In a recent transportation study for the City of Basel, Switzerland, the proposed conical volume-delay functions have been used successfully in practice. A dramatic improvement in the convergence of the equilibrium assignment was observed when switching from the previously used BPR functions to the corresponding conical functions, with no practically significant changes in the resulting network flows. This study was carried out using the EMME/2 transportation planning software (Spiess [4]).
Conclusions
In trying to overcome the known disadvantages of the BPR functions, we have developed a new class of volume-delay functions, the conical functions. The interpretation of the parameters used to characterize the specific congestion behavior of a road link, i.e. capacity c and steepness 
, is the same for both BPR and conical function, which makes the transition to conical functions particularly simple. Since the difference between a BPR function and a conical function with the same parameter is very small within the feasible domain, i.e. v/c <1, the BPR parameters can be transferred directly in most cases.
Further research would be needed to develop statistical methods for directly estimating the parameters of the conical functions, using observed speeds and volumes.
References
