lec 10_traffic stream models2

8/6/2019 Lec 10_traffic Stream Models2

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Dr. Lina Shbeeb 1

Traffic stream flow models

Transportation engineering


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Dr. Lina Shbeeb 2

Traffic stream flow models

When we analyse traffic flow we are concern with theinteraction between different vehicles in the traffic stream

Traffic condition varies from almost free flow (relativelyfew vehicles are occupying the roadway to highlycongested conditions( roadway is jammed with slowvehicles)

The determinant of traffic flow models is the car-followingrule adopted by drivers in an attempt to maximize theirspeed while maintaining an acceptable level of safety.

Basic variables that describe the prevailing conditionwithin traffic stream are Traffic flow Traffic concentration Traffic speed


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Dr. Lina Shbeeb 3

Notation used in relationship among speed,

spacing and acceleration

V= initial speed of the two vehicles

dl= deceleration rate of the leading vehicle

df= deceleration rate of the following vehicle

=perception reaction time

x= safety margin after stop

L=length of vehicle

N= number of vehicle in train (N=1 for cars


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Dr. Lina Shbeeb 4

Vehicle flowing concepts

2 1

v

Direction of travel

L Spacing S

2 1 2 1

L

v

v

=perception reaction time

v2

2df x

v2

2dl


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Dr. Lina Shbeeb 5

Vehicular stream models

The braking distance of the leading vehicle is

If the perception reaction time and braking distance of the following vehicle is

included, then the total distance covered by the following vehicle is

In terms of the initial spacing, length of vehicle and safety margin andxl

By equating the last two equations, the spacing is estimated by

l

l

dvx2

2

=

f

f

d

v

vx 2

2

+=

olfxNLxsx +=

+++= xNLd

v

d

vvs

lf22

22


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Dr. Lina Shbeeb 6

Traffic flow types

Uninterrupted flow (Freeway) Interrupted flow (Arterials with traffic light signal) Vehicles in uninterrupted flow conditions are spaced so to provide

ample time and distance for a following vehicle to perceive andreact to decelerate safely without colliding with a leading vehicle thatsuddenly decelerate and stop.

The choice of the spacing between vehicle as shown in the nextslide is function of the deceleration that took place.

There are three values of deceleration that are relevant to theoperations safety level d

n= normal or comfortable deceleration (safest condition operation)

de= emergency deceleration (low level of safety if the spacing is

selected so that the following vehicle need to apply emergency braking)

= instantaneous or stonewall stop Combination of leading-following vehicle deceleration are give inTable 3.2.1 and their relation to the spacing versus speed are givenin Figure 3.2.2


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Dr. Lina Shbeeb 7


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Dr. Lina Shbeeb 8

Stream variables Flow (q)

The equivalent hourly rate at which vehicles pass a pointon a highway during a time period less than 1 hour

q = (n x 3600)T

Where;

n=# of vehicles passing a point in T seconds

q=equivalent hourly flow rate (veh/hour)

Density (k) veh/mi

The number of vehicles traveling over a unit length (usually

1 mile) of a highway at an instant in time Speed, u (mph or fps): Distance traveled by a vehicle

during a unit of time. Speed at anytime tis the slope of thetime-space diagram


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Dr. Lina Shbeeb 9

Density (k)

Concentration

Number of vehicles traveling

over a unit length of highway

at an instant in time

Usually veh/mile or vpmpl

Example: 4 vehicles over 600 feet of roadway

Over a mile

k = 4 veh. x 5280 feet = 35.2 veh/mi

600 ft mile


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Dr. Lina Shbeeb 10

Speed (u)

Time mean speed ( )Arithmetic mean of the speeds of vehicles

passing a point on a highway during an

interval of time (radar gun or road tube study)

tu

=

=n

iit

u

n

u1

1

Where;

n = # of vehicles

ui= speed (ft/sec or mi/hr)


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Dr. Lina Shbeeb 11

Speed (u)

Space mean speed ( )Harmonic mean of the speeds of vehicles passing

a point on a highway during an interval of time

(total distance traveled by 2 or more vehicles divedby time required to travel that distance)

su

=

=n

i

i

s

t

nLu

1

Where;

n = # of vehicles

ti= time to cross section of highway (sec)

L=length (ft)

(ft/sec)


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Dr. Lina Shbeeb 12

Space vs. Time Mean Speed

Example

For a 500-foot section, the following were measuredVehicle Measured Time to Travel 500 ft

(sec)Measured Velocity (mph)

1 6.0 63

2 6.5 583 5.3 60

4 5.8 65

5 5.9 64

6 6.1 61

7 5.7 66

8 5.2 72

9 5.5 68

10 5.4 69


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Dr. Lina Shbeeb 13


Example

Calculate time mean speed and space mean

speed.

==n

iit unu 1

1

ut = 63+58+60+65+64+61+66+72+68+69 = 64.5 mph

10


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Dr. Lina Shbeeb 14


Example

Calculate space mean speed.

us = (500 ft) ( 10 ) = 85.61ft/sec=58.4 mph

6.0+6.5+6.3+5.8+5.9+6.1+5.7+5.2+5.5+5.4

us < ut (always)

==

n

ii

s

t

nLu

1


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Dr. Lina Shbeeb 15

Time Headway (h)

The difference between the time the front of a

vehicle crosses a point on the highway and the time

the front of the next vehicle crosses the same point

(seconds)

t1

t2

h = t2 t1


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Dr. Lina Shbeeb 16

Space Headway (s)

The distance between the front of a

vehicle and the front of the following

vehicle (ft)

(s)


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Dr. Lina Shbeeb 17

Gap

The distance between the back of a

vehicle and the front of the following

vehicle (ft)

(d)


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Dr. Lina Shbeeb 18

Line A-A:Stationary

observers

whose location

does not

change with

time

Line B-B: Arial photograph of the

stream at a given instant


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Dr. Lina Shbeeb 19

Flow-Density Relationships

q = k us

us= q s

s = 1/k

k = q t

h = t s

q = flow

k = density

us= Space mean speed

s = Average space headway

h = Average time headway

t = Avg. travel time for unit distance


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Dr. Lina Shbeeb 20

Flow-Density Example

If the spacing between vehicles is 500 feet what is thedensity?

s = 1/k k = 1/s = 1 veh/500 feet

= 0.002 vehicles/foot = 10.6 veh/mile

If the space mean speed is 45.6 mph, what is the flow rate?

q = kus= (10.6 veh/mile)(45.6 mph) = 481.5 veh/hr


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Dr. Lina Shbeeb 21

Traffic Flow Diagrams

Explains the relationship between density(k), flow (q), and speed (u)

Density is the number of vehiclesphysically occupying the roadway, flow isvehicles moving past a point per unit time

So a number of vehicles can occupy the

roadway and have a low flow rate


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Dr. Lina Shbeeb 22

Greenshield Linear Model

km

s

peed(mph)

C o n c e n t r a t i o n ( v e h / m i )

kj

0

0

um

uf

=

j

f

kkuu 1


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Dr. Lina Shbeeb 23

Greenshields Linear Model

Continued

km

kj

Flow

(veh/hr)

0

qm

0

C o n c e n t r a t i o n ( v e h / m i )


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Dr. Lina Shbeeb 24

Greenshields Linear Model

Continued

k m k j

Flow

(veh/hr)

0

qm

0C o n c e n t r a t i o n ( v e h / m i )

Conges

ted

flow

Uncong

ested

flow


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Dr. Lina Shbeeb 25

0

0 q m

um

uf

speed(mph)

F l o w ( v e h / h r )

UncongestedFlow

Congested

Flow


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Dr. Lina Shbeeb 26

General rule

Car following rule: Traffic experts suggest

that keeping a distance of one car length

for each 10mph increment of speed. This

result distance is the safe gap that shouldbe at least provided between vehicles


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Dr. Lina Shbeeb 27

Example A driver that follow the car following rule. The car length

he/she uses is 15 ft. develop the equations of stream flow. Solution:

The safe spacing is function of speed to determine the

length of the gap plus the car length.

u

xq

bewillqthenkofinsteaduuseweIf

kukq

kukus

k

vehmiu

Lu

Ls

+=

==

+==+

==

=+=

+=

10

3500103500

103500

10350010

35001

/5280

5.115

10

lec 10_traffic stream models2

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