This document proposes a method for improving highway traffic merging by tuning each car's behavior. It discusses using car-to-car interactions to induce zipper merging configurations through modeling car movements with a cellular automata approach. Simulations show that drawing "orange lines" to ban lane changes and introduce repulsive interactions between cars can spatially change configurations to achieve larger degrees of zipper merging. This results in improved merging efficiency and increased traffic flow rates compared to non-zipper merging, especially when there is a delay for cars to restart after stopping.

1. Introduction of my study:
A method for improving merging of
highway traffic by tuning each car’s behavior
Suri-Jyokyo-no-kai (SJK seminar)
18th, Jun, 2012
Ryosuke Nishi
1

2. Table of contents
• Background of traffic flow
– Engineering and physics
• Direction of my study
– Utilize each car’s behavior for improving flow
• Main topic: improving merging efficiency
• Conclusions
2

3. Background
• Easing jams is very significant
– Financial loss of traffic jam in Japan is 11 trillion
yen/year*
• Traffic science is composed of many fields
– Engineering
– Physics
– Economics
– Phycology and other fields
* Road Bureau, Ministry of Land, Infrastructure, Transport and Tourism,Japan.
平成18 年度達成度報告書・平成19 年度業績計画書第2 部ii施策-2 効果的な渋滞対策の推進.
http://www.mlit.go.jp/road/ir/ir-perform/h19/02.pdf 3

4. Progress in traffic engineering
• Dynamics of traffic flow (at least 1930’s～)
– Data accumulation（velocity-headway relationships）
– A lot of models (kinematic, fluid, car-following)
• Development of strategies controlling traffic
– Ramp metering
– Route guidance
– Variable speed limits
4

5. Traffic flow in Physics（mainly 1990’s～）
• Self-driven particles (SDPs)
– Cars, pedestrians, animals, molecular motors
– action≠reaction: phenomenological modeling
• Microscopic – macroscopic phenomena
– free-jam phase transitions
– meta-stable branches, synchronized flow
– experiment of spontaneous traffic jams
– a lot of models（OV model, NaSch model, IDM）
5

6. Direction of my study
• To ease jams with each car’s behavior with least
devices
– lateral interactions
Controllers(traffic lights, speed signs)
Road
Car’s behavior
infrastructure
6

7. We focus on interchanges and junctions
(major place where jams occur in Japanese three highways)
percentage
We used the data in the following web sites (Feb. 2012)
East Nippon Expressway Company Limited, http://www.e-nexco.co.jp/activity/safety/mechanism.html,
Central Nippon Expressway Company Limited, http://www.c-nexco.co.jp/traffic/jam/cause/,
West Nippon Expressway Company Limited, http://www.w-nexco.co.jp/traffic_info/trafficjam_comment/index2.html 7

8. To induce zipper merging in weaving sections
• Jam caused by disorderly lane-changes
– Impossible for cars in a road to see cars in the other road before entering
merging area
– High demand to change lanes
Disorderly lane-changes
merging bifurcation
8

9. Emergent zipper merging by drawing orange lines
• Orange lines banns lane-changes
– Car-to-car repulsive interactions achieves zipper
configurations
Disorderly lane-changes
Orange line
Zipper configurations 9

10. Spatial change of configurations
before lane-changes
Orange lines
Orange lines
Lane1
Lane2
10

11. Modeling of cars’ movements：
Cellular Automata (CA)
• Parallel update: discrete time, updating simultaneously
• Movements：stochastic process
– If the next cell is empty, car 𝑖 moves to it with
probability 𝑣 𝑖𝑡 between time 𝑡 and 𝑡 + 1
11

12. • Time update of 𝑣 𝑖𝑡 :
Multiple lanes stochastic optimal velocity Model
[1], [2]
𝑡 𝑡
– 𝑉(⊿𝑥1,𝑖 , ⊿𝑥2,𝑖 ) : optimal velocity (OV) function
𝑡 𝑡
• ⊿𝑥1,𝑖 , ⊿𝑥2,𝑖 : distances of car 𝑖
– 𝑎 (0 ≤ 𝑎 ≤ 1): sensitivity parameter
• 𝑣 𝑖𝑡 approaches 𝑉 more quickly as 𝑎 becomes larger
12

13. • Interactions between two lanes
– Four kinds of
– Deceleration-like Interactions ：
13

14. The measurement of the alternative
configuration : Simulation
• Example of a
configuration
• 10 states at 𝑥 = 𝑘, 𝑘 + 1 denoted by 𝑆1 , … , 𝑆10
14

15. • Perfect alternative
configuration： 𝑆3
𝐶𝑗 (1 ≤ 𝑗 ≤ 10)： The number of 𝑆 𝑗 in simulations
• 𝐺(𝑘)： the degree of alternative
configurations at 𝑥 = 𝑘
The number ofthe perfect state state
The number of the perfect
𝐺(𝑘)
That of the states holding
That of the states holding vehicles at cars at 𝑥 = 𝑘
15

16. Spatial change to large 𝐺 with car-to-car
interactions
– simulations（dots）, mean-field（lines）
zipper
p= 1
𝑞 = 𝑟 = 0.8
𝐺
d = 100
α = 0.05
𝛽 𝑗 = 𝑣 (𝑗 = 1,2)
105 ≤ 𝑡 < 2 × 105
* #simu: 10
* *
space[cell]
16
R. Nishi, H. Miki, A. Tomoeda, K. Nishinari, Phys. Rev. E 79, 066119 (2009)

17. The measurement of the alternative
configuration: Cluster approximation
• Calculation of the stationary state of the configurations
on the four cells at 𝑥 = 𝑘, 𝑘 + 1
• Π 𝑡𝑘 (𝑗)(1 ≤ 𝑗 ≤ 10) : The probability of having the
state 𝑆 𝑗 at time 𝑡 at 𝑥 = 𝑘, 𝑘 + 1
• 𝚷 𝑡𝑘 = Π 𝑡𝑘 1 , … , Π 𝑡𝑘 10 𝑇 : The state vector of the
four cells at 𝑥 = 𝑘, 𝑘 + 1 at time 𝑡
17

18. • State transition
： State transition matrix at 𝑥 = 𝑘, 𝑘 + 1
• The stationary state:
• The degree of the alternative configuration
∞
𝐺𝑘
18

19. Estimate zipper merging with flow rate
• A simple system with two-lane lattice and 1cell
Car-to-car interactions
OFF：non-zipper merging
ON： zipper merging
𝛼
1
𝛼
𝑑
19

20. Modeling with CA
• Parallel update（discrete time）
• Exclusive volume effect：impossible to move if the next
cell is occupied
• To move stochastically with at most 1 cell in 1 time step
Deceleration-like
interactions
Hopping prob. 𝑣𝑖 = 0 𝑣 𝑖 = 𝑝(≤ 1) 𝑣𝑖 = 1
configurations * *
*：any states
* 20

21. • When two cars exist just before merging
– One car chosen in random has to stop
t t+1 probability
21

22. Slow-to-start rule
• Delay of restarts due to inertia
• Only Just after stopping due to exclusive volume effect,
Hopping probability is multiplied by 𝑠 0 ≤ 𝑠 ≤ 1 [3]
– s = 0 (heaviest delay, cars must rest for 1 step)
– s = 1(no delay)
t t+1
𝑣𝑖 = 0 𝑣𝑖 = 𝑠 × 𝑝 , 𝑣𝑖 = 𝑠 × 1
* * * *
* *
22

23. Transitions of hopping probability 𝑣 𝑖
23

24. No slow-to-start at merging area in zipper merging
Non-zipper merging
Move with prob. 1 irrespective of cars on
neighboring lane
Slow-to-start rule （inertia of restarting）
Zipper merging
24
Induce zipper configurations with 𝑝 (0< 𝑝 ≤ 1)
No blocked cars

25. Flow rate 𝑄： 𝑄 𝑝 < 1 > 𝑄 𝑝 = 1 for small 𝑠 (large inertia)
• Deceleration-like interactions makes flow rate larger
– By avoiding slow-to-starting at merging area by
𝑄(𝑝<1) > 𝑄(𝑝=1)
Injection prob. 𝛼
s = 0(heavest delay)
s = 1(no delay)
Slow-to-start effect : 𝑠
25
R. Nishi, H. Miki, A. Tomoeda, D. Yanagisawa, K. Nishinari, J. Stat. Mech. (2011) P05027

26. Flow rate difference：
𝑄 𝑝<1 − 𝑄 𝑝=1
for various 𝑝
26

27. Flow rate 𝑄
versus
injection rate 𝛼
27

28. Dependence of system-size 𝑑
28

29. Cluster approximations of flow rate
• Simulations (dots), Cluster approximation (lines)
29

30. Conclusions
• A method to improve the efficiency of
merging
– by induce zipper merging by car-to-car
interactions
• Spatial change to zipper configurations before
merging with car-to-car interactions
• Zipper configurations realizes higher flow rate
– When slow-to-start effect (inertia) is large
30

31. Reference
• [1] M. Bando, K. Hasebe, A. Nakayama, A.
Shibata, and Y. Sugiyama, PRE 51, 1035 (1995)
• [2] Masahiro Kanai, Katsuhiro Nishinari, and
Tetsuji Tokihiro, PRE 72, 035102 (2005)
• [3] Simon C. Benjamin, Neil F Johnson, and P.
M. Hui, J. Phys. A: Math. Gen. 29 (1996) 3119–
3127.
31