1. Local interaction and
traffic jam
Beom Jun Kim
(Dept. of Physics, Sungkyunkwan Univ., Korea)

2. Traffic problem
• In L.A., each car driver spends 56 hours
in traffic jam per year.
• In Germany, opportunity cost caused by
traffic jam sums up 100,000,000 US
dollars per year.
• Environmental effect (global warming,
air pollution, ...)
is a big

3. Easy
solution
• Build more roads !!
• Road area ≈ % of city area in Seoul (2005). Build more???
• Highway construction costs USD per km in Korea. Build
more??
• Let’s walk and bike !!
• I will not be here with you now.
22
20 million
No

4. What causes the
jam?
• Ant circle
• Ant’s traffic rule: follow your friend
and go astray a bit sometime. If
you find food, bring it home, and
let your friend know (leave
pheromone behind).
• No food, only pheromone ⇒ great
circle of ants ⇒ all die.
• We humans are much smarter than ants.
So..

5. We use cars!!!
• Intelligence of agents hardly matters.
• Emergent behavior from local interactions.

6. Why traffic jam
occurs?
• Traffic jam can occur without extrinsic inhomogeneity.

7. Model
• H. K. Lee et. al., PRL 92, 238702 (2004).
• Mechanical restriction: Acceleration and
deceleration capabilities are limited.
• Human overreaction: Driver’s excessive
response to the local traffic conditions.

8. Hitting on you?
• Collision-free condition with the limited
deceleration capability D:

9. We humans
• Accelerate/decelerate more than
necessary.
• Human behavior: simplified to either
“optimistic (0)” or “defensive (1)”.
• Optimistic (defensive) driver keeps shorter (longer)
distance to the car in front, and steps on brake in shorter
(longer) time. In other words, defensive drivers assume
the worst.

10. Let’s drive!
• Update rule:
• Parameters:
• H. K. Lee et. al., PRL 92, 238702 (2004).

11. Change Density &
Measure Flux
• One lane road of 60km long.
• Periodic boundary condition.
• Car density : ρ = # of vehicles/km
• Traffic flux : J = ρv ( # of vehicles/hour)
• Fundamental diagram (J versus ρ)

12. Traffic flow is history dependent
• Slow increase of ρ ⇒ broad range of free-flow.
• Once jammed, decrease of ρ doesn’t help much.
ρ
J
How ??

13. Heating Pad
Supersaturated solution of sodium acetate
(NaCH3COO)
•Supercooled liquid: Metastable
•Solid: Stable
Local perturbation drives the system back to stable
state (jammed state in traffic, and solid state in
heating pad).

14. Heating Pad: Metal
plate
•Perturbation provides nucleation center.
•Traffic: a stopped car acts as a
nucleation center for traffic jam.

15. Supercooled Coke
YouTube

16. Traffic Jam
YouTube

17. In More Detail
ρ (vehicles/km)
<v> (km/h)
• No hysteresis for (Free ⇔ Synch)
• Strong hysteresis for (Synch ⇔ Jam)

18. Iron-fist solution
1.Monitor the change of ρ.
2.If ρ is about to exceed ~34 veh/km,
block all the highway entrances.
3.ρ decreases below some value (e.g.,
25 veh/km).
4.Open the gate, and keep watching!
• I will be happy to be the last one
entering, but hate to be the first one
being stopped.
• Game theoretic situation; Nash

19. Statistical Physics
Way of Thinking
• Jam is due to interactions.
• Un-jamming can be done by additional
local interactions.
But How?
• In the present model, alter the human
factor (optimistic/defensive), avoiding the
overreaction.

20. Autonomous Cruise Control
• Gather local traffic information.
• Change driving pattern in a smart way.
But what is smart way?
• In the present model, alter the human
factor (optimistic/defensive), avoiding the
overreaction.

21. Don’t overreact, and stay
calm.
A. Downstream jam (you are approaching the jam):
You’d better be cautious. Otherwise, you will
brake suddenly, making your follower surprised
(and she will make her follower surprised too).
B. Upstream jam (you are leaving the jam):
You’d better be optimistic (or speed up) so that
your follower can leave the jam earlier (and her
follower too).
• I tried both but only A was found to work:
Be prepared for the future, and don’t be
too happy after you suffer from misery.

22. Watch out downstream jam!
• If the n-th car in front of you has speed smaller
than vc, you’d better be careful ( ).
• Tuning of x and n to maximize <v>:
• The value of n doesn’t matter much (10 ≤ n ≤ 30).
• The best value of vc = 8 in the simulation unit (≃ 43.2km/h)
• Be careful when the 10-th car in front of you is
slower than 43km/h.
• Cars must be equipped with a device (measure
the speed and send out the signal to other cars).

23. Fasten your seat belt.
optimistic fast driver
defensive fast driver
optimistic slow driver
defensive slow driver
you are here

24. No Free Lunch
• Jam is
dissolved when
ACC is on
(Jam ➱ Synch).
• If you keep
ACC on in
Synch phase,
<v> is lower
than ACC = off.
Good news
Bad news
• ACC removes hysteresis behavior!

25. Summary
• Traffic problem was studied by using a
CA model.
• Strong hysteresis behavior found
between Synch and Jam phases. Once
in the Jam phase, it becomes very
difficult to return to Synch phase.
• A simple ACC was suggested: If you are
approaching downstream jam, drive
carefully.
• www.kbsnews.com (search 김범준)