lec 10_traffic stream models2
TRANSCRIPT
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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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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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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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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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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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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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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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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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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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Space vs. Time Mean Speed
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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Space vs. Time Mean Speed
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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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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Space Headway (s)
The distance between the front of a
vehicle and the front of the following
vehicle (ft)
(s)
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Gap
The distance between the back of a
vehicle and the front of the following
vehicle (ft)
(d)
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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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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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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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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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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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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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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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0
0 q m
um
uf
speed(mph)
F l o w ( v e h / h r )
UncongestedFlow
Congested
Flow
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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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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