Congestion pricingCongestion pricing or congestion charges is a system of surcharging users of public goods that are subject to congestion through excess demand, such as through higher peak charges for use of bus services, electricity, metros, railways, telephones, and road pricing to reduce traffic congestion; airlines and shipping companies may be charged higher fees for slots at airports and through canals at busy times. Advocates claim this pricing strategy regulates demand, making it possible to manage congestion without increasing supply.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Toll roadA toll road, also known as a turnpike or tollway, is a public or private road (almost always a controlled-access highway in the present day) for which a fee (or toll) is assessed for passage. It is a form of road pricing typically implemented to help recoup the costs of road construction and maintenance. Toll roads have existed in some form since antiquity, with tolls levied on passing travelers on foot, wagon, or horseback; a practice that continued with the automobile, and many modern tollways charge fees for motor vehicles exclusively.
Traffic congestionTraffic congestion is a condition in transport that is characterized by slower speeds, longer trip times, and increased vehicular queueing. Traffic congestion on urban road networks has increased substantially since the 1950s. When traffic demand is great enough that the interaction between vehicles slows the traffic stream, this results in congestion. While congestion is a possibility for any mode of transportation, this article will focus on automobile congestion on public roads.
Global optimizationGlobal optimization is a branch of applied mathematics and numerical analysis that attempts to find the global minima or maxima of a function or a set of functions on a given set. It is usually described as a minimization problem because the maximization of the real-valued function is equivalent to the minimization of the function . Given a possibly nonlinear and non-convex continuous function with the global minima and the set of all global minimizers in , the standard minimization problem can be given as that is, finding and a global minimizer in ; where is a (not necessarily convex) compact set defined by inequalities .
Electronic toll collectionElectronic toll collection (ETC) is a wireless system to automatically collect the usage fee or toll charged to vehicles using toll roads, HOV lanes, toll bridges, and toll tunnels. It is a faster alternative which is replacing toll booths, where vehicles must stop and the driver manually pays the toll with cash or a card. In most systems, vehicles using the system are equipped with an automated radio transponder device.
Multi-objective optimizationMulti-objective optimization or Pareto optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, or multiattribute optimization) is an area of multiple-criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is a type of vector optimization that has been applied in many fields of science, including engineering, economics and logistics where optimal decisions need to be taken in the presence of trade-offs between two or more conflicting objectives.
Bus laneA bus lane or bus-only lane is a lane restricted to buses, often on certain days and times, and generally used to speed up public transport that would be otherwise held up by traffic congestion. The related term busway describes a roadway completely dedicated for use by buses, whilst bus gate describes a short bus lane often used as a short cut for public transport. Bus lanes are a key component of a high-quality bus rapid transit (BRT) network, improving bus travel speeds and reliability by reducing delay caused by other traffic.
Nonlinear programmingIn mathematics, nonlinear programming (NLP) is the process of solving an optimization problem where some of the constraints or the objective function are nonlinear. An optimization problem is one of calculation of the extrema (maxima, minima or stationary points) of an objective function over a set of unknown real variables and conditional to the satisfaction of a system of equalities and inequalities, collectively termed constraints. It is the sub-field of mathematical optimization that deals with problems that are not linear.
