Subject: RE: [manet] Question regarding Mobility

From: "John Mullen" <[email-masked]>
Date: Mon, 24 Nov 2003 08:44:52 -0700

Hi Richard,

Well, we can argue mobility models, but in the end, it is how well they
reflect node behavior in a real situation that matters.  The "choose a
location and move to it" model is attractive because that is how people
move around.  The "bounce off the boundary" model is not so attractive
because people don't usually move this way.  People will choose
different models because they are thinking of different contexts.

However, the mobility model may not be that important.  Because of
shadowing and fading, received signals can easily vary by a factor of
100 to 1 from their expected values and will tend to do so as a function
of the rate at which the environment is changing.  (Not just the one
node's speed, by that of all other objects and nodes in the vicinity.)
As a result, it may be the node's speed, together with data rate, packet
length, transmission frequency, etc. that are the greater factors and
the differences among many of the various mobility models may just be a
moot point.

John Mullen

-----Original Message-----
From: Richard Ogier [mailto:[email-masked]] 
Sent: Friday, November 21, 2003 7:28 PM
To: John Mullen
Cc: 'Richard Ogier'; 'MANET'
Subject: Re: [manet] Question regarding Mobility

John,

Thanks for the pointer.   Frankly,  instead of studying bad mobility 
models (like
random waypoint), I prefer to use a good mobility model that ensures 
node positions
are uniformly distributed.  One model that achieves a uniform 
distribution (assuming
zero pause time) is a random walk model, where each node moves in a 
random direction
for T seconds, then chooses a new random direction.  If the node hits a 
boundary,
it bounces off as in billiards (angle of reflection equals angle of 
incidence).

There is another model called the "random direction" model, in which the

node chooses
a new random direction only when it hits the boundary.  However, I don't

think
this model achieves a uniform distribution (assuming zero pause time).

The following paper discusses these model and several others (but does 
not talk about
probability distributions):

T. Camp, J. Boleng, and V. Davies. A survey of mobility models for ad 
hoc network research. Wireless Communications & Mobile Computing (WCMC):

Special issue on Mobile Ad Hoc Networking: Research, Trends and 
Applications, 2(5):483--502, 2002.

Richard

John Mullen wrote:

>Hi Richard,
>
>You are correct in the matter of non-independent speed, however, I am 
>unaware of any result that takes this into consideration.  In "The 
>spatial node distribution of the random waypoint mobility model." (1st 
>German Workshop on Mobile Ad-Hoc Networks (WMAN'02), Ulm, Germany, 
>2002.), Christian Bettstetter discusses this problem at length and 
>develops a couple of approximate distributions.  He also performed some

>simulations which seem to indicate the approximations are pretty close.

>Bettstetter has published more on this topic, so you may want to check 
>out his web page:
>
>http://www.lkn.ei.tum.de/~chris/#Publications
>
>John Mullen
>
>-----Original Message-----
>From: [email-masked] [mailto:[email-masked]] On Behalf Of 
>Richard Ogier
>Sent: Friday, November 21, 2003 9:38 AM
>To: Philippe Jacquet
>Cc: MANET
>Subject: Re: [manet] Question regarding Mobility
>
>
>Philippe Jacquet wrote:
>
>>Yes, Peter, the distribution changes if you introduce mobility and it
>>depends on the mobility model. Take the random way point model where 
>>each node has a distinct a random destination point selected uniformly

>>in a square, and each node moves to this destination at constant
speed.
>>
>
>>In this case, the stationary density at point (x,y) (assuming a 1x1
>>square) is *( x* log x+(1-x)*log(1-x))*(y*log y +(1-y)*log(1-y)) which

>>differs from uniform density (which is equal to 1 at any point in the 
>>1x1 square).
>>
>>Philippe
>>
>Philippe,
>
>Your result implies that you can consider the x and y directions 
>independently. I don't think this is the case, because the speed in the

>x direction depends on the (x,y) direction of movement. I did some 
>calculations, and I think your result assumes that the time to go from 
>one random point to the next random point is constant (thus, if the 
>distance between the 2 points is greater, the speed must be greater).
>
>Just for fun I tried to derive the steady state distribution in one 
>dimension for a unit interval [0,1] and got the following result 
>(assuming constant speed and zero pause time):
>
>   C * x*(1-x)   (C is a normalization constant)
>
>The x*(1-x) term is simply the probability that the point x lies 
>between two random numbers uniformly distributed in [0,1]. I ran a 
>simulation on the unit interval [0,1] which confirms this result. In 
>particular, the probability that the node is near x = 0.25 is 0.75 
>times the probability that the node is near x = 0.50.
>
>Unfortunately, this result cannot be extended to 2 dimensions by taking

>the product of this term for the x and y directions, because the x and 
>y components of the node speed are not independent.
>
>Richard
>
>>----- Original Message -----
>>From: Peter Pham <[email-masked]>
>>To: MANET <[email-masked]>
>>Sent: Thursday, November 20, 2003 2:03 AM
>>Subject: [manet] Question regarding Mobility
>>
>>
>>>Hi all
>>>I am interested in modelling ad hoc networks. In the stationary
>>>scenario (nodes do not move), I can assume that the mobile nodes are 
>>>distributed randomly according to Poisson distribution (many assumed 
>>>so). However, is this assumption still valid under the mobility ? Can

>>>anyone give me some advice ?
>>>
>>>Peter Pham
>>>
>>>
>>>
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>>
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>
>
>
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---

From: "Philippe Jacquet" <[email-masked]>
Date: Tue, 25 Nov 2003 15:25:26 +0100

John,

Amir Qayyum, developped a simulator model which use the billard model. It
was called movinet. This may be good to model people moving on an exhibition
field. The way point model is better for modeling players on a soccer
field;-)  An interesting model is when the map is a torus: nodes
disappearing on one end reappear on the other end. This would really put the
route control under stress ! To be more realistic nodes should change
identity when reappearing, therefore simulating an open network.

Philippe