Fig. 1. BPR functions for (A) small and (B) large v/c ratios
Unfortunately, these BPR functions also have some inherent drawbacks, especially when used with high values of 
:
- a)
- While for any realistic set of travel volumes, we can assume that
(or at least not much larger than 1) this is usually not the case during the first few iterations of an equilibrium assignment. Values of v/c may well reach values of 3, 5 or even more. To illustrate this, the link time of a link with 
and a v/c ratio of 3 is increased by a factor of 
, which means that every minute free flow time becomes roughly one year of congested time! These aberrations slow down convergence by giving undue weight to overloaded links with high -values and can also cause numerical problems, such as overflow conditions and loss of precision.
- b)
- For links that are used far under their capacity, the BPR functions, especially when high values of alpha are used, yield always free flow times independent of actual traffic volume. To illustrate this, consider again a link with and a capacity of 1000. Whether the volume is 0 or 300, the volume delay function yields exactly the same numeric value (assum
