Editing Route assignment (section)

===Frank-Wolfe algorithm===
Dafermos (1968) applied the [[Frank-Wolfe algorithm]] (1956, Florian 1976), which can be used to deal with the traffic equilibrium problem.  Suppose we are considering a highway network.  For each link there is a function stating the relationship between resistance and volume of traffic.  The [[Federal Highway Administration|Bureau of Public Roads]] (BPR) developed a link (arc) congestion (or volume-delay, or link performance)  function, which we will term  ''S<sub>a</sub>(v<sub>a</sub>)''

<math>
S_a \left( {v_a } \right) = t_a \left( {1 + 0.15\left( {\frac{{v_a }}
{{c_a }}} \right)^4 } \right)
</math>

*t<sub>a</sub> = free flow travel time on link ''a'' per unit of time
*v<sub>a</sub> = volume of traffic on link ''a'' per unit of time (somewhat more accurately: flow attempting to use link ''a'').
*c<sub>a</sub> = capacity of link ''a'' per unit of time
*S<sub>a</sub>(v<sub>a</sub>) is the average travel time for a vehicle on link ''a''
	
There are other congestion functions.  The CATS has long used a function different from that used by the BPR, but there seems to be little difference between results when the CATS and BPR functions are compared.