Super-diffusive Behavior of Mobile Nodes 


Motivating Example

Mobility is the most important component in mobile ad-hoc networks (MANETs) and delay-tolerant networks (DTNs). To observe key characteristics in mobile traces and use sound mobility models that can capture these properties are critical for network performance evaluations. We observe the super-diffusive behavior in all mobile traces, and suggest to use a mobility model that can capture this characteristic properly.   

The following figures show sample trajectories of real mobility trace and from some synthetic models. These provide us a strong motivation that mobile nodes follow super-diffusive movement patterns.

  

As shown above, there exists "statistical similarity" between the real trace and a synthetically generated trajectory from a super-diffusive model (e.g., Levy Walk). The power-law step-length distribution used in Figure (c) generates occasional very-long jumps followed by many small steps with random orientations.


Super-diffusive behavior

The figure on the right shows the MSD of human mobile node on a log-log scale. For different human movement methods, MSD increases faster than linear () in all cases, which implies super-diffusive behavior.


 NCSU (North Carolina State University) GPS trace

The NCSU GPS traces were collected at NCSU campus. One student carried a GPS device (Garmin eTrex Legend Cx) to collect the GPS traces. This device can record the x, y co-ordinates of a mobile user's position, angle and velocity every second, where the resolution for the location is less than 3-5 meters with 95% accuracy. It however cannot record the trajectory when the mobile user is inside a building or under a tunnel where GPS signal is weak.

NCSU GPS traces are now available !   Click here to download GPS Traces


 Effect of diffusive property on network performance

The figure on your right shows the effect of different diffusive behaviors of mobile nodes on network performance under the epidemic routing protocol. For underlying mobility models, a class of Levy walk models with different m for the step-length distribution are chosen to reflect different diffusive behaviors. For a class of Levy walk models, step-length density is characterized by

                          

where is required for any valid probability density function.

As shown in the figure, varying degrees of diffusive behavior (parameterized by m) result in widely different network performance. We see that faster diffusive behavior of mobile nodes (smaller m) gives higher delivery ratio under the same transmission range. This result implies that diffusive behavior of mobile nodes, if not properly captured, may result in misleading conclusion in performance study of network protocols.

 


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