Prove using the inverse of the Erlang-B loss function

Sep 2009
Hi all,

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!