A closed form network connectivity formula one-dimensional MANETs

In this paper, a closed form network connectivity formula for a one-dimensional mobile ad hoc network (MANET) is developed. Precisely, we derive the probability that a MANET is fully connected given a certain number of nodes randomly and uniformly placed along a path between a source and destination pair. This formula is particularly useful in the process of design and deployment of a MANET. The formula also provides a critical constraint function to the problem of network optimization. It formulates the relationship between the number of mobile nodes required for a particular MANET given a desired network connectivity probability. An approximation is employed to achieve the final closed form expression. The approximation is then tested by simulation to show the accuracy of our formula under practical network conditions.