I would like to know if its possible to prove the following using the ceil of the Erlang-B loss function, that is, function
F = ErlagB ^-1(load,target loss rate) or for the sake of clarity
F = ErlagB ^-1(load)
Consider x an increment of load, then prove that:
F(k*x) >= [F((n+1)*k*x)-F((n+2)*k*x)] , n=0..N; k =1..K
I think it is worth to point out that F is a real-valued concave function.
My intuition tells me that this is true, I have even tested using matlab that it holds but I'm not very prominent at maths....that's why I'm here :P
Do you think it's true and that it can be proved, if so, how?
Thank your very much for your valuable help!