John Glen Wardrop
Encyclopedia
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.
In studies about traffic assignment, 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 stochastic user equilibrium (SUE) wherein no driver can unilaterally change routes to improve his/her perceived travel times.
Wardrop's second principle states: At equilibrium the average journey time is minimum. This 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). Economists 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.
The concepts are related to the idea of Nash equilibrium
Nash equilibrium
In game theory, Nash equilibrium is a solution concept of a game involving two or more players, in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only his own strategy unilaterally...
in game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...
developed separately. However in transportation networks, there are many players, making the analysis more difficult than in games with small numbers of players.
In studies about traffic assignment, 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
Frank Knight
Frank Hyneman Knight was an American economist who spent most of his career at the University of Chicago, where he became one of the founders of the Chicago school. Nobel laureates James M. Buchanan, Milton Friedman and George Stigler were all students of Knight at Chicago. Knight supervised...
.
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 stochastic user equilibrium (SUE) wherein no driver can unilaterally change routes to improve his/her perceived travel times.
Wardrop's second principle states: At equilibrium the average journey time is minimum. This 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). Economists argue this can be achieved with marginal cost
Marginal cost
In economics and finance, marginal cost is the change in total cost that arises when the quantity produced changes by one unit. That is, it is the cost of producing one more unit of a good...
road pricing
Road pricing
Road pricing is an economic concept regarding the various direct charges applied for the use of roads. The road charges includes fuel taxes, licence fees, parking taxes, tolls, and congestion charges, including those which may vary by time of day, by the specific road, or by the specific vehicle...
.
The first mathematical model of network equilibrium was formulated by Beckmann, McGuire and Winsten in 1956.