traffic flow distance-time diagram and shockwaves lecture 14 ce 2710 norman w. garrick
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Traffic Flow Distance-time Diagram and Shockwaves Lecture 14 CE 2710 Norman W. Garrick . Distance. Slope = speed. s. h. Fix Position. Time. Fix Point in Time. Time-Distance Diagrams of Traffic Flow. Vehicle 1 u 1 = 50 mph (constant). Vehicle 2 u 2 = 30 mph (constant). - PowerPoint PPT PresentationTRANSCRIPT
Traffic Flow Distance-time Diagram and Shockwaves
Lecture 14CE 2710
Norman W. Garrick
Norman W. Garrick
Time-Distance Diagrams of Traffic Flow
Vehicle 2u2 = 30 mph (constant)
Vehicle 1u1 = 50 mph (constant)
Distance
TimeFix Point in Time
Slope = speeds
h
Fix Position
Norman W. Garrick
Time-Distance Diagrams of Traffic Flow
Distance
Time
Norman W. Garrick
Time-Distance DiagramsActual Traffic Flow
Ref: Papacostas and Prevedouros
Norman W. Garrick
Shock Waves
A shock wave occur when there is a change in the travel condition on the roadway that affect the stream flow.
For example, a shock wave occur when drivers slow down to look at an accident (rubberneck) - this can cause a traffic jam that is seemingly more dramatic than one would expect given the nature of the act that caused it.
Shock waves can be associated with a particular vehicle in the stream slowing down or stopping
A shock wave is also associated with the traffic pressure being released and a traffic jam dissipating
Norman W. Garrick
Example of a Shock WaveAt a Stop
Traffic is flowing normalFlow, q = 500 veh/hr Conc, k = 10 veh/mi
T = t1 sec
Norman W. Garrick
Example of a Shock WaveAt a Stop
T = t2 sec
Flagman stops first vehicle in the queue
Shockwave
Norman W. Garrick
Example of a Shock WaveAt a Stop
T = t3 secMore vehicles have joined the queue
The shockwave have moved backwards
Shockwave 1
On either side of the shockwave there are two different state of flow
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Example of a Shock WaveAt a Stop
T = t4 secFlagman releases queue
Shockwave 1
There is now a second shockwave and a third state of flow - the flow state for traffic released from the queue
Shockwave 2
State 3q = 1000 veh/hrk = 110 veh/mi
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Distance-Time Diagram for Shock Wave
Distance
Time
XShockwave 1
Shockwave 2
Norman W. Garrick
Calculation of Shockwave Travel
The speed of the shockwave can be calculated using the above equation
The sign is important so remember to number the travel states from upstream to downstream
If the sign is +ve it means that the shockwave is moving downstream
usw = (q2-q1) / (k2-k1)
Shockwave 1
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Calculation of Shockwave Travel
Shockwave 1
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Speed of Shockwaveusw1 = (q2-q1) / (k2-k1)
(0-500) / (260-10) = - 2 mph
Shockwave 1 is moving upstream at 2 mph
What is the length of the queue after 3 minutesLength = u*t = 2 mph * 3/60 hr = 0.1 mile
How many vehicles are in the queue after 3 minutesno. of vehicles = k * L = 260 *0.1 = 26 vehicles
Norman W. Garrick
Calculation of Shockwave Travel
Speed of shockwave 2
usw2 = (q3-q2) / (k3-k2)(1000-0) / (110-260) = - 6.67 mph
Shockwave 2 is moving upstream at 6.67 mph
Shockwave 1 Shockwave 2
State 3q = 1000 veh/hrk = 110 veh/mi
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Calculation of Shockwave Travel
How long will it take to clear the queue if the flagman held the queue for 3 minutes
Length after 3 minutes = u*t = 2 mph * 3/60 hr = 0.1 mile
usw1 = - 2 mph usw2 = - 6.67 mph
Therefore the queue will dissipate at rate of 4.67 mphTime to dissipate a 0.1 mile queue is L/speed0.1 mile / 4.67 mph = 0.021 hr = 12.6 minutes
Shockwave 1 Shockwave 2
State 3q = 1000 veh/hrk = 110 veh/mi
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi