VL 07: Transport Sector and Modeling

Question 1

How can a congested network like a traffic network arrange itself?

Answer 1

1. The selfish situation (Nash-Equilibrium)

2. The social optimum

Question 2

What conditions apply for traffic flows?

Answer 2

• Capacity

- Flow balance/Kirchhoff

Question 3

What is a Wardrop equilibrium/Nash equilibrium?

Answer 3

In a Wardrop equilibrium all used routes between an O-D-pair have equal and minimum costs while all unused routes have greater or equal costs.

Question 4

What is the social optimum?

Answer 4

In the social optimum the average travel cost is minimized.

Question 5

What do you call such a situation?

Every player controls only a very small (infinitesimal) portion of the demand. At equilibrium, an infinitesimal demand cannot be served better (i.e. at a lower price) by choosing an under- or unused path.

Answer 5

Non-atomic

Question 6

How do you calculate the coordination ratio?

Answer 6

R = system cost “selfish routing”/system cost “social optimum”

(Eselsbrücke: Der Fisch schwimmt oben!)

Question 7

What is the price of anarchy?

Answer 7

The coordination ratio

Question 8

What is the Braess’ Paradox?

Answer 8

Adding an arc may lead to more congestion instead of reducing congestion in the network when assuming selfish routing.

Question 9

Selfish Routing - Two Paths

How do you calculate the flows?

Answer 9

c(P1) = c(P2)

Set the costs of the paths equal to each other!

Question 10

Social Optimum

How do you calculate the flows?

Answer 10

min C = Flow(P)*c(P)

Question 11

Selfish Routing - Three Paths

How do you calculate the flows?

Answer 11

What paths use the same edges?

For those paths compare the costs for the intervall [0,full load] –> if none is always better than the other one, the equilibrium has to be on these two paths