If the latency functions are linear, adding an edge can never make total travel time at equilibrium worse by a factor of more than 4/3. Possible instances of the paradox in action Prevalence In 1983, Steinberg and Zangwill provided, under reasonable assumptions, the necessary and sufficient conditions for Braess's paradox to occur in a general transportation network when a new route is added. (Note that their result applies to the addition of any new route, not just to the case of adding a single link.) As a corollary, they obtain that Braess's paradox is about as likely to occur as not occur when a random new route is added. Traffic Braess's paradox has a counterpart in case of a reduction of the road network (which may cause a reduction of individual commuting time). In Seoul, South Korea, traffic around the city sped up when a motorway was removed as part of the Cheonggyecheon restoration project. In Stuttgart, Germany, after investments into the road network in 1969, the traffic situation did not improve until a section of newly built road was closed for traffic again. In 1990 the temporary closing of 42nd Street in New York City for Earth Day reduced the amount of congestion in the area. In 2008 Youn, Gastner and Jeong demonstrated specific routes in Boston, New York City and London where that might actually occur and pointed out roads that could be closed to reduce predicted travel times. In 2009, New York experimented with closures of Broadway at Times Square and Herald Square, which resulted in improved traffic flow and permanent pedestrian plazas. In 2012, Paul Lecroart, of the institute of planning and development of the Île-de-France, wrote that "Despite initial fears, the removal of main roads does not cause deterioration of traffic conditions beyond the starting adjustments. The traffic transfer are limited and below expectations". He also notes that some private vehicle trips (and related economic activity) are not transferred to public transport and simply disappear ("evaporate"). The same phenomenon was also observed when road closing was not part of an urban project but the consequence of an accident. In 2012 in Rouen, a bridge was destroyed by fire. Over the next two years, other bridges were used more, but the total number of cars crossing bridges was reduced. Electricity In 2012, scientists at the Max Planck Institute for Dynamics and Self-Organization demonstrated, through computational modelling,