Wardrop's Principle
John Glen Wardrop was an English transport analyst who developed Wardrop's first and second principles of equilibrium.
The concepts are related to the idea of Nash equilibrium in game theory developed separately. However in transportation networks, there are many players, making the analysis more difficult than in games with small numbers of players.
Network equilibrium models are commonly used for the prediction of traffic patterns in transportation networks that are subject to congestion. The idea of traffic equilibrium originated as early as 1924, with Frank Knight
In 1952, Wardrop stated two principles that formalize this notion of equilibrium and introduced the alternative behavior postulate of the minimization of the total travel costs.
Wardrop's first principle of route choice, which is identical to the notion postulated by Knight, became accepted as a sound and simple behavioral principle to describe the spreading of trips over alternate routes due to congested conditions.
Wardrop's first principle states: The journey times in all routes actually used are equal and less than those which would be experienced by a single vehicle on any unused route. Each user non-cooperatively seeks to minimize his cost of transportation. The traffic flows that satisfy this principle are usually referred to as "user equilibrium" (UE) flows, since each user chooses the route that is the best. Specifically, a user-optimized equilibrium is reached when no user may lower his transportation cost through unilateral action.
A variant on this is the marginal cost road pricing.
The first mathematical model of network equilibrium was formulated by Beckmann, McGuire and Winsten in 1956.
Reference
Wardrop, J. G., 1952. Some theoretical aspects of road traffic research, Proceedings, Institution of Civil Engineers, PART II, Vol.1, pp. 325-378.
