Wardrop Equilibrium

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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).

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