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Yraffic Flow Characerisics
1
Traffic Streams
2
 Traffic streams are made up of individual drivers and
vehicles, interacting in unique ways with each other and
with elements of the roadway and general environment.
Because the judgments and abilities of individual drivers
come into play, vehicles in the traffic stream do not and
cannot behave uniformly.
Further, no two similar traffic streams will behave alike,
even under equivalent circumstances, as driver behavior
varies with local characteristics and driving habits.
Traffic streams, however, can be described in quantitative
terms with the use of some key parameters like volume,
speed and density.
Traffic Streams
 Traffic facilities are broadly separated into two principal
categories:
1. Uninterrupted flow facilities, and
2. Interrupted flow facilities
 Uninterrupted Flow Facilities are those on which no
external factors cause periodic interruption to the traffic
stream. Example: Freeway
 Interrupted Flow Facilities are those having external
devices that periodically interrupt traffic flow. Example:
Urban Roadways.
The principal devices creating interrupted flow are
primarily traffic signal and also STOPand YIELD signs, etc.
Traffic Streams
4
Uninterrupted and Interrupted Flow are terms
that describe the facility and not the quality of
flow.
A congested freeway where traffic is almost
coming to a halt is still classified as
uninterrupted 単ow facility, because the reason
for congestion is internal to the traPic stream.
Awell-timed signaling system on an arterial may
result in almost uninterrupted traffic flow, but
still is classified as interrupted flow facility.
Traffic Stream Parameters
5
TraPic Stream Parameters fall into two
broad categories:
Nacrozcopic parameters, and
Nicrozcopicparameterz.
Macroscopicparameters characterizethe
traPic stream as a whole
Microscopic parameterscharacterizethe
behavior of individual vehicles in the
traPic stream with respect to each other.
Traffic Stream Parameters
6
Macroscopicflow
traffic in the aggregate.
overall speeds, traffic flows, densities,
etc.
Microscopic flow
 traffic at the level of the individual vehicle
 observe the paiticular behaviors of drivers,
and of individual vehicles in the traffic
stream.
 vehicle headways & lane-chan9ing behavior
(merging, diverging, weaving, passing, etc.)
critical 0 microscopic level.
Traffic Strea Pa meters
7
A traPic stream may be described
macroscopically by three parameters:
1. Volume or Rate of Flow
2. Speed
3. Density
Traffic Strea
8
Pa meters
Volume and Flow
Pa/wme is defined as the number of vehicles
that pass a point on a highway, or a given lane
or direction of a highway, during a specified time
interval.
 Usually expressed as vehicles per unit time, for
example, vehicles per hour or vph.
Aate a///owis the equivalent hourly rate at
which vehicles pass a point on a highway lane
during a time period less than 1 hour.
Traffic Stream Parameters
9
Volume and Rate of Flow are two
diPerent measures.
Volume is the actual number of vehicles
observed or predicted to be passing a
point during a given time interval.
Rate of flow represents the number of
vehicles passing a point during a time
interval less than 1 hour, but expressed
as an equivalent hourly rate.
Traffic Stream Parameters
10
Avolume of 200 vehicles observed
in a 10-minute period implies a rate
of flow of (200 x 60)/10 = 1200
veh/hr.
Note that 1200 vehicles do not pass
the point of observation during the
study hour, but they do pass the
point at that rate for 10 minutes.
Traffic Strea Pa meters
11
 . The maximum number of vehicles per
unit time that a particular
transportation facility may accommodate
(veh/h).
Traffic Strea
12
Pa meters
Acommon time interval for volumes is a
day.
Daily volumes are frequently used as the
basis for highway planningand general
observations of trends.
TraPic volume projections are often
based on measured daily volumes.
Traffic Stream Parameters
13
Dai"ly Volumes and Their Uae (ontd..)
 There are four commonly used daily volume parameters:
Average AnnualDaily Traffic (AADT): is the average 24-hr
traffic volume at a given location over a full 365-day year.
Average Annual Weekday Tracce {AAWT): is the average
24-hr traffic volume occurring on weekdays over afull
365-day year.
3
. AverageDai/y Traffic {NDT): is an average 24-hr volume at
a given location for some period of time less than a year,
but more than one day.
Average Weekday TraTlic AWT): is an average 24-hr
traffic volume occurring on weekdays for some period less
than oneyear.
Traffic Stream Parametem
14
Weekdays
Table 3-7 Illustration of Daily Volume fbrameters
of Days MamhIy Weekday AWT
5/2
t
9,455
JJ,D00
8,409
9,091
J0,y3g
JD,45S
11,304
J2r381
ADT
Month (days) fdays) veh) gveht fvpd)
13,710
14,643
12,419
j3,333
J4,5T.6
16,667
18,710
1B,38Z
Jan 22 3T 425,000 2O8;000
Feb. 20 28 410,00D 22q,gg0
Rav 31 38>,ooo J85,OOO
4
0}
22
2 T
30
31
400,000
450,000
2000DO
21 5,000
ul
Aug.
#
JJ
31
31
S8O,00O
szo,ooo
26O,DQO
260,000
P
Oct.
Nov. .
Dec.
2*
22
21
22
3
31
30
3
490,000
420,000
4J5,0O0
400,000
205,000
jg0,0gg
2O0,00O
z o,ooo
9,318
8,636
9,523
9,545
J6,333
13,548
13,833
T2,9O3
Year 260 365 5,44S,OOD 2,583,000
J563,000/26O = 9,93S vpd
AADT = $,445,000/365 = 14,91 8 vpd
Traffic Stream Parameters
15
Hourl Volumes and Their Use
 While daily volumes are useful in highway planning, they
cannot be used alone for design or operational analysis
purposes.
 Traffic volume varies considerably during the course of a
24-hr day.
 The single hour of the day that has the highest hourly
volume is referred to as the peak hour.
 Traffic volume within this hour is of greatest interest to
traffic engineers in design or operational analysis.
Traffic Strea Pa meters
16
Sub-hourl Volumes and Rates of Flow
 The variation within a given hour is also of considerable
interest for traffic design and analysis.
The quality of traffic flow is often related to short-term
fluctuations in traffic demand.
A facility may have capacity adequate to serve the peak-
hour demand, but short-term peaks of flow within the
peak hour may exceed capacity, thereby creating a
breakdown.
Traffic Stream Parametem
17
 Sub-hourl Volumes and Rates of Flow
Table 3-9 Illustration of Hourly Volume and
Rate of Flow
2
Volume fdr Time
Cot 2/O.25
eate of Flow for
1 interval Time interval
Time Interval (velt) {yp}s)
S:OOS: l5 P.M.
5:155.30 P.M.
1000
4I O
O
4OOO
too
S:3O5:45 r.ter. I2oo 4eoo
5:456:00 P.M. 900 3600
5:OO6:00 r.M. 4200 Vph  hourly volume
Traffic Stream Parameters
18
Sub-hourl Volumes and Rates of Flow
contd..
The relationship between hourly volume and the
maximum rate of flow within the hour is defined
by the Peak Hour Factor (PHF).
PHF 

