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John Glen Wardrop
John Glen Wardrop (1922–1989), born in Warwick, England, was an English mathematician and transport analyst who developed what became known as Wardrop's first and second principles of equilibrium in the field of traffic assignment. He studied at Downing College, Cambridge, and worked in Operational Research at British Bomber Command during the Second World War. He then helped to set up, and later headed, the Traffic Section of the Road Research Laboratory near Slough (Part of the Directorate of Scientific and Industrial Research within the UK Civil Service) where he published his work on equilibrium. He subsequently followed Dr Reuben Smeed to University College London, becoming Reader Emeritus in Traffic Studies. Wardrop equilibria 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Warwick
Warwick ( ) is a market town, civil parish and the county town of Warwickshire in the Warwick District in England, adjacent to the River Avon. It is south of Coventry, and south-east of Birmingham. It is adjoined with Leamington Spa and Whitnash. It has ancient origins and an array of historic buildings, notably from the Medieval, Stuart and Georgian eras. It was a major fortified settlement from the early Middle Ages, the most notable relic of this period being Warwick Castle, a major tourist attraction. Much was destroyed in the Great Fire of Warwick in 1694 and then rebuilt with fine 18th century buildings, such as the Collegiate Church of St Mary and the Shire Hall. The population was estimated at 37,267 at the 2021 Census. History Neolithic Human activity on the site dates back to the Neolithic, when it appears there was a sizable settlement on the Warwick hilltop. Artifacts found include more than 30 shallow pits containing early Neolithic flints and pottery an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
England
England is a country that is part of the United Kingdom. It shares land borders with Wales to its west and Scotland to its north. The Irish Sea lies northwest and the Celtic Sea to the southwest. It is separated from continental Europe by the North Sea to the east and the English Channel to the south. The country covers five-eighths of the island of Great Britain, which lies in the North Atlantic, and includes over 100 smaller islands, such as the Isles of Scilly and the Isle of Wight. The area now called England was first inhabited by modern humans during the Upper Paleolithic period, but takes its name from the Angles, a Germanic tribe deriving its name from the Anglia peninsula, who settled during the 5th and 6th centuries. England became a unified state in the 10th century and has had a significant cultural and legal impact on the wider world since the Age of Discovery, which began during the 15th century. The English language, the Anglican Church, and Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traffic Assignment
Route assignment, route choice, or traffic assignment concerns the selection of routes (alternative called paths) between origins and destinations in transportation networks. It is the fourth step in the conventional transportation forecasting model, following trip generation, trip distribution, and mode choice. The zonal interchange analysis of trip distribution provides origin-destination trip tables. Mode choice analysis tells which travelers will use which mode. To determine facility needs and costs and benefits, we need to know the number of travelers on each route and link of the network (a route is simply a chain of links between an origin and destination). We need to undertake traffic (or trip) assignment. Suppose there is a network of highways and transit systems and a proposed addition. We first want to know the present pattern of traffic delay and then what would happen if the addition were made. General Approaches Long-standing techniques The problem of estimat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operations Research
Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. It is considered to be a subfield of mathematical sciences. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems. Because of its emphasis on practical applications, operations research has overlap with many other disciplines, notably industrial engineering. Operations research is often concerned with determining the extreme values of some real-world objective: the maximum (of profit, performance, or yield) or minimum (of loss, risk, or cost). Originating in military efforts before World War II, its techniques have grown to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank Knight
Frank Hyneman Knight (November 7, 1885 – April 15, 1972) 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 Milton Friedman, George Stigler and James M. Buchanan were all students of Knight at Chicago. Ronald Coase said that Knight, without teaching him, was a major influence on his thinking. F.A. Hayek considered Knight to be one of the major figures in preserving and promoting classical liberal thought in the twentieth century. Paul Samuelson named Knight (along with Harry Gunnison Brown, Allyn Abbott Young, Henry Ludwell Moore, Wesley Clair Mitchell, Jacob Viner, and Henry Schultz) as one of the several "American saints in economics" born after 1860. Life and career Knight ( BA, Milligan College, 1911; BS and AM, Tennessee, 1913; PhD, Cornell, 1916) was born in 1885 in McLean County, Illinois, the son of Julia Ann (Hyneman) and Winton Cyrus Knight. After his earl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nash Equilibrium
In game theory, the Nash equilibrium, named after the mathematician John Nash, is the most common way to define the solution of a non-cooperative game involving two or more players. In a Nash equilibrium, each player is assumed to know the equilibrium strategies of the other players, and no one has anything to gain by changing only one's own strategy. The principle of Nash equilibrium dates back to the time of Cournot, who in 1838 applied it to competing firms choosing outputs. If each player has chosen a strategy an action plan based on what has happened so far in the game and no one can increase one's own expected payoff by changing one's strategy while the other players keep their's unchanged, then the current set of strategy choices constitutes a Nash equilibrium. If two players Alice and Bob choose strategies A and B, (A, B) is a Nash equilibrium if Alice has no other strategy available that does better than A at maximizing her payoff in response to Bob choosing B, and Bob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Game Theory
Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has applications in all fields of social science, as well as in logic, systems science and computer science. Originally, it addressed two-person zero-sum games, in which each participant's gains or losses are exactly balanced by those of other participants. In the 21st century, game theory applies to a wide range of behavioral relations; it is now an umbrella term for the science of logical decision making in humans, animals, as well as computers. Modern game theory began with the idea of mixed-strategy equilibria in two-person zero-sum game and its proof by John von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard method in game theory and mathema ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marginal Cost
In economics, the marginal cost is the change in the total cost that arises when the quantity produced is incremented, the cost of producing additional quantity. In some contexts, it refers to an increment of one unit of output, and in others it refers to the rate of change of total cost as output is increased by an infinitesimal amount. As Figure 1 shows, the marginal cost is measured in dollars per unit, whereas total cost is in dollars, and the marginal cost is the slope of the total cost, the rate at which it increases with output. Marginal cost is different from average cost, which is the total cost divided by the number of units produced. At each level of production and time period being considered, marginal cost includes all costs that vary with the level of production, whereas costs that do not vary with production are fixed. For example, the marginal cost of producing an automobile will include the costs of labor and parts needed for the additional automobile but not the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Road Pricing
Road pricing (also road user charges) are direct charges levied for the use of roads, including road tolls, distance or time-based fees, congestion charges and charges designed to discourage the use of certain classes of vehicle, fuel sources or more polluting vehicles. These charges may be used primarily for revenue generation, usually for road infrastructure financing, or as a transportation demand management tool to reduce peak hour travel and the associated traffic congestion or other social and environmental negative externalities associated with road travel such as air pollution, greenhouse gas emissions, visual intrusion, noise pollution and road traffic collisions. ''Executive Summary, pp. v''. In most countries toll roads, toll bridges and toll tunnels are often used primarily for revenue generation to repay long-term debt issued to finance the toll facility, or to finance capacity expansion, operations, and maintenance of the facility itself, or simply as genera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Of Anarchy
The Price of Anarchy (PoA) is a concept in economics and game theory that measures how the efficiency of a system degrades due to selfish behavior of its agents. It is a general notion that can be extended to diverse systems and notions of efficiency. For example, consider the system of transportation of a city and many agents trying to go from some initial location to a destination. Let efficiency in this case mean the average time for an agent to reach the destination. In the 'centralized' solution, a central authority can tell each agent which path to take in order to minimize the average travel time. In the 'decentralized' version, each agent chooses its own path. The Price of Anarchy measures the ratio between average travel time in the two cases. Usually the system is modeled as a game and the efficiency is some function of the outcomes (e.g. maximum delay in a network, congestion in a transportation system, social welfare in an auction, etc.). Different concepts of equilibriu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frank–Wolfe Algorithm
The Frank–Wolfe algorithm is an iterative first-order optimization algorithm for constrained convex optimization. Also known as the conditional gradient method, reduced gradient algorithm and the convex combination algorithm, the method was originally proposed by Marguerite Frank and Philip Wolfe in 1956. In each iteration, the Frank–Wolfe algorithm considers a linear approximation of the objective function, and moves towards a minimizer of this linear function (taken over the same domain). Problem statement Suppose \mathcal is a compact convex set in a vector space and f \colon \mathcal \to \mathbb is a convex, differentiable real-valued function. The Frank–Wolfe algorithm solves the optimization problem :Minimize f(\mathbf) :subject to \mathbf \in \mathcal. Algorithm :''Initialization:'' Let k \leftarrow 0, and let \mathbf_0 \! be any point in \mathcal. :Step 1. ''Direction-finding subproblem:'' Find \mathbf_k solving ::Minimize \mathbf^T \nabla f(\mathbf_k) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Economists
English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national identity, an identity and common culture ** English language in England, a variant of the English language spoken in England * English languages (other) * English studies, the study of English language and literature * ''English'', an Amish term for non-Amish, regardless of ethnicity Individuals * English (surname), a list of notable people with the surname ''English'' * People with the given name ** English McConnell (1882–1928), Irish footballer ** English Fisher (1928–2011), American boxing coach ** English Gardner (b. 1992), American track and field sprinter Places United States * English, Indiana, a town * English, Kentucky, an unincorporated community * English, Brazoria County, Texas, an unincorporated community * Engli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
