Traffic Flow Characteristics

Traffic Flow (q)

Flow is the rate at which vehicles pass a given point on the roadway (reported in veh/hr)

n=number of vehicles passing a point in the roadway in T seconds

q= the equivalent hourly flow, veh/h

Density (k)

Number of vehicles present on a given length of roadway (usually miles or kilometers)

L

Headway

Space Headway or Spacing (d) in m

Spacing Headway

Distance between the front bumper of the leading vehicle and the front bumper of the following vehicle

Headway

Test Point

Time Headway (h) in sec

A

B

A

B

Stop Stopwatch

Start Stopwatch

Now, get the time headway

Time that elapses between the arrival of the leading vehicle and the following vehicle at the designated test point

Mean Speed

Time mean speed

Space mean speed

Distance / average time

Number of vehicles / Summation of inverse of speed

Summation of speeds / number of vehicles

Space mean speed is always lower than the time mean speed

Flow-Density Relationships

700 Veh/km

• How many Kilometers per hour

Test Point

10 km/hr

• How many vehicles in each kilometer

Vehicles move 10 Km/hr

You get 700 veh in each of these Km

Then you get how many vehicles per hour

Then the total number of vehicles per hour is 10*700=7000 veh = 7000/4= 1750 veh/lane

Flow-Density Relationships

Test point

You get one vehicle each h seconds

h = 5 sec

How many you would get in one hour (3600 seconds)

Then q = 3600/5= 720 veh/hr

Flow-Density Relationships

Test point

Spacing Headway= 20 m

q= 1000 veh/hr

You have the distance between vehicles

Find the distance traveled in one hour

1000*20 = 20000 m/hr = 20 km/hr

You have how many vehicles pass a point in one hour

1 km

Flow-Density Relationships

Test point

Speed = 10 km/hr

hr/km

Inverse of speed

q=750 veh/hr

veh/km

Veh/hr

Count vehicles during the time needed to clear the 1 km

Time to travel or clear 1 km = 1/10= 0.10 hr/km = 6 min

How many vehicles would you get at the test point in 6 mins?

750*0.10= 75 veh

Then k= 75 veh/km

Flow-Density Relationships

Distance

Time

Speed

Problem 1

Data obtained from aerial photography showed six vehicles on a 180 m-long section of road. Traffic data collected at the same time indicated an average time headway of 4 sec.

Determine:

The density on the highway

The flow on the road

The space mean speed

Greenshield’s Model

Relationship between speed, density and flow based on observations by Greenshield.

Relationship between speed and density

Greenshield’s Model

Relationship between desntiy and flow.

Free Flow Conditions

Capacity

Forced Flow Conditions

Greenshield’s Model

Relationship between speed and flow.

Free Flow Conditions

Capacity

Forced Flow Conditions

Greenshield’s Model

Mathematical Relationships Describing Traffic Flow

Speed and Desity:

Greenshield’s Model

Mathematical Relationships Describing Traffic Flow

Flow and density:

Flow and speed:

Greensberg’s Model

Mathematical Relationships Describing Traffic Flow

Speed and Desity:

Problem 2

The speed-density relationship for a given road is represented using the following equation:

Determine the flow-density and flow-speed relationship

Evaluate the free-flow speed, jam density, and capacity of the road.

Problem 2

The speed-density relationship for a given road is represented using the following equation:

Determine the flow-density and flow-speed relationship

Evaluate the free-flow speed, jam density, and capacity of the road.

Problem 2

The speed-density relationship for a given road is represented using the following equation:

Determine the flow-density and flow-speed relationship

Evaluate the free-flow speed, jam density, and capacity of the road.

Problem 2

The speed-density relationship for a given road is represented using the following equation:

Determine the flow-density and flow-speed relationship

Evaluate the free-flow speed, jam density, and capacity of the road.

OR

Shockwave Equation

Variables Related to Shockwave Problem:

q = flow

k = density

u = v =speed

Problem 3

The traffic flow on a highway is q1= 2000 veh/hr with speed of v1=80 km/hr. As the result of an accident, the road is blocked. Assume spacing at jammed condition is 3.63 meters.

• What is the wave speed?
• What is the rate at which the queue grows, in units of vehicles per hour (q)?

Given:

Region 1

q1 = 2000 veh/hr

v1 = 80 km/hr

Region 2

d2 = 3.63m

Jammed conditions  v2 = 0 and q2 = 0

Problem 3

The traffic flow on a highway is q1= 2000 veh/hr with speed of v1=80 km/hr. As the result of an accident, the road is blocked. Assume spacing at jammed condition is 3.63 meters.

• What is the wave speed?
• What is the rate at which the queue grows, in units of vehicles per hour (q)?

Problem 3

The traffic flow on a highway is q1= 2000 veh/hr with speed of v1=80 km/hr. As the result of an accident, the road is blocked. Assume spacing at jammed condition is 3.63 meters.

• What is the wave speed?
• What is the rate at which the queue grows, in units of vehicles per hour (q)?

Problem 4

The southbound approach of a signalized intersection carries a flow of 1000 veh/hr/ln at a velocity of 50 km/hr. The duration of the red signal indication for this approach is 15 sec. If the saturation flow is 2000 veh/hr/ln with a density of 75 veh/km, the jam density is 150 veh/km, determine the following:

• The length of the queue at the end of the red phase.
• The backward recovery wave velocity.
• The maximum distance of the end of the queue from the stop line.

Problem 4

The southbound approach of a signalized intersection carries a flow of 1000 veh/hr/ln at a velocity of 50 km/hr. The duration of the red signal indication for this approach is 15 sec. If the saturation flow is 2000 veh/hr/ln with a density of 75 veh/km, the jam density is 150 veh/km, determine the following:

• The length of the queue at the end of the red phase.

Problem 4

The southbound approach of a signalized intersection carries a flow of 1000 veh/hr/ln at a velocity of 50 km/hr. The duration of the red signal indication for this approach is 15 sec. If the saturation flow is 2000 veh/hr/ln with a density of 75 veh/km, the jam density is 150 veh/km, determine the following:

• The backward recovery wave velocity.