hourly volume U
maximum rateof flow 4xVJ
5
where, V = hourly volume
minute volume within the h::t
'高 = maximum 15-
Traffic Strea Pa meters
19
Sub-hourly Volumes and Rates of Flow [contd..)
 The maximum value of PHF is 1.00, which occurs when
the volume in each 15-min period is equal.
The minimum value is 0.25, which occurs when the entire
hourly volume occurs in one 15-min interval.
The normal range of values is between 0.70 and 0.98,
with lower values signifying a greater degree of variation
in flow during the peak hour.
Traffic Strea Pa meters
20
eed
Speed is the second principal parameter describing the
state of a given traffic stream.
In a moving traffic stream, each vehicle travels at a
diPerent speed.
 Thus, the traffic stream doesnot have asingle
characteristic speed but rather a distribution of individual
vehicle speeds.
From the distribution of vehicle speeds, a number of
average or typical values may be used to characterize
the traffic stream asa whole.
Traffic Strea
21
Pa meters
eed contd..
Average or mean speeds can be computed in two different ways:
Time Mean Speed (TLS) is defined as the average speed of all
vehicles passing a point on a highway over some specified time
period.
:fipace Mean Speed(ENE) is defined as the average speed of all
vehicles occupying a given section of a highway over some
specified time period.
Time mean speed is a point measure, while space mean speed is
a measure relating to a length of highway or lane.
Traffic Strea
52
Pa meters
eed contd..
SIWS 

