Fig. 2. Hyperbolic conical sections.
Since the mathematical derivation is quite simple but lengthy and only involves basic geometry and elementary algebra, we shall simply state the resulting function and show that it indeed satisfies the conditions 1 to 7 set forth above.
Let the class of conical congestion functions be defined as
where 
is given as
and 
is any number larger than 1.
In order to prove that the desired properties hold for 
, we need to evaluate the the first derivative of , which is
Let us now show, point by point, that the properties 1 to 7 indeed hold for :
we obtain
