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 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 stochastic user equilibrium (SUE) wherein no driver can unilaterally change routes to improve his/her perceived travel times.
Wardrop's second principle At equilibrium the average journey time is minimum. implies that each user behaves cooperatively in choosing his own route to ensure the most efficient use of the whole system. Traffic flows satisfying Wardrop's second principle are generally deemed "system optimal" (SO). Economist's argue this can be achieved with marginal cost road pricing.
The first mathematical model of network equilibrium was formulated by Beckmann, McGuire and Winsten in 1956.