[brite-users] Waxman concerns

Thomas Erlebach te17 at mcs.le.ac.uk
Fri Jul 21 16:12:04 EDT 2006

Hi David,

> Furthermore, why when using the waxman model is there even a difference
> between growth types?  Waxman unlike BA does not have any room for
> growth, it simply connects nodes based on distance and weights, (isn't
> that correct).  But, in effect, Brite does N*M for inc growth, and N-1
> for all growth. 
> Why isn't the number of links based upon topology and the alpha value?
> Now, given the Waxman model:
> P(u, v) = ae-d/(bL)  
> a should be the value to affect the number of links. 
> However given default simulator conditions the varying of a (alpha) has
> NO affect on the number of links. And the simulator simply creates N*M
> or N-1 depending on growth type selected. 

I'm just guessing here, but I think that the brite implementation
of Waxman with incremental growth works as follows:

The nodes are created one by one, and each new node connects
to M existing nodes. The probability of connecting the new node
u to an existing node v is calculated by the Waxman formula you
have given above.

This also explains why the parameter a has no effect on the number
of links (nor, in fact, on the resulting graph) for incremental growth;
the factor a is irrelevant due to normalization.

In summary, Waxman with incremental growth as implemented in brite
is not the same as the original Waxman model. It is rather a
variant of the BA model: instead of making the probability of
connecting to an existing node proportional to the degree of that
node (as is done in the BA model), it is made proportional to the
value of the Waxman formula for a connection to that node.

Cheers, Thomas

Thomas Erlebach (te17 at mcs.le.ac.uk)
Reader in Algorithms, Dept. of Computer Science, University of Leicester

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