1. Vortex-Based Zero-Conflict
Design of Urban Road Networks
David Eichler1
, Hillel Bar-Gera2
, Meir Blachman
1. Physics Department, Ben-Gurion University of the
Negev
2. Department of Industrial Engineering and
Management, Ben-Gurion University of the Negev
2. Part I: Motivation
Conflicting (intersecting) traffic flow is
a liability and a drag.
Green lights are tolerable, red lights can
be extremely annoying.
3. Traffic conflict is dangerous.
• Replacing conflicting flow with merging
(e.g. roundabouts) saves lives. 60% fewer
fatalities at roundabouts than at traffic
intersections, including signaled ones.
• Roundabouts are slow (capacity per lane =
1200 vs. 1900 vph ) and cause much traffic
congestion during rush hours
• Traffic signals also cause congestion…
obviously
• IS THERE A BETTER WAY?
4. Saturated traffic flow from a resting state
is a rarefaction wave.
Flow rate (vehicles passing per unit time) = vehicular
density (vehicles per unit length) x “sound speed”
(length traveled per unit time(
=one vehicle per human reaction time
Saturated traffic flow rate [velocity/distance between
cars] through unsignalled, unconflicted intersection is
also one vehicle per human “reaction time”
]because distance ~ velocity x reaction time[ .
5. But reaction time to acceleration from rest is slower than
reaction to braking. So in saturated traffic flow vehicles can
flow into the back end of a traffic jam faster than they can
flow out the front. This is why the jam persists long after the
cause has disappeared (phantom jams) . Saturated traffic
flow at much more than 2200 vph is observed to be unstable
to jamming.
Jamming observed even on conflict free race tracks!
6. So there is a cost for stopping and
starting.
Eliminating traffic conflict at road
intersections would avoid stopping, and this
increases intersection capacity.
7. II. Conflict – free intersections
)or zero traffic conflict (ZTC) intersections(
Definition: a turning movement is an ordered pair of directions (legs
stemming from an intersection(
e.g. NS, SN, SE, etc.
Definition: A maximal ZTC road intersection is one in which no
additional turning movement can be added while keeping the other
with zero conflict.
A “sidewalk” turn can never conflict with any other turning
movement.
8. We assume two lanes per leg, with merging, but in reality,
more lanes could be added. This assumption is equivalent to
insisting that there are no disconnected lanes in the same
direction, e.g.
We do not assume the driving must be all on
right or all on left.
9. We wish to classify all conflict-free intersections.
Classification via number of sidewalk turns proves
useful.
11. The familiar four conflict-free intersections permitted by Israeli
traffic signals.
M M
M M
All maximal conflict-free 4
way intersections with 4 right
sidewalk turns
12. 3b. 3c. 3d.
3e.
3a.
M
Note that 3a,c,d,e are not maximal conflict-free
intersections because additional turning
movements can be added without blocking
existing ones.
Lemma: In fact, any adjacent legs that are both
1-way would allow additional turning
movement with one change, so it cannot be
maximal ZTC intersection. (HBG(
13. 3b. 3c. 3d.
3e.
3a.
M
Note that 3a,c,d,e are not maximal conflict free
intersection because additional turning
movements can be added without blocking
existing ones.
Lemma: In fact, any adjacent legs that are both
1-way legs would allow additional turning
movement with one directional change, so it
cannot be maximal ZTC intersection. (HbG(
14. lemma: There are no 4-way ZTC
intersections with 3 sidewalk turns in the
same direction and 1 in the opposite
direction [e.g. 3 right and 1 left sidewalk
turn] (HbG). The legs on both sides of the opposite
direction sidewalk turn are one-way, and therefore by
Lemma the resulting designs cannot be maximal ZTC.
(See Fig. 3c, 3d & 3e for illustration(.
15. 12c.
12d.
12b.
b.
12a.
c. e. f.
12e. 12f
additional maximal connected zero-traffic-conflict four-leg
intersection designs.
3
STMs
3
STMs
3
STMs
3
STMs
2R +2L
STMs
2R +2L
STMs
M
M
MM
12d
16. Theorem: There are no other maximal 4-way
conflict-free intersections (than the above 9) to
within obvious symmetries (HbG(.
Proof: There are no others with 4 right sidewalk turns
…with 2 right and 2 left
sidewalk turns
….with 2 of one and only 1 of the other
….with only 2 or 1 total sidewalk turns
17. III. Can we use this set of conflict-free
intersections to build an efficient conflict-
free traffic network?
Note Braess’s paradox: Reducing freedom to
pursue individual interests is sometimes in
everyone’s interest.
26. How do these compare with simply
eliminating left turns (which would lessen, but
not eliminate, the need for traffic signals(?
Note: the calculations below are for uniformly
distributed origins and destinations.
27. Table 1: average additional distance for 10 by 10 nodes
grid designs. )Average rectilinear distances are 6.00
blocks under CBP )center-of-block parking( and 6.04
under SP )street parking).)
U turn
Park Acc Unrestricted NoLeft OneWay Target LC1 LC2
PU SP NLAD 1.26 3.49 2.22 3.32 4.59 3.67
PU SP FAD 0.05 0.96 2.22 2.12 2.74 2.76
PU CBP NLAD 0.20 1.80 0.58 1.63 2.84 1.79
PU CBP FAD 0.16 0.16 0.58 1.39 1.61 1.71
AU SP NLAD 1.02 1.75 2.22 2.58 3.10 3.12
AU SP FAD 0.05 0.96 2.22 2.09 2.49 2.73
AU CBP NLAD 0.20 1.48 0.58 1.51 2.05 1.73
AU CBP FAD 0.16 0.16 0.58 1.39 1.58 1.68
Street
parking
Central
block
Prohibited
U turn
Allowed U
turn
28. Table 2: average additional distance for 10 by 20 nodes grid designs.
)Average rectilinear distances are 9.33 blocks under CBP )center-of-block
parking( and 9.37 under SP )street parking.)
U turn Park Acc Unrestricted NoLeft OneWay LC3 LC4
PU SP NLAD 1.19 3.56 2.17 5.50 4.23
PU SP FAD 0.04 0.97 2.17 3.80 2.50
PU CBP NLAD 0.15 1.85 0.58 3.73 2.44
PU CBP FAD 0.13 0.13 0.58 2.77 1.67
AU SP NLAD 1.02 1.78 2.17 4.24 3.07
AU SP FAD 0.04 0.97 2.17 3.62 2.41
AU CBP NLAD 0.15 1.59 0.58 3.16 2.19
AU CBP FAD 0.13 0.13 0.58 2.76 1.66
Street Parking
Central block
parking
LC4 always beats LC3
29. Table 3: average additional distance for 20 by 20 nodes grid designs. )Average rectilinear distances are 12.67 blocks under CBP and 12.69 under SP
U turn
Park Acc Unrestricted NoLeft OneWay Target
PU SP NLAD 1.13 3.63 2.11 4.63
PU SP FAD 0.03 0.98 2.11 3.48
PU CBP NLAD 0.10 1.90 0.56 2.85
PU CBP FAD 0.09 0.09 0.56 2.74
AU SP NLAD 1.01 1.81 2.11 3.96
AU SP FAD 0.03 0.98 2.11 3.46
AU CBP NLAD 0.10 1.72 0.56 2.80
AU CBP FAD 0.09 0.09 0.56 2.74
30. Features in data:
The most important factor in increased
distance cost of conflict elimination is getting
a bad start. Street parking vs. center-of-block
parking makes a larger difference than U-
turn option, lane access or even network
design.
Relative cost of conflict elimination should
decline with length of trip.
31. 0 2 4 6 8 10 12 14 16 18
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Unrestricted
NoLeft
OneWay
Target
LC1
LC2
Rectilinear distance
Averageadditionaldistance(blocks)
Figure 11: Average additional distance as a function of the rectilinear OD distance for 10 by 10 nodes network assuming street-parking
nearest-lane-access-direction with prohibited-U-turns )SP/NLAD/PU(. Reference designs are: unrestricted, one-way and no-left turn; proposed
low-conflict designs are: Target, LC1 and LC2.
10x 10 SP NLAD Prohibited U turns
36. Relative cost (percentage of increased trip
length) of conflict elimination decreases with
size of city, whereas cost of traffic signals
does not.
Conjecture: for large cities, conflicting
traffic flow and attendant traffic signals
increase travel time.
37. What about pedestrians?
Vortexes should allow much easier design of
green waves. Pedestrian crossing time much less
than typical waiting time. Green wave can be
~85% of vortex length. This should make it
much easier to stay on one.
3D infrastructure for pedestrians – e.g. bridges,
tunnels – far cheaper than for vehicles.
117. Is there an algorithm for determining the
best conflict-free routing scheme for a
given town?
So far, the algorithms we try are not as good as our
imagination.
118. Note any game where the “players” are intersections,
each trying to reduce its own waiting time, encourages
equality, and this is not what is desired.
e.g. signaled intersections are typically designed to
favor the longer queue - i.e. equalize waiting time
between crossing options - on the grounds that total
waiting time at that intersection is thereby reduced.
(Let the few wait for the many, don’t have the many
waiting for the few.) But, by encouraging equality
between conflicting traffic streams, it encourages traffic
conflict, because each traveler has less of a reason to
favor one route over another. Need strong central
authority that reduces personal options.
119. So the following alternative strategy was
tried: Discourage equality, reduce options.
Eliminate the crossing option with the
lower demand.
But it doesn’t work as well as guessing.
Brute force would require at least O(9n2
(
But invoking 4-fold symmetry, on 9
x 9 town (=64 blocks), choosing
vortex sign for each block, reduces
total number of choices to ~ 94
216-4
123. Concluding remarks:
Cities don’t need traffic signals, except
possibly for pedestrians.
Travel time would probably be reduced
with conflict-free routing.
Optimizing solution an unsolved
problem, but not hopeless.
