We now turn our attention to the the variant of the transit assignment problem in which the link travel times 
are no longer constants, but are continuous non-decreasing functions of the corresponding link flows 
. Such a dependence of the link cost on the transit volume may represent an actual slowing down of the transit vehicle due to the number of passengers, but it may also be interpreted as a generalize cost which includes a ``discomfort'' term which increases as the vehicles get crowded.
In this context, the transit assignment problem is no longer separable by destination node, since the link costs depend on the total flow of passengers. The total transit volumes are the sum of the volumes bound for each of the destinations.
As the expected cost of any given strategy is no longer fixed, but depends on the total volumes, the optimal strategies are now defined by Wardrop's second principle, which implies that only strategies with minimal expected cost will be used by the travelers (Wardrop, 1952). The resulting equilibrium assignment is equivalent to the following convex minimization problem:
subject to
