Yaakov
I ran the exhaustive search for solutions just to get a feel for the
properties of this approach.
In increments of 1 there are 406 solutions* that meet both the known
delay constraints and the non-zero constraints.
28 of these solutions set x12 = 1, and one set x12 to 28.
The average of the solutions was indeed
x12 = 10, x21 = 40, x23 = 10, x32 = 220, x13 = 40, x31 = 10
but there were 405 other valid solutions such as
n = 397, x12 = 25, x21 = 25, x23 = 1, x32 = 229, x13 = 46, x31 = 4
n = 398, x12 = 25, x21 = 25, x23 = 2, x32 = 228, x13 = 47, x31 = 3
n = 399, x12 = 25, x21 = 25, x23 = 3, x32 = 227, x13 = 48, x31 = 2
n = 400, x12 = 25, x21 = 25, x23 = 4, x32 = 226, x13 = 49, x31 = 1
(meets the x12 = x21 approximation)
Nothing meets the x23 = x32 approximation, indeed x23 never get out of
the range 220:229, and there are four cases that meet the x13 = x31
approximation.
The assertion here is that taking an average of the solutions over a
number of cycles in the graph is better than taking an approximation
over a single cycle in the graph (the standard TWTT approach), and the
example above which includes gross asymmetry illustrates this.
However we need to get a better handle on the mathematics before we
fully understand this. For example what if this are a lot of symmetric
paths and a few asymmetric paths. Without doing either the math or the
simulation, I would expect that this would result in the asymmetric
paths degrading the symmetric approximation, the question is by how much?
This approach is interesting and definitely warrants further
investigation. It would be interesting to run the model over the
measured data from a number of real networks.
If the approximation had greater validity than the standard single cycle
approach (and it might, although there might be a better set of
weighting depending on the size of the cycle for example), building a
protocol to support it in a link state IGP would be easy.
- Stewart
* There was only one solution in incs of 10, and it was x12 = 10, x21 =
40, x23 = 10, x32 = 220, x13 = 40, x31 = 10
_______________________________________________
TICTOC mailing list
[email protected]
https://www.ietf.org/mailman/listinfo/tictoc
