Stable mobility models for MANETS

Kim Blackmore

Roy Timo (DE/NICTA)

Leif Hanlen (NICTA)

What is a MANET?

What’s in a data network?

What if it’s Mobile Ad Hoc?"Application" protocols

"Transport"protocols

Routing

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)

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

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

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.

If node speed is randomly selected from [0,M], then time averaged node speed goes to zero.

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

Notation

S1

S2

S3

S4

S5

S6

S = fs1;s2;s3;s4;s5;s6g

X =Q V

v=1 Sv

x1 = (s2;s2;s5;s5)

x0 = (s2;s3;s6;s6)

V=4 nodes

6 possible positions

Estimating probability from simulations

• Generate a long sample path

• Count the number of times event A appears over N time steps

x = x0;x1;x2; : : :

P N ¡ 1n=0 1A

¡xn;xn+1; : : :

¢

1A

¡xn;xn+1; : : :

¢=

½1; if xn ;xn+1; : : : 2 A0; otherwise

• Estimate the probability is

• But how do we know

• Converges to ProbA?• Converges at all?

Estimating probability from simulations

ProbA ¼ 1N

P N ¡ 1n=0 1A

¡xn ;xn+1; : : :

¢

limN ! 11N

P N ¡ 1n=0 1A

¡xn ;xn+1; : : :

¢

A mobility model is Stable if:

For each bounded function the limit

exists (with probability one).

f : X 1 ! R

­f®(x) = lim

N ! 1

1N

N ¡ 1X

i=0

f¡xn;xn+1;xn+2; : : :

¢

A mobility model is Ergodic iff

For each event A, the limit

converges to the stationary mean probability of A.

Prob[A]=­1A

®(x) = lim

N ! 1

1N

N ¡ 1X

i=0

1A¡xn;xn+1;xn+2; : : :

¢

Result - The RWMM is stable and ergodic

Contributions

Definitions of stable and ergodic MANET mobility models

RWPMM is stable and ergodic

Where to next?

• Stable routing protocols

• DSR is stable..

THE END