Improved Spatial and Temporal Mobility Metrics for Mobile Ad Hoc Networks Elmano Ramalho Cavalcanti and Marco Aur´ elio Spohn Systems and Computing Department Federal University of Campina Grande, Brazil Email: {elmano,maspohn}@dsc.ufcg.edu.br Abstract—This work shows that two well-known spatial and temporal mobility metrics for mobile ad hoc networks (MANETs) have drawbacks, possibly leading to invalid results. Based on the concept of spatial dependence in the absence of move- ment among mobile nodes, we propose mobility metrics able to promptly capture spatial and temporal dependence among mobile nodes. Through simulation, we compared the proposed metrics over a diversified set of synthetic mobility models. The results revealed that our spatial metrics can capture spatial dependence in scenarios having different levels of node pause time. Our temporal metric also demonstrated to be better suited for capturing different levels of temporal dependence, without being biased by node speed. Thus, the proposed mobility metrics can accurately capture spatial and temporal node behavior in MANETs. Index Terms—ad hoc network; mobility metric; spatial depen- dence; temporal dependence; I. I NTRODUCTION To support the growth and development of mobile ad hoc networks (MANETs), researchers from industry and academia have designed a variety of protocols, spanning the physical to the application layer. Analytic modeling and simulation are amongst the most used methods for evaluating MANET protocols. The former has limitations due to the lack of generalization, and the intrinsic high level of complexity [5]. The latter is by far the most used method for designing and evaluating MANET protocols. A mobility model is one of the most important components in the simulation of MANETs. This component describes the movement pattern of mobile nodes (e.g., people, vehicles), im- pacting on protocol performance [2], [4], [11], [15], topology and network connectivity [3], [8], [16], data replication [10], and security [7]. Bai et al. [2] demonstrated that the perfor- mance of a protocol can vary dramatically depending on the adopted mobility model. Mobility models can be classified into four categories: ran- dom, temporal-based, spatial-based (or group-based), and with geographic restriction [1] (Figure 1). Aiming at measuring quantitatively and qualitatively mobility models, one can use mobility metrics. Bai et al. [2] proposed a framework to analyze the impact of mobility on performance of routing protocols for MANET. They proposed two metrics to quantify the spatial and temporal dependence of mobile nodes. Since then, several works has been based on these metrics for many purposes [13], [14], Fig. 1. Categories of mobility models in MANETs [1]. [17], [19], [20]. However, we show that those metrics have important drawbacks (Section III). After that, we introduce spatial and temporal metrics that overcome the described limitations, and also propose another spatial metric, based on the average distance among nodes (Section IV). In order to evaluate the proposed metrics, we conducted an extensive simulation using four well know synthetic mobility models (Section V). Afterwards, we perform a comprehensive analysis of metrics behavior (Section VI). II. TERMINOLOGY The following terminology is needed to define the mobility metrics, and it will be used throughout this paper: • T - Simulation time; • N - Number of mobile nodes; • X, Y - Length and width of the scenario; • R - Radio communication range; • x(i, t) is the x-coordinate of node i at time t (idem for y(j, t)). • θ(i, t) is the velocity angle of node i at time t. • v(i, t) is the velocity of node i in the time t and v(i, t 0 ..t k ) means that the velocity of node i remains constant from t 0 to t k . • Cos(i, j, t) is the cosine of angle between the velocities of nodes i, j : Cos(i, j, t)= v(i, t) • v(j, t) | v(i, t)|·| v(j, t)| (1) • SR(i, j, t) is the speed ratio between nodes i, j at time t: SR(i, j, t)= min(v(i, t),  v(j, t)) max(v(i, t),  v(j, t)) (2) 189 UBICOMM 2010 : The Fourth International Conference on Mobile Ubiquitous Computing, Systems, Services and Technologies Copyright (c) IARIA, 2010 ISBN: 978-1-61208-100-7