affect society. A WSN is composed of numerous sensor nodes which have the ability to sense, compute and communicate in order to gather information about their surroundings. The efficiency of a given WSN is determined by its lifetime. Network lifetime is the duration of time for which it can maintain sensing coverage and network connectivity, which respectively involves the ability to detect an event in a region and to report the sensed data to its destination. In much related work, the network is considered unserviceable the moment when the entire area cannot be fully covered or when the network is not completely connected. However, in many application scenarios, as long as the percentage of disconnected sensor nodes and uncovered areas are above a threshold value, the utility of the network will not be harmed. This latter view will be applied in this thesis. We first derive the probability distribution of the lifetime of a single sensor node by modeling a sensor node as an M/M/ 1 queue which alternates between idle and busy periods. Then, the network connectivity probability is determined by discovering the percentage of sensor nodes that can communicate with the destination given that the monitored region is partially covered. The sensor nodes are randomly deployed in a grid-based network according to the Poisson distribution. Given the average of the number of sensor nodes in a cell, the connectivity probability of two adjacent cells is determined. From this result, we can then derive the probability that a sensor node can communicate with a sink. Finally, the results found for the probability distribution of the lifetime of a single sensor node and the network connectivity probability are integrated to determine the network lifetime
