The 9th ACM MOBIWAC 2011
Degree of Node Proximity: A Spatial Mobility Metric for MANETs M.Sc. Elmano Ramalho Cavalcanti http://sites.google.com/site/elmano
DSC-UFCG, Brazil Nov 03 2011 1
Outline Introduction and Motivation DSD x DNP Simulation Results and Observation Conclusions and Future Work
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Introduction and Motivation Mobility models describes the movement patterns of mobile nodes, having an impact on several areas: Protocol performance, topology and network connectivity, data replication, security…
Mobility metrics are used to measure the features of mobility models: Link-related: duration, estimation, availability, etc. Node-related: degree, speed, spatial, temporal, etc. 33
Introduction and Motivation The IMPORTANT framework (Bai et al. 2003) presented DSD, a spatial mobility metric. Cited by > 700 papers (Google scholar) Several works were based on these metrics for a wide range of purposes…
However, DSD has a critical shortcoming! 44
Introduction and Motivation The problem: “DSD does not consider spatial dependence (correlation) during periods of absence of node movement” ⇒ Spatial dependence degree decays over node
pause time…
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Outline Introduction and Motivation DSD x DNP Simulation Results and Observation Conclusions and Future Work
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Degree of Spatial Dependence (DSD) GOAL: to measure the level of dependence between the moviments of mobile nodes. • Based on the cossine similarity between nodes’ velocities. • Newer spatial metrics (e.g., LDSD [Zhang et al. 2009]), are also based on cossine.
i, j : nodes’ velocities 77
t: time step
DSD’s drawback • If one or both nodes is not moving?
• There will be no speed vector, and then, according to the DSD formula, there will be no correlation: DSD(i,j,t) = 0 • Is this right?
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Degree of Node Proximity • Based on average distance between nodes • Idea: if two mobile nodes keep near each other for a long period, it could means there is a relationship between their movements. • Range of DNP values: [-1,+1] (same as DSD)
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Outline Introduction and Motivation DSD x DNP Simulation Results and Observation Conclusions and Future Work
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RWP
Simulation Mobility Models FEATURE Randomness Group-based Temporal Grid-based
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RWP RPGM GM MAN X X X RPGM
X
MAN
Simulation Configuration T: 900 s N: 100 nodes 10 Repetitions and 99% CI R: 100, 150, 200 m X,Y: 1000 m Node min. speed: 1, 3, 5 m/s Node max. speed: 10, 20, 30 m/s Max. pause time: 0, 100, 200, ... , 900 s (RPGM) nodes per group: 10, 25, 50 12
Outline Introduction and Motivation DSD x DNP Simulation Results and Observation Conclusions and Future Work
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Results and Observations BASIC STATISTICS COMPARISON
=> DSD and DNP can both distinguish RPGM (group model) for individual models 14 14
Results and Observations Spatial Metrics – RPGM scenario I
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a) RPGM with 2 groups of 50 nodes
Results and Observations Spatial Metrics – RPGM scenario I
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b) RPGM with 4 groups of 25 nodes
Results and Observations Spatial Metrics – RPGM scenario I
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c) RPGM with 10 groups of 10 nodes
Results and Observations Degree of Node Proximity (DNP) RPGM
RWP MAN
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(s = 5 m/s, S = 30 m/s, R = 100 m)
Results and Observations Spatial Metrics – RPGM scenario I
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c) RPGM with 2 groups of 50 nodes
Results and Observations Spatial Metrics – RPGM scenario I
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c) RPGM with 4 groups of 25 nodes
Results and Observations Spatial Metrics – RPGM scenario I
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c) RPGM with 10 groups of 10 nodes
Results and Observations How good can we predict DNP value from the mobility models’ input parameters? Regression Analysis: ln(ΦDNP) = .113 ln(A) − .002 √MPT − 1.705 .587/NG − .15 ln(A) − .004 √MPT − .21 .158 ln(A) + .055 ln(NB) + .003 √MPT − 2.21
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// RWP //RPGM //MAN
Results and Observations Regression models’ summary Model R2 adj. RWP 0.792 RPGM 0.852 MAN 0.825
Std. Error 0.02311 0.04025 0.03393
Provide substantial precision for determining DNP of a network 23
Outline Introduction and motivation DSD x DNP Simulation Results and Observation Conclusions and Future Work
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Conclusions and Future Work New spatial mobility metric – DNP: More realistic than DSD at capturing the SD in scenarios having different pause timing levels. 2. It is not biased towards node speed. 3. Generic measure for characterizing overall mobility in wireless ad hoc networks. 1.
Future: To evaluate DNP x DSD on more complex mobility models (e.g., TVCM, SLAW)
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Thanks! The code for DNP (and other mobility metrics) is available at: http://sites.google.com/site/elmano/code (Trace Analyzer 2.1 beta)
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DNP formulas
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