Subject: RE: [manet] random waypoint model

From: [email-masked]
Date: Tue, 28 Jan 2003 11:01:36 +0000

> Not everyone assumes that the Random Waypoint Model must  range speed in
> (0,Vmax].  In fact, all our research ranges speed in [Vmin, Vmax] when we
> use the Random Waypoint.  Furthermore, we usually keep Vmin and Vmax
within
> ten percent of Vavg.  We have never published a result using 0 as Vmin for
> all velocity cases.

If I'm not mistaken, the mean speed tends towards the harmonic mean
averaged over [Vmin, Vmax] which is (Vmax-Vmin)/log(Vmax-Vmin)
(natural log). For Vmin = 0.9v and Vmax=1.1v this is 0.9967v,
which is close enough to v for practical purposes. (For Vmin equal
to zero this is zero, hence the original result.) This ignores any
waiting at waypoints. Coincidentally this speed range is also one
we have used.

There is another property of the random waypoint model which has
slightly undesirable consequences, that performance of even an
ideal AHRP using a random waypoint model as v->0 is not the same
as the static case. This is because the spatial distribution of
a node's position using a random waypoint model in a bounded
area is not uniform, there is a greater probability of finding
a node near the centre of the area. Where radio ranges are
limited and node density is not high this is quite noticeable
(giving better results for the random waypoint model than the
static distribution).

My colleagues who observed and explained the above have also used
a random walk model with reflections which avoids the above result,
having a uniform spatial distribution. Of course this represents
real life behaviour even less than the random waypoint model does.

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