Downs-Thomson paradox

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Downs-Thomson paradox, also referred to as the Pigou-Knight-Downs paradox, states that the equilibrium speed of car traffic on the road network is determined by the average door-to-door speed of equivalent journeys by (rail-based or otherwise segregated) public transport.

It follows that increasing road capacity can actually make overall congestion on the road worse. This occurs when the shift from public transport causes a disinvestment in the mode such that the operator either reduces frequency of service or raises fares to cover costs. This shifts additional passengers into cars. Ultimately the system may be eliminated and congestion on the original (expanded) road is worse than before.

The general conclusion, if the paradox applies, is that expanding a road system as a remedy to congestion is not only ineffective, but often counterproductive. This is also known as Lewis-Mogridge Position and was extensively documented by Martin Mogridge with the case-study of London on his book Travel in towns: jam yesterday, jam today and jam tomorrow?

An article of 1968 from Dietrich Braess now at the Faculty of Mathematics in Ruhr University, already pointed out the existence this counter-intuitive occurrence on networks - the Braess' paradox states that adding extra capacity to a network, when the moving entities selfishly choose their route, can in some cases reduce overall performance.

There is a recent interest in the study of this phenomenon since the same may happen in computer networks and not only in traffic networks. Increasing the size of the network is characterized by behaviors of users similar to that of travelers on transportation networks, who act independently and in a decentralized manner in choosing their optimal routes of travel between origins and their destinations.

This is an extension of the induced demand theory and consistent with Downs (1992) theory of “triple convergence”. Downs (1992) formulated this theory to explain the difficulty of removing peak-hour congestion from highways. In response to a capacity addition three immediate effects occur. Drivers using alternative routes begin to use the expanded highway, those previously traveling at off-peak times (either immediately before or after the peak) shift to the peak (rescheduling behavior as defined previously), and public transport users shift to driving their vehicles.

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On a Paradox of Traffic Planning, translated from the (1968) original D. Braess paper from German to English by D. Braess, A. Nagurney, and T. Wakolbinger (2005), Transportation Science 39/4, 446-450.