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Copyright ©2018 by Paul Niquette. All rights reserved.

Animated Rond-Point
Representation of European Roundabout (Rond-Point in French)
with cars giving way and signaling, by Mintguy / Fredrik
Built in 1930. the Los Alamitos Circle was first seen eighty years ago by your puzzle-master, whose father explained its technical features.  He expressed admiration for the invention, which obviated traffic signals and assured safe, continuous flow of vehicles merging and diverging.  "Some day," he told his son, "all intersections will be circles."  That prediction has come true -- at least where your puzzle-master lives:  Half of the world's roundabouts are located in France, and the name here is Rond-Point.

rpiCompared to a typical intersection with either boulevard stop signs or traffic signals, the Rond-Point offers many benefits, including…

1.     Reduced likelihood and severity of collisions
2.     Elimination of queuing associated with traffic lights
3.     Giving way on entry generally obviates the need for full stops
4.     Reduced pollution from engine emissions attributable to idling time
5.     Preservation of vehicle momentum requiring less energy for acceleration
6.     Reduction of sound levels from braking and engine noise in accelerations
7.     Preventing driver confusion associated with perpendicular junctions
8.     Allowing U-turns and exit-retries within the normal flow of traffic
9.     Improved accommodation for pedestrians
Safety (Item 1 in the list above) holds primacy: Reducing the likelihood and severity of collisions must be the principal justification for the immense investments being made by the French to replace intersections with Rond-Points. 

Sophisticated solvers might not be surprised to learn that 50% of all vehicle crashes worldwide occur at intersections.  Here's how that estimate was reached...

A simple search on YouTube for “vehicle collisions” produces hundreds of video compilations taken by dashcam.  In preparing the Rond-Point puzzle, I watched 10 videos wherein 270 crashes appeared.  A total of 147 occurred at intersections (54%).  The remaining 123 crashes (46%) occurred on roads or highways; they featured all kinds of spin-outs, over-speeding, rear-ends and others.

Fig 1Figure 1 is a sketch of a signalized intersection with left-turn 'pocket' lanes.  Here is shown only straight-through flow with no turns depicted. 

Only Wi-Wo and Ei-Eo are authorized to move through the intersection by green signals, while vehicles at Si and Ni are held out of the intersection by their respective red signals. 

There are four potential collision points, but they are 'accessible' only if a vehicle on Si-So or Ni-No violates the red signal.

Crash videos showed that happening a lot!


Fig 2Figure 2 is a sketch of the same signalized intersection, this time with all allowable turns depicted.  

We see two potential collision points.  One is between Wi-Wo colliding with the left-turning Ei-No; the
other is between Ei-Eo colliding with the left-turning Wi-So -- both authorized by green signals.

The driver of a left-turning vehicle must yield right-of-way to the straight-through vehicle, which often calls for stopping in the middle of the intersection. 

As many as half of the intersection crash videos showed left-turn collisions!  

Merging of vehicular flows are shown at four points in Figure 2.  After stopping for the red signal, the right-turning Si-Wo must yield to the straight-through Wi-Wo, then merge; likewise after stopping for the red signal, Ni-Eo must yield to the straight-through Ei-Eo, then merge. 

It may be appropriate to assume that the generally slower,
right-turning Wi-No yields to the generally faster left-turning Ei-No and the right-turning Ei-So yields to the left-turning Wi-So. 

Meanwhile the driver of a left-turning vehicle Ei-No or Wi-So must grant priority first to the near head-on vehicles appearing on the right prior to the potential collision point then apparently that same driver will expect priority to be given by turning vehicles on the right at the merging point. 

Several intersection crash videos showed apparent merging confusions and resulting sideswipes!

Finally, with respect to Item 8 in the list above, a conventional intersection cannot allow a U-turn or a 'retry' for a missed exit within the normal flow of traffic.  Several videos show crashes caused by panicky lane changes -- often followed by sudden right or left turns
at intersections. 

fig 3F
igure 3
depicts a Rond-Point, which is postulated here to replace the intersection shown in Figures 1 and 2 above.

One sees immediately that there are neither traffic signals nor stop signs.  Moreover, there are no locations where traffic lanes actually cross one another to form potential collision points.
Merging of vehicular flows are shown at four points, one for each incoming lane. 

Diverging of vehicular flows can be seen at the four outgoing lanes.  All are utterly benign, inasmuch as neither collisions nor side-swipes can occur where vehicular flows diverge.

Every vehicle entering a Rond-Point (on traffic lanes marked in orange) must yield to vehicles that are already established in the circle (on the circumferential traffic lane marked in green, which signifies 'perpetual right-of-way').  Vehicles on outgoing lanes
(also marked in green) are diverging and thus cannot conflict with vehicles in the circle.

Rules for drivers are elementary: On entry to a Rond-Point, always grant priority to vehicles approaching on the left.  That generally calls for slowing and if necessary stopping outside the circle.  A driver of a vehicle established in the circle only has to maintain safe separation from the vehicle ahead and watch for the appropriate exit.  With respect to Item 8 in the list above, a driver can stay in the circle as necessary to re-access a missed exit or
to make a U-turn

None of the 270 vehicular crashes on the 10 dashcam videos were shown to have occurred at Rond-Points.  They were compilations from the U.S. and Europe along with 142 vehicle crashes in Russia, “Ебена мать!” (“holy shit!”).  So I watched six more videos that showed 131 vehicle crashes only in FranceThe break-down: 7.6% crashes at intersections, 89./3% crashes elsewhere. 

Inasmuch as half the world's roundabouts are rond-points in France, there are simply not all that many intersections available for French vehicles to crash at.  In the six video compilations, there were exactly four crashes at rond-points out of 131 crashes (3.1%).  Two were collisions that occurred at exits actually outside the rond-point, and two were single-car spin-outs inside the rond-point.

rpiCompared to a typical intersection, therefore, the Rond-Point clearly offers advantages in traffic safety as described above.  What about traffic performance
  • From a driver's perspective, performance of a traffic system is judged based on allowable vehicle speed -- faster the better, measured in mi/hr or km/hr.
  • From a traffic engineer's perspective, performance is judged based on flux -- again, faster the better, measured in veh/hr accommodated by the system.
Both speed and flux are limited by density, measured in veh/mi or veh/km, and density is itself a function of both speed and flux. Indeed, speed = flux / density and flux = speed x density.
In the the list above of Rond-Point advantages, Item 3 seems quite promising...
Giving way on entry generally obviates the need for full stops.
...inasmuch as every traffic stop decreases vehicular speed.  Here, then, is our question...

What is the effect of the Rond-Point on vehicular Speed?