Even if the above algorithm is terminated before complete convergence is reached, the solution obtained will always satisfy the conservation of flow constraint (5), whereas some of the capacity constraints (6) may still be violated by a certain amount. This is typical for dual based algorithms, and also has the additional advantage that the algorithm will even converge to a solution if the primal problem is infeasible, i.e. if the total park&ride demand exceeds the available total parking space ( 
). In the later case, the algorithm simply converges to a solution in which --loosely speaking-- the parking capacity constraints are violated the least possible.
If they are needed, the shadow prices can be computed as 
once the algorithm has terminated. These values (converted back into cost or impedance values by dividing by the appropriate model coefficients) can be very useful for analyzing the sensitivity of existing capacities or for deciding where to locate additional parking capacity.
Practical Model Implementation
While the previous sections looked at the posed problem from an abstract and theoretical point of view, let us now turn our attention to the practical implementation and use of such a model.
First, it is important to note that the variables 
used in the mathematical formulation are not easy to handle in real life (there are far to
