Mobility Increases the Connectivity of Wireless Networks

Abstract

In this paper, we investigate the connectivity for large-scale clustered wireless sensor and ad hoc networks. We study the effect of mobility on the critical transmission range for asymptotic connectivity in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -hop clustered networks and compare to existing results on nonclustered stationary networks. By introducing <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -hop clustering, any packet from a cluster member can reach a cluster head within <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> hops, and thus the transmission delay is bounded as Θ(1) for any finite <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> . We first characterize the critical transmission range for connectivity in mobile <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -hop clustered networks where all nodes move under either the random walk mobility model with nontrivial velocity or the i.i.d. mobility model. By the term nontrivial velocity, we mean that the velocity of a node <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</i> is ω( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> )), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> ) is the transmission range of the node. We then compare with the critical transmission range for stationary <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -hop clustered networks. In addition, the critical number of neighbors is studied in a parallel manner for both stationary and mobile networks. We also study the transmission power versus delay tradeoff and the average energy consumption per flow among different types of networks. We show that random walk mobility with nontrivial velocities increases connectivity in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -hop clustered networks, and thus significantly decreases the energy consumption and improves the power-delay tradeoff. The decrease of energy consumption per flow is shown to be Θ([(log <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> )/( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</i> )]) in clustered networks. These results provide insights on network design and fundamental guidelines on building a large-scale wireless network.