Question

A roadworks site is set up on a road carrying a flow of 1200 vehicles per hour at a speed of 60 kilometres per hour. The roadworks restricts the capacity of the road to half of the arrival flow, causing a queue to build up of vehicles that travel at a speed of 10 kilometres per hour. a) Identify the flow and density conditions of the arriving traffic stream, and of the slow-moving queue of vehicles b) Sketch these two traffic conditions on a fundamental diagram (flow-density curve), and identify the shock wave between them. What is the speed of the shock wave, and is it moving forwards or backwards? How long would it take the back of the queue of slow moving vehicles to reach an intersection that is located one kilometre upstream of the roadworks site? c) d)

Answer 1

Given data, A road works site is set up on a road carrying a flow of 1200 vehicles per hour at a speed of 60 kilometers per hour. For arriving Traffic, V = 60 kmph q_A = 1200 vech/per. Therefore Density is given as q_A = > k * v k_A = > 1200/60 = 20 kech/km For slowing moving sequence q_0 as flow = > 1200/2 = > 600 vech/ht. & V = > 10 kmph q = kv k_B = > 600/10 = 60 km/hr shock wave-slow-density curve. \r\n W_AB = q_A - q_B/k_A - k_B = > speed of shock wave. = > 1200 - 600/20 - 60 = > 600/-40 = > -15 kph - > Backward The shock is moving Backward. velocity of slow moving vehicles = > 10 kmph velocity of shock wave = > 15 kmph Therefore time taken = > d/v = 1/15 = 0.066 hr = 239 second = 3.9 mms.