Traffic Flow FundamentalsIntroduction

Traffic flow is usually classified as eithera. Uninterrupted Flowb. Interrupted Flow

TYPES OF FLOW

A. UNINTERRUPTED FLOW

- flow occurring at long sections of road where vehicles are not

required to stop by any cause external to the traffic stream

B. INTERRUPTED FLOW

-flow occurring at long sections of road where vehicles are required to stop by

any cause outside the traffic stream such as traffic signs, traffic signal lights

Uninterrupted Flow can be described

using any of the following traffic

variables:

a. Flow rate or volume

b. Speed

c. Density or Concentration

UNINTERRUPTED FLOW

A. FLOW RATE OR VOLUME

- number of vehicles passing a point during a specified period of time

- may be expressed as:

where q=flow rate in vehicles/min or vehicles/day =volume in vehicles/hrN=no. of vehiclesT=observation period

EXAMPLESuppose a 15 minute count of vehicles bound for Manila was conducted at a particular location on Quezon Avenue. A summary is shown in the table below.

TYPE 15-MINUTE COUNTCar/van 420

Jeepney 300

Bus 16

Truck 28

The total number of vehicles counted in 15 minutes is 764. Therefore, the flow rate is q = 764 x 4 = 3056 vehicles per hour.

B. SPEED-rate of motion in distance

per unit time

Time Mean Speed

Space Mean Speed

Time Mean Speed

Also known as spot speed, time mean speed is the arithmetic mean of the speeds of vehicles passing a point within a given interval of time and is given by

where uᵢ=speed of vehicle i, in kph Δx=trap length, in meters

tᵢ=time It takes to traverse trap length, in seconds

where =individual speed of vehicles observed within time, T

n=no. of measured vehicles

EXAMPLEThe speeds of 25 cars were observed. 10 cars were noted to travel

at 35kph, 8 cars at 40 kph, 2 cars at 50kph, and 5 cars at 45kph.

Assuming that each car was traveling at constant speed, determine

the time mean speed.

Using ,

= 39.8 kph

Space Mean Speed

Also known as harmonic mean speed is the rate of movement of a traffic stream within a given section of road

where uᵢ=speed of vehicle i, in kph =individual speed of vehicles observed within time, T n=no. of measured vehicles

EXAMPLEThe speeds of 25 cars were observed. 10 cars were noted to travel

at 35kph, 8 cars at 40 kph, 2 cars at 50kph, and 5 cars at 45kph.

Assuming that each car was traveling at constant speed, determine

the space mean speed.

Using ,

= 39.26 kph

-number of vehicles in a given length of road at an

instant point in time

where

k = traffic density in vehicles per unit distance,

n = number of vehicles occupying some length of

roadway at some specified time, and

l = length of roadway.

C. DENSITY

OTHER TRAFFIC VARIABLES

Other variables used to described traffic

flow are simply variants of the previous

variables.

a. Time Headway

b. Spacing

c. Time Occupancy

Time interval between passage of consecutive vehicles at a specified point on the road with a unit of time per vehicle and is given as

The average time headway and flow rate are related as follows

TIME HEADWAY

EXAMPLEDuring morning peak hour, the average headway of UP-Katipunan jeepneys is estimated at 5 minutes. If the passenger demand during the same period is 240, determine whether there is a need to increase he number of jeepney units (or shorten the headway) for this route. Assume that passenger demand is evenly distributed within that period and the average load/occupancy is 14 passengers per jeepney.

Using , the number of jeepneys per hour is 12 jeepneys per hour.With 14 passengers per jeepney, the total number of passengers per jeepney that can take a ride is 168 passengers.Since the demand during morning peak hour is 240 passengers, it can be said that there is a need to increase the number of jeepney units during peak period.

SPACINGDistance between two vehicles measured from the front bumper of the vehicle to that of another and is computed as the inverse of density

EXAMPLEDuring heavy traffic congestion, it was observed that the average

spacing of vehicles in queue in the innermost lane in EDSA is 6.5m.

Determine the jam density or density of stopped vehicles.

Using ,

The jam density is 153.85 vehicles/km

TIME OCCUPANCY

-a useful measure of traffic flow which can only be measured if a detector is installed at a specific point on a carriageway and is define as the total time a detector is occupied divided by the total time of observation-is given by

where =the detection time of the vehicle

A relationship exists among the three most

important traffic variables: flow rate, space

mean speed and density.

a. Observed Relations

b. Empirical Relations

RELATIONSHIP OF FLOW, SPEED AND DENSITY

A. OBSERVED RELATIONS

Speed-Density Relation

Volume-Density Relation

Speed-Volume Relation

B. EMPIRICAL RELATIONS

Speed-density relation

Volume-density relation

Volume-speed relation

SPEED-DENSITY RELATION

The linear relationship shows that

as density increases, speed

decreases.

The equation of the line gives

Greenshields’ model,

Where =free flow speed

=jam density

VOLUME-DENSITY RELATIONSHIP

SPEED-FLOW RELATIONSHIPS