Restricted Mobility Improves Delay-Throughput Trade-offs in Mobile Ad-Hoc Networks

arXiv:0807.1228v1 [cs.PF] 8 Jul 2008 Restricted Mobility Improves Delay-Throughput Trade-offs in Mobile Ad-Hoc Networks Michele Garetto † Emilio Leonardi ∗ † Dipartimento di Informatica, Università di Torino, Italy ∗Dipartimento di Elettronica, Politecnico di Torino, Italy ABSTRACT In this paper, we analyze asymptotic delay-throughput trade-offs in mobile ad-hoc networks comprising heterogeneous nodes with restricted mobility. We show that node spatial heterogeneity has the ability to drastically improve upon existing scaling laws estab- lished under the assumption that nodes are identical and uniformly visit the entire network area. In particular, we consider the situation in which each node moves around its own home-point according to a restricted mobility process which results into a spatial stationary distribution that decays as a power law of exponent δ with the dis- tance from the home-point. For such restricted mobility model, we propose a novel class of scheduling and routing schemes, which significantly outperforms all delay-throughput results previously obtained in the case of identical nodes. In particular, for δ = 2 it is possible to achieve almost constant delay and almost constant per-node throughput (except for a poly-logarithmic factor) as the number of nodes increases, even without resorting to sophisticated coding or signal processing techniques. 1. INTRODUCTION Over the last decade we have seen a flurry of theoretical studies aimed at establishing fundamental scaling laws of ad-hoc networks as the number of nodes increases. Gupta and Kumar first consid- ered the case of n static nodes and n random source-destination (S-D) pairs, obtaining the disheartening result that the maximum per-node throughput decays at least as 1/√n [1]. In contrast to static networks, Gossglauser and Tse [2] have shown that a constant per-node throughput can be achieved in mo- bile ad-hoc networks by exploiting the store-carry-forward com- munication paradigm, i.e., by allowing nodes to store the data and physically carry them while moving around the network. The result in [2] was proven under the assumption that nodes independently move according to a generic, ergodic mobility process which re- sults, for each node, into a uniform stationary distribution over the space. This mobility model is actually a generous one, as it allows each node to equally come in contact with any other node, achiev- ing a full, homogeneous mixing. In practical cases, however, the mobility pattern of individual Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. nodes is expected to be restricted over the network area, as users spend most of the time in proximity of a few preferred places [3], and rarely go outside their region of habit. This observation has al- ready motivated some researchers to study the impact of restricted mobility models. In [4] a one-dimensional mobility model is con- sidered, in which each node uniformly visits a randomly chosen great circle on the unit sphere, obtaining again a constant through- put. In [5,6] the authors consider a two-dimensional, restricted mo- bility model which produces, for each node, a rotationally invariant spatial distribution centered at a home-point uniformly chosen in the area; the resulting throughput varies with continuity in between the two extreme cases of static nodes (Gupta-Kumar) and fully mobile nodes (Grossglauser-Tse), depending on how the physi- cal network extension scales with respect to the average distance reached by the nodes from their home-point. This result confirms that throughput is maximized when the nodes span the entire ex- tension of the network area. However, the authors of [5,6] have not analyzed the delay under their restricted mobility model. Driven by the optimality of the homogeneous mixing assump- tion in terms of throughput, many authors have analyzed asymp- totic delay-throughput trade-offs under the same assumption. This choice is also motivated by the fact that the most popular mobil- ity models adopted in the literature (such as random walk, random way-point) produce a uniform stationary distribution over the area.1 Indeed, when considering also the data transfer delay, the precise details on how the nodes move become important. Several mobil- ity models have been analyzed, ranging from the simple reshuffling model [7], to the Brownian motion [8], and variants of random walk and random way-point [9, 10]. In all of these studies, nodes have been assumed to be identical and fully mobile, i.e., their trajecto- ries ‘fill the space’ over time, uniformly visiting the entire network area. Starting from a di

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