where, d is the distance traversed, n is the
number of travel times observed and 7,is the
travel time for /-th vehicle.
1 JOOO 18.0 7OOO/18 US.6
2 1OOO 20.O 1OOOWO SO.0
3 OOO z2.O 1OOO22 - 45.S
4 ]OOO ]9.O 1 OOO/19 : 52.6
S
6
IOOO
]ODO 2O.
OOCL"20
1OOOWO
- 5 0. O
SO.O
Toto贈s
Aer8ee
6000
i I 9z6
119.O
1s.a 3O3.T/6
303.z
= 50.6
Traffic Stream Parametem
23
 eed contd..
Table S-IO Comyutatiarj of Time M e a n Spee
anc4 Space M e a n Spee<l
D i s t a n c e T r a v e l T i m e Speed
or 6OOO119 - TO.4 lps
Traffic Strea Pa meters
24
Relationship between time mean speed
and space mean speed
Time mean speed is greater to equal to space
mean speed
 The two speeds have the following
relationship:
Vs
Traffic Strea
25
Pa meters
eed contd..
They are two forms of space mean speed.
The Average Travel Speed computation uses
total average travel time while Average Running
Speed computation uses the average running
time.
Running time is defined as the time during
which the vehicle is in motion while traversing a
given highway segment.
Traffic Strea
26
Pa meters
eed contd..
Example
Consider the case of a 1-mile section of a roadway. On the
average, it takes a vehicle 3 minutes to traverse the section, 1
minute of which is stopped time experienced at signalized
intersections.
AverageTrave 1Speed 
 ' mph 

2()mph
60
Avera geEtinning
Traffic Strea
27
Pa meters
eed contd..
 Operating Speed is defined as the maximum safe speed at
which a vehicle can be conducted in a given traffic stream,
without exceeding the design speed of the highway
segment.
 Operating speed is difficult to measure. It requires that a
test car be driven through the traPic stream in a manner
consistent with the definition.
 Asmaximum safe speed" is a judgmental matter,
consistent measurements among test-car drivers are not
often achieved.
Traffic Strea Pa
28
meters
Densi
Density, the third measure of traPic
stream conditions, is defined as the
number of vehicles occupying a
given length of highway or lane.
Usually expressed as vehicles per
mile (vpm) or vehicles per mile per
lane (vpmpl).
Density is difficult to measure
directly, as an elevated point is
required.
Traffic Strea
29
Pa meters
Densi coctd...
It can, however, be computed from speed
and flow rate using the relationship as
follows:
Where, q = flow rate (vph)
v, = space mean speed (mph), and
k = density (vpm).
Traffic Strea Pa meters
ac" a and Time Headwa
Spacing and Time Headway are microsco ic measures,
because they apply to individual pairs of vehicles within
the traffic stream.
 /pac7ny is defined as the distance between successive
vehicles in a traffic lane, measured from some common
reference point on the vehicles, such as the front bumpers
or front wheels.
Spacing 0 given point ,o
Traffic Strea Pa meters
31
ac" a and Time Headwa
 Fime 6ea#rrayis the time between successive vehicles
as they pass a point along the lane, also measured
between common reference points on the vehicles.
Particular
location
Traffic Strea
32
Pa meters
Clearance (ft) =
(spac財ng)(average
vehic/e /ength)
Gap (sec) =
(headwdfi)(time
eqciva/ence of the
averape vehicfe
fenpth)
Traffic Strea Pa meters
contd..
ac!n and Time Headwa
 Average values of Spacing and Time Headway are
related to the macroscoic arameters as follows:
da
k=5280, 3600

9'
where, k = density (vpmpl), vs = 多Iverage speed
(ft/sec), q = rate of 単ow (vphpl), dv' average spacing
(ft), and ha = average time headway (sec).
Traffic Strea Pa meters
34
Lane occupancy: measure used in freeway
surveillance.
 Ratio of the time that vehicles are present at a
detection station in a traPic lane compared to the
observation time.
dirt cti高n .f travel
I. 
Lengih ot vehicle
C. I9istancc between lotps tif detector
Traflic Strea Pa
35
meters
Lane occupancy
LO
total time vehicle detectoris occupied
totalobservation time T
 Time that the vehicle used to travel 1+6: t0 + C
f. - Length of vehicle
C - Distance between uops of detector
TraWic Strea
36
Pa meters
ane occupancy
Assume k vehicles are evenly spread out on 1 mile
highway at speed v, mile/hr
Density
= kvehicle/mile
is: (Br束)/v,
Therefore:
LO 

X
(L +C) k
k = LO z6280
m i l e s
Total time needed to have all vehicles pass the detector
(vehicle/mile)
Speed, Flow
Relationship
37
Density
Assume
 We have
損= ABk
q /rr=W 6k2
i -- A 8k
A > 0.B > 0
Density, 贈 (veh/mi)
束
pv
A Ap v

B B B
2B ' '
Density, k (veh/mi)
(b)
Properties of speed-density
curve
38
The product of the x-y coordinates of
the point Pis the 単ow associated with
Max flow occurs at: 属 - A2Bk

0  -
3k
k,
k
represenls the
, and densitv k
k' k
A
2//
Properties of speed-flow
curve
39
The slope of the line connecting any point on the
curve and the origin is the inverse of the density
Nax flow occurred at: as 0
t A
Properties of flow-density
curve
40
The slope of the line connecting any point on the
curve and the origin is the space mean speed
General properties for a
traffic flow model
41
Need to satisfy four boundary
conditions
Flow is zero at zero density
Flow is zero at maximum density
Mean free-flow speed occurs at zero density
Flow-density curves are convex (i.e. there is a
point of max flow)
Connections beMeen speed,
42
density and flow
A: almost zero density, free-flow speed, vey low
volume
B: increased density, reduced speed, increased volume
 C: increased density, reduced speed, max volume
D: jam density, min speed (crawling), vey low volume
Density. k D Flow. q
0
Density, k
Traffic Strea Pa meters
43
Since a given flow may occur under two
completely diPerent operating conditions (stable
and unstable), volume or rate of flow cannot be
used as a measure describing the operational
quality of the traffic stream.
Speed and density, however, are good measures
of the quality of operations, as both uniquely
describe the state of the traPic stream.
Macroscopic Models of Traffic Flow
44
The two most commonly used macroscopic
models are:
The Greenshields Model
The Greenberg Model
Macroscopic Models of Traffic Flow
t単 !tn.! liretds Mot≒n.1
45
The general model connecting speed,
flow, and density discussed so far is a
linear model proposed by Greenshield in
1935.
He suggested that the speed and
density were linearly related as follows:
Macroscopic Models of Traffic Flow
  !e'n.' liie ldc Mc高≒o.I
46
It can be shown that:
The maximum fiow (i.e., capacity) occurs when the speed
of the traffic stream is half of the free-flow speed:
* f
" 2
The maximum flow (i.e., capacit:y) occurs when the density
is half of the jam density:
k
The maximum flow, q a,:
Macroscopic Models of Traffic Flow
 !e'損beroz I i I座
47
Greenbergdeveloped a model in 1959,
taking speed, flow and density
measurements in the Lincoln Tunnel.
Used a fluid-flow analogy concept.
The model is of the following form:
Macroscopic Models of Traffic Flow
  !e'nberoz I i f損
48
It can be shown that:
The maximum flow occurs when speed
The maximum flow occurs when density (k) is
related with jam density (ki) as follows:
Then, the maximum flow (q ax) iS the product of
the density (k) and speed (vs) at maximum flow.
Macroscopic Models of Traffic Flow
贈1 f,r I" / Modelx
49
The Greeshields Model can be used for light or
heavy traffic conditions.
The Greenberg Nodel is useful only for heavy
traPic conditions.

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  • 2. Traffic Streams 2 Traffic streams are made up of individual drivers and vehicles, interacting in unique ways with each other and with elements of the roadway and general environment. Because the judