Slides of the introductory lecture on Traffic signal synchronization, course of Traffic Engineering and ITS, Prof. Gaetano Fusco, Sapienza University of Rome

1. Prof. Gaetano Fusco
gaetano.fusco@uniroma1.it
http://w3.uniroma1.it/gaetanofusco
Traffic Signal
Synchronization
Prof. Gaetano Fusco
gaetano.fusco@uniroma1.it
http://gaetanofusco.site.uniroma1.it/
Academic Year 2015-2016, Spring Semester
Course of Traffic Engineering and ITS

2. Motivations for synchronization
• Delay at junctions is the most relevant
component of travel times in urban road
networks
• Signal synchronization (or signal coordination)
sets a relationship among green starts at near
junctions.
• The goal is to reduce or, if possible, make nil
junction delay.
• Reduction of delay depends on the distance
between junctions, traffic flow patterns and
vehicle speed.
Traffic Engineering and ITS 05/05/17 Page 2

3. Problem Description
• The synchronization problem with maximal
bandwidth consists in:
• Finding the vector of offset θij that minimizes the
delays of vehicles traveling along the artery
• Given:
– The distance between consecutive
intersections: li
– The signal settings at each intersection: C, gi
– The synchronization speed in the two
directions, assuming that vehicles travel at
that speed along the artery: v1, v2
(or a suitable interval vmin ≤ v ≤ vmax)
05/05/17Traffic Engineering and ITS Page 3

4. Ideal synchronization
Section One
Traffic Engineering and ITS
05/05/17 Page 4

5. 05/05/17Traffic Engineering and ITS Page 5
Ideal synchronization

6. • Only in one case the node delay can be zero:
– All junctions are equally spaced;
– No entering or exiting traffic along the
artery;
– Traffic flow lower than a given value.
• Then:
– Cycle length and green splits are equal at
all junctions.
– All vehicles along the artery run at the
same speed and form so a uniform and
compact platoon.
05/05/17Traffic Engineering and ITS Page 6
Ideal synchronization

7. Ideal synchronization
• …then:
– A vehicle progression along the artery can
be found so that vehicles are not delayed
at nodes.
– At each node, the green must start as the
first vehicle of the platoon arrives and must
end just after the last vehicle has passed
the intersection.
05/05/17Traffic Engineering and ITS Page 7

8. A
Ideal synchronization
C
C
A
2
3
1
v1
t
x
r g=b
05/05/17Traffic Engineering and ITS Page 8

9. C
C θ1,2 = 0,5C
θ2,3 = 0,5C
x1,2= A
x2,3= A
2
3
1
v1 v2
t
x
t1,2
t2,1
r
g=b
A
Ideal synchronization
05/05/17Traffic Engineering and ITS Page 9

10. Mathematical Formulation
• The time interval between the green start at
near junctions spaced as A, i and j (offset θij)
equals the travel time tij:
• if v1=v2=v and m=1:
• Constraints on speed v and cycle C:
vmin ≤ v ≤ vmax
Cmin ≤ C ≤ Cmax
integer
21
m,mC
v
A
v
A
tt jiij =+=+
v
A
CC
v
A
v
A
tt jiij
2
, =⇒=+=+
05/05/17Traffic Engineering and ITS Page 10

11. Ideal synchronization
• The condition Cmin is given by the saturation
degree of the most critical junction:
Cmin= maxi{Cmin,i}
• The condition Cmax is given by the minimum
speed:
Cmax = 2A/vmin
• If Cmin > Cmax the problem has no solution.
05/05/17Traffic Engineering and ITS Page 11

12. Ideal synchronization
• If Cmin > Cmax the problem has no solution.
• High saturation degrees mean high values for
Cmin.
• The synchronization is possible if Cmax is low, or
if the distance A between junctions is short or
the synchronization speed v is low.
• For example, if: Cmin=70s; v=10m/s, the distance
must be:
A= vCmin/2  A >350m!
05/05/17Traffic Engineering and ITS Page 12

13. Formulation of Maximal
Bandwidth Problem
Section Two
Traffic Engineering and ITS
05/05/17 Page 13

14. “Real” synchronization
• Ideal synchronization is usually unfeasible
because:
– Junctions are not equally spaced
– Flow is not uniform along the artery
– Green splits are not equal.
• To solve realistic problems, two different
approaches have been proposed,
corresponding to two optimization problems:
• Minimum delay problem;
– non convex
• Maximal green bandwidth problem
– concave, but different of delay minimization.
05/05/17Traffic Engineering and ITS Page 14

15. Green Bandwidth
• The green bandwidth is defined as the set of
possible trajectories at a constant speed that
are uninterrupted along the artery.
05/05/17Traffic Engineering and ITS Page 15

16. “Real” Synchronization
0 20 40 60 80 100 120 140 160 180
0
100
200
300
400
500
05/05/17Traffic Engineering and ITS Page 16

17. Example of real maximal bandwidth
0 20 40 60 80 100 120 140 160 180
0
100
200
300
400
500
05/05/17Traffic Engineering and ITS Page 17

18. Green Bandwidth (2)
• The green bandwidth is defined as the set of
possible trajectories at a constant speed that
are uninterrupted along the artery.
• Such possible trajectories are not coincident,
in general, with the real trajectories of the
vehicles.
05/05/17Traffic Engineering and ITS Page 18

19. Green bandwidth and actual platoon
progression are different things
g=λC r = (1-λ)C
b
i+1
i
l
v
Bandwidth
Delayed vehicles
Delayed vehicles
Bandwidth
05/05/17Traffic Engineering and ITS Page 19