In a single lane road, traffic volume of 1000 vehicle/h moving at 20 km/h, comes to a halt due to an accident. If jam density is 150 vehicle/km

Q. In a single lane road, traffic volume of 1000 vehicle/h moving at 20 km/h, comes to a halt due to an accident. If jam density is 150 vehicle/km, the velocity of the shock wave generated (in absolute value) is_____________km/h.

1. 200
2. 100
3. 1000
4. 500

Ans: 100

Solution:

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.

Where,

vsw = propagation velocity of shock wave (miles/hour)

qb = flow prior to jam (vehicles/hour)

qa = flow after jam (vehicles/hour)

kb = traffic density prior to jam (vehicles/mile)

ka = traffic density after the jam (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.

Now, qb = 1000 V/h and qa = 0 (Because V= 0)

Velocity of the shock-wave =(0-1000)/(150-50)=-1000/100=-100