On the Connectivity and Average Delay of Mobile Ad Hoc Networks

We present new closed-form analytical expressions for the probability of connectivity and average delay of a mobile ad hoc network with N nodes which move according to the random waypoint (RWP) mobility model. The minimum transmission range for which the network is connected is also derived. Our results show that by increasing the number of nodes, the probability of connectivity increases and the minimum transmission range decreases. It is also shown that the average delay is maximum for the minimum transmission range and this maximum increases by increasing the number of users. In transmission ranges for which the networks are disconnected, increasing the number of users increases the average delay; however, this is reversed when the networks are connected. Particularly, our results show that mobility contributes to the network connectivity, but at the expense of tolerating more average delay when the networks are disconnected. However, mobility decreases the average delay in the connected regions.