The random waypoint model is a commonly used mobility model in the simulation of ad hoc networks. It is known that the spatial distribution of network nodes moving according to this model is, in general, nonuniform. However, a closed-form expression of this distribution and an in-depth investigation is still missing. This fact impairs the accuracy of the current simulation methodology of ad hoc networks and makes it impossible to relate simulation-based performance results to corresponding analytical results. To overcome these problems, we present a detailed analytical study of the spatial node distribution generated by random waypoint mobility. More specifically, we consider a generalization of the model in which the pause time of the mobile nodes is chosen arbitrarily in each waypoint and a fraction of nodes may remain static for the entire simulation time. We show that the structure of the resulting distribution is the weighted sum of three independent components: the static, pause, and mobility component. This division enables us to understand how the model’s parameters influence the distribution. We derive an exact equation of the asymptotically stationary distribution for movement on a line segment and an accurate approximation for a square area. The good quality of this approximation is validated through simulations using various settings of the mobility parameters. In summary, this article gives a fundamental understanding of the behavior of the random waypoint model.

In this paper, we propose a novel general technique, based on renewal theory, for analyzing mobility models in ad hoc networks. Our technique enables an accurate derivation of the steady state distribution functions for node movement parameters such as distance and speed. We first apply our technique to the random waypoint model and provide alternative proofs for previous claims about the discrepancy between the steady state average speed and the average speed associated with the simulated distribution [1]. Our main contribution is a new methodology for simulating mobility which guarantees steady state for node movement distributions from the start of the simulation. Our methodology enables the correct and efficient simulation of a desired steady state distribution, and can be implemented in a manner transparent to the user. We support our claims through both formal proofs as well as extensive simulations.

In this paper we study the critical transmitting range (CTR) for connectivity in mobile ad hoc networks. We prove that r M = c for some constant c 1, where r M is the CTR in presence of M-like node mobility and n is the number of network nodes. Our result holds for an arbitrary mobility model M such that: (1) M is obstacle free, and (2) nodes are allowed to move only within a certain bounded area.

In this paper we consider sensor networks for intrusion detection, such that node deployment, node failures and node behavior result in coverage gaps and a fraction of disconnected nodes in an otherwise dense and well-connected network. We focus on the time delay for a mobile intruder to be detected by a sensor with a connected path to the sink, in contrast to existing results for the detection time by a sensor with arbitrary connectivity. We model our network using a supercritical percolation model on the plane, implying the existence of a unique unbounded connected component, and we assume that the sink belongs to this component. We analyze the distribution of the distance traveled by a moving target until it comes within sensing range of a node in the giant component, providing analytical bounds for linear intruder mobility and thorough simulation results for other mobility models. We show that the probability that the intruder proceeds undetected exhibits non-memoryless behavior over shorter distances and an exponentially decreasing tail. We also show that the time of contact with the giant component incurs considerably more delay than the time of first contact with any node, in networks with less than 10 % of nodes without a path to the sink, which means that even a small percentage of node failures may have a drastic impact on the performance of intrusion detection by a wireless sensor network.

Abstract — An analysis of network connectivity of onedimensional Mobile Ad hoc Networks with a particular mobility scheme is presented, focusing on the random waypoint mobility scheme. The numerical results are verified using simulation to show their accuracy under practical network conditions. Observations on RWP properties further lead to approximations and an eventual simple network connectivity formula. Index Terms — Wireless LAN, land mobile radio data communication, computer network performance. I.