Stable mobility models for MANETS

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Stable mobility models for MANETS

• Kim Blackmore
• Roy Timo (DE/NICTA)
• Leif Hanlen (NICTA)

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What is a MANET?
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Whats in a data network?

• What if its Mobile Ad Hoc?

"Application" protocols
Routing
"Transport" protocols
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MANET Routing

• For example, DSR dynamic source routing
• Each source maintains a cache of known paths (to
  previous destinations)
• Route discovery
• if you want a path to somewhere not in the cache
• Route maintenance
• if you try to use a cached path but it fails
• Reactive routing (or could try proactive)

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Simulations to test routing protocols

• Because there are so many layers of complexity
  below the routing
• Control the lower layers to isolate effect of
  routing protocol
• Synthetic mobility model to describe node
  movement
• Random Waypoint is most popular

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Random Waypoint Mobility Model

• Start point
• Uniform at random
• Waypoint 1
• Uniform at random
• Travel to waypoint 1
• At random speed
• Choose waypoint 2
• Repeat

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The problem with simulations

• Are the results meaningful?
• J. Yoon, M. Liu, and B. Nobel, Random Waypoint
  Considered Harmful," in Proc. IEEE INFOCOM,
  2003.
• J. Yoon, M. Liu, and B. Nobel, Sound Mobility
  Models," in Proc. IEEE MobiHoc, 2003.
• William Navidi and Tracy Camp. Stationary
  distributions for the random waypoint model. IEEE
  Transactions on Mobile Computing, 3(1), 2004.
• J. Boudec, M. Vojnovic, The Random Trip Model
  Stability, Stationary Regime, and Perfect
  Simulation," IEEE/ACM Trans. Networking, vol. 14
  no. 6, Dec. 2006.

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If node speed is randomly selected from 0,M,
then time averaged node speed goes to zero.
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Will simulation time-averages converge?

• Yes
• We prove a strong law of large numbers for the
  RWPMM
• Previous attempts used the wrong definition of
  stability

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Notation
V4 nodes 6 possible positions
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Estimating probability from simulations

• Generate a long sample path
• Count the number of times event A appears over N
  time steps

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Estimating probability from simulations

• Estimate the probability is
• But how do we know
• Converges to ProbA?
• Converges at all?

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A mobility model is Stable if

• For each bounded function
  the limit
• exists (with probability one).

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A mobility model is Ergodic iff

• For each event A, the limit
• converges to the stationary mean probability of
  A.

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Result - The RWMM is stable and ergodic
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Contributions

• Definitions of stable and ergodic MANET mobility
  models
• RWPMM is stable and ergodic

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Where to next?

• Stable routing protocols
• DSR is stable..
• THE END