Wadrops’ Principle

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Definition: Wadrops’ Principle

It is based on a user equilibrium  where the situation of congestion is such that  the transportation time cannot be lowered  without collaborating with others . It states that the time used  in travelling in used  paths  is equal to or lesser  than those taken  to travel in unused paths . It means it is better to divide the journey distance in two available paths to lower the transportation time .The ratio in which it is divided is calculated using integral calculus.

Formula Used:

Min (S) = ∑   n∫ ( t(w) dw

where   t (w) is a function of flow  and  n is  corresponding period of travel


Let us consider a speed limit on path one to be  80 and  path 2 having a  limit of 65. The total  distance to be travelled is  5 kms through Paths A  and Path B in the figure mentioned below


T1 = 8+4(X1)

T2 = 12+(X2)2

=x1 ∫(8+4W) Dw  +     x2∫(12+ w2)dw

= 8x1+2x12 + 12x2 +x23/3

= 24x1 + 6x12 + 36x2 +x2

Now substituting  x2= 4.5 –x1

And   differentiating the equation to  zero we get the ration in which the distances have to be divided.

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