Atasco de tráfico: onda expansiva

lectura en 2 min.

Si te interesa la gestión y simulación del tráfico, verás que este video es realmente interesante. Unos investigadores de Japón realizaron un experimento con vehículos reales, para demostrar las razones por las que en ocasiones se originan atascos en las carreteras, y como sus consecuencias se propagan como una onda expansiva y se mantienen durante horas incluso (New Journal of Physics: Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam).

El experimento consistió en hacer circular a 22 conductores que debían mantener una velocidad constante de 30 km/h. Al principio de la experiencia, todo parece ir correctamente, pero cuando la distancia con el vehículo anterior disminuye, el posterior reduce su velocidad, éste reduce su distancia con el siguiente, y así sucesivamente. Llegados a un umbral crítico, se comienzan a crear embotellamientos, y este problema se sucede como una onda expansiva hacia el resto de vehículos.

En ocasiones en las carreteras sufrimos los efectos de esta onda, aunque aparentemente no han habido accidentes en la carretera e incluso horas después de haberse originado. Si te parece interesante puedes jugar con este simulador de tráfico. También puedes leer los artículos sobre simulación del tráfico en esta web (simulación del tráfico I y II).

Shock waves

Shock waves that occur in traffic flow are very similar to the waves produced by dropping stones in water. A shock wave propagates along a line of vehicles in response to changing conditions at the front of the line. Shock waves can be generated by collisions, sudden increases in speed caused by entering free flow conditions, or by a number of other means. Basically, a shock wave exists whenever the traffic conditions change.

The equation that is used to estimate the propagation velocity of shock waves is given below.

vsw = (qb – qa)/(kb – ka)

Where
vsw = propagation velocity of shock wave (miles/hour)
qb = flow prior to change in conditions (vehicles/hour)
qa = flow after change in conditions (vehicles/hour)
kb = traffic density prior to change in conditions (vehicles/mile)
ka = traffic density after change in conditions (vehicles/mile)

Note the magnitude and direction of the shock wave.

(+) Shock wave is travelling in same direction as traffic stream.
(-) Shock wave is traveling upstream or against the traffic stream.

For example, let’s assume that an accident has occurred and that the flow after the accident is reduced to zero. Initially, the flow was several vehicles per hour. Also, the density is much greater after the accident. Substituting these values into the shock wave equation yields a negative (-) propagation velocity. This means that the shock wave is traveling against the traffic. If you could look down on this accident, you would see a wave front, at which vehicles began to slow from their initial speed, passing from vehicle to vehicle back up the traffic stream. The first car would notice the accident first, followed an instant later by the second car. Each vehicle begins slowing after its driver recognizes that the preceding vehicle is slowing.

Applet en java sobre el modelo de onda de choque circular.

Referencias:

  1. M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Jpn. J. Ind. Appl. Math. 11, 203 (1994).
  2. M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, Phys. Rev. E 51, 1035 (1995).
  3. T. S. Komatsu, S. Sasa, Phys. Rev. E 52 5574 (1995).