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The Downs–Thomson paradox (named after Anthony Downs and J. M. Thomson), also referred to as the Pigou–Knight–Downs paradox (after Arthur Cecil Pigou and Frank Knight), 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 make traffic congestion worse, when the shift from public transport causes a disinvestment in that mode such that the operator reduces frequency of service or raises fares to cover costs. This shifts additional passengers into cars. Ultimately the system may be eliminated and traffic congestion 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 known as Lewis–Mogridge Position and was extensively documented by Martin Mogridge in the case-study of London on his book Travel in towns: jam yesterday, jam today and jam tomorrow?
A 1968 article by Dietrich Braess, now at the Faculty of Mathematics in Ruhr University, pointed out the existence of 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 as well as 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 optimal routes between origin and destination.
This is an extension of the induced demand theory and consistent with Downs (1992) theory of "triple convergence", formulated 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.
Restrictions on validity
According to Downs the link between average speeds on public transport and private transport "only applies to regions in which the vast majority of peak-hour commuting is done on rapid transit systems with separate rights of way. Central London is an example, since in 2001 around 85 percent of all morning peak-period commuters into that area used public transit (including 77 percent on separate rights of way) and only 11 percent used private cars. When peak-hour travel equilibrium has been reached between the subway system and the major commuting roads, then the travel time required for any given trip is roughly equal on both modes."
- On a Paradox of Traffic Planning, translated from the 1968 D. Braess paper from German to English by D. Braess, A. Nagurney, and T. Wakolbinger (2005), Transportation Science 39/4, 446–450.
- Downs, Anthony, Stuck in Traffic: Coping with Peak-Hour Traffic Congestion, The Brookings Institution: Washington, DC. 1992. ISBN 0-8157-1923-X
- Mogridge, Martin J.H. Travel in towns: jam yesterday, jam today and jam tomorrow? Macmillan Press: London, 1990. ISBN 0-333-53204-X
- Thomson, J. M. (1972), Methods of traffic limitation in urban areas. Working Paper 3, Paris, OECD.