where the argument of the delay function is the v/c ratio, c being a measure of the capacity of the road.
Many different types of volume-delay functions have been proposed and used in practice in the past (for a review article see Branston [1]). By far the most widely used volume delay functions are the BPR functions (Bureau of Public Roads [2]), which are defined as
With higher values of 
, the onset of congestion effects becomes more and more sudden. This can be seen in Figures 1, a and b, which show the BPR type congestion function
for exponents =2, 4, 6, 8, 10 and 12. This range of alpha values is also indicative of the wide range that is used in practice, but note that the values of are usually not restricted to integers.
The simplicity of these BPR functions is certainly one reason for their wide spread use. It is also very convenient that for any value we have 
, i.e. when traffic volume equals the capacity, the speed is always half the free flow speed.
