ADDING A NEW ROAD MAY NOT EASE TRAFFIC

We always think that adding a new road will ease traffic congestion. On the contrary, it may create a traffic jam. Let us see this paradox in detail.

    Look at the above diagram carefully.  There are two roads to go from start to end.  One via A and another via B.   First road has a narrow bridge between ‘start’ and A.  The second road has narrow bridge between B and 'End'.
     The time taken to cross the narrow bridge depends on number of vehicles.  More cars mean more time.  The time taken to cross the bridge is given by N/100, where N is the number of vehicles crossing the bridge.  Hence, the time taken to go from "start to A or B to end" is N/100 because of bridges.
    The time taken to go from A to End or start to B (hilly roads) is always 45 minutes irrespective of the traffic.

On a fine morning, 4000 vehicles try to go from start to end. Naturally, (Probability theory) half of them will go via A and another half (2000) of them will go via B.
The time taken for the drivers going via A
= 2000/100 +45 here N=2000
= 20+45 =65 minutes.
The time for the drivers going via B = 2000/100 +45 = 65 minutes. refer figure
Hence both the roads require 65 minutes time. So far, so good.

    Now the national highways department construct a new road from A to B to reduce congestion and time.  The time taken to go from A to B through the new road is practically zero.
    The highways department thinks in these lines: "suppose 1000 cars start from 'start'.  They will reach A in 1000/100 =10 minutes.
Then they will reach B in no time. From B to end, it will again take 1000/100 =10 minutes.  Totally, it will take only 20 minutes for the drivers to go from start to end", a good reduction.

But now, there is a new short route, everybody wants to use this route. Suppose 4000 drivers take the same route. What will happen? The time of travel will be 4000/100+4000/100=40 +40 =80 minutes. The time has increased from 65 to 80 minutes. Hence the new road from A to B, only increased the congestion. So, it is better to remove the new road. This is called Brass's paradox.

In Seoul, south Korea, the congestion eased, the traffic speeded up. When a motorway was removed as part of the restoration project.
In 2009, Newyork, experimented with closures of Broadway at times square and Herald Square which resulted in improved traffic flow and permanent pedestrian plazas.

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