Network equilibrium laboratory

Braess Paradox

A faster-looking connection can make the whole network worse. Explore the paradox in road traffic and in a small electric grid where a connected tie line can force costly redispatch.

Traffic penalty

+15min

Grid savings from removal

$9.1k/hr

Equilibrium type

Worseafter shortcut

Grid status

Congestedtie connected

Original network

Drivers split between two equal routes at equilibrium.

65 min

Top route

2000

Bottom route

2000

Travel time

65

Shortcut added

Individual choices shift the system into a worse equilibrium.

80 min

Shortcut users

4000

Old-route users

0

Travel time

80

Tie connected

The low-impedance tie creates loop flow and may bind its thermal limit.

Congested

Total cost

$14.1k

G1 dispatch

360

G2 dispatch

140

Tie removed

Removing the troublesome connection can restore cheaper dispatch.

Optimal

Total cost

$5.0k

G1 dispatch

500

G2 dispatch

0