How Far From Optimal Is Traffic At Equilibrium
At worst, traffic in equilibrium is twice as bad as socially optimal
Proof
= starting point for car j
= target for car j
Strategies for car j are possible paths from to
Each edge e has a travel function for some
Energy on edge e with x drivers:
Total time spent by all drivers on that edge:
- ((where there are x terms))
E(e) is less than or equal to T(e) and
Resulting Inequality
If Z is a traffic pattern:
If we start from a socially optimal traffic pattern Z and end in an equilibrium pattern Z':
Thus we can see that worst is twice as bad as optimal.
Read more about this topic: Braess's Paradox
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