I am working on a paper which I have implemented also. I am trying to match the simulation with the analytical model but I am facing some difficulties.
I have to equations p(ps) and ps(p) . p(ps)is the probability that a certain user begins transmission in the next slot and ps(p) probability that the considered user successfully finishes its transmission without the awareness of collision.
I have tried to solve the equations by fixed point method. I took initial value of p let p(1) and calculated ps let ps(1), then used it to calculated p(2) and so on unless I obtained error less than 10^-8. The p(ps) equation depends on CWmin i.e. the initial contention window and Wmax i.e. the number of transmission attempts. I am changing my CWmin from 22 to 2^15 along with Wmax (13 to 0) which shows my CWmax ( max contention window) (DCF protocol).
The problem is that for error 10^-8 it is not converging for CWmin from 22 to 27 for any initial value . If i reduce error to 10^-3 it converges but different CWmin converges for different initial value.
why this problem is arising ? How can I solve it ?
I am trying to find a value that works for all CWmin and same error.
2) Another thing i tried is I plotted both equations and found intersection points and used them to find throughput but still the result doesn't match.
Please let me know if the following references/sites are useful to you:
1. Numerical methods - Fixed Point Iteration, does it converge ...
https://math.stackexchange.com/questions/646344/fixed-point-iteration-does-it-convergeDoes the fixed point iteration(s) converge(s) to the fixed points if you start with a close enough ... How do I find out if it converges or diverges?
2. Formulations to overcome the divergence of iterative method of fixed
...
http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0123-921X2015000200015Keywords: divergence, fixed point, linear convergence, open methods, ... x which cause f(x) = 0, it is possible using two ways: analytical direct methods that are ...
Dennis
Dennis Mazur
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