# Wardrop Equilibrium

### From Traffic Analysis and Microsimulation

In 1952, John Glen Wardrop articulated principles that have been widely used to simplify the mathematics associated with routing in traffic models:

*Under equilibrium conditions, traffic arranges itself in congested networks in such a way that no individal trip maker can reduce his path costs by switching routes.*

Wardrop wrote that if all trip makers perceive costs in the same way (i.e. there are no stochastic effects or PERTURBATION):

*Under equilibrium conditions traffic arranges itself in congested networks such that all used routes between an O-D pair have equal and minimum costs, while all unused routes have greater or equal costs.*

In some cases the socially-optimal pattern of trip-making differs from the pattern that occurs when each individual driver acts according to his or her own self-interest. Therefore, Wardrop articulated the following *design* principle which would apply to a well-designed transportation network:

*Under social equilibrium conditions traffic should be arranged in congested networks in such a way that the average (or total) travel cost is minimized.*

Further work on socially-optimal networks has been done by Smeed, Goodwin and others.

Reference: Ortuzar & Willumsen, *Modelling Transport* (New York: John Wiley & Sons, 1990).