, where M is a positive constant. The steepness of the congestion curve is limited. This in turn limits also the values of the volume delay function not to get too high when considering v / c ratios higher than 1, avoiding the problems mentioned in a) above.
Conditions 1 to 4 hold, of course, for the BPR function and are stated to ensure compatibility with them. Conditions 5, 6 and 7 are imposed in order to overcome the BPR functions' drawbacks a), b) and c) mentioned above.
[Page]At least one class of congestion functions exists indeed, as we will show in the remaining part of this note.
Conical Congestion Functions
Consider an obtuse three-dimensional cone intersected with the two-dimensional X-Y plane. Figure 2 shows the projection of the cone, as well as one possible resulting hyperbolic section. These hyperbolic cone sections have all the desired properties and constitute the base for the conical congestion functions, as we shall name them.
The name ``hyperbolic congestion functions'' would also be appealing, but it has been used in the past for functions of the form 
