Anybody who has been driving in its streets could not deny that Metro Manila is the capital of ‘unplanned’ U-turn slots, thanks or no thanks to former MMDA Chairman Bayani Fernando. Did the installation improve traffic flow? Jay Samuel L. Combinido and May T. Lim of the National Institute of Physics, UP Diliman, may have the answer as they modelled U-turn traffic flow in their latest paper in Physica A .
The authors used an extended Nagel-Schreckenberg (NaSch) model to simulate U-turn traffic. The NaSch model is a cellular automata model which is considered the ‘simplest realistic traffic simulator’. In the extended model for the U-turn used by the author, they transform the lattice, impose lane changing rules, and require a controllable behavioral responses of cars with a single parameter. A complete detail of the simulation protocol can be read in their paper. They calibrated their simulation with empirical data from the C.P. Garcia Avenue and from a U-turn in Katipunan Ave, Quezon City.
By varying the densities of the car reservoir on the U-turn and the exit, they have seen that the flow has two distinct phases – free and congested flow. What does it mean in terms of car flow? When the exit density is zero which means initially there are no cars at the exit (see schematic), there is still congestion at a certain density of car reservoir on the U-turn (critical U-turn density). When the density of the car reservoir on the U-turn is higher than this critical density, there is an increased interaction between the cars leading to congestion even when the density of the exit is zero. Below this critical U-turn density, the cars flow freely. When the exit density is increased, the critical U-turn density value becomes lower, indicating that the flow of the cars is suppressed at the exit and that the flow capacity of the U-turn decreases. Moreover at higher values of the exit density, the shift (decrease) in the critical U-turn density is larger.
Lesson 1: There is a certain region of values of the densities in which U-turns are effective.
They have obtained that flow is higher when there is no lane changing. BUT, lane changing may be advantageous to reduce bottleneck “when cars changed lanes at every opportunity”. Bottlenecks are created when only one lane is allowed to change lanes.
Lesson 2: When in a U-turn, do not change lanes.
How did they know that the model work? Simple, look at the real world situation. At the right is the comparison of the empirical observations with the simulation. The simulation fits well the observation which indicates that the model does work.
Are U-turns effective? The authors have this to say,
“statistical measurements have shown that U-turns provide decreased congestion and increased car flow compared to left-hand turns…BUT at high densities, instead of reducing congestions, U-turns worsen traffic situations.”
 J. S. Combinido and M.T. Lim, Modeling U-turn traffic flow, Physica A 389 (2010) 3640 – 3647. DOI: 10.1016/j.physa.2010.04.009.