Prove using the inverse of the Erlang-B loss function

Sep 2009
12
0
I would like to know how to prove that:

considering that function F is the ceil of the inverse of the Erlang-B loss function, that is, receives as input parameters the load and a particular target loss rate and its output is the upper integer of the result (the number of channels required)

Let h denote the amount of traffic carried by one connection (for example)
Well, I know that F(h) is always greater or equal than F((n+2)h) - F((n+1)h) for n = 0...N

In other words, the number of channels required by the first connection is always greater or equal than the increment that it will generate if the system is already loaded by some connections.

Does anyone knows how can I prove that mathematically ???

Thank you very much in advance for your valuable help!
 
Sep 2009
12
0
Just to let you know that F is a real-valued concave function...I think it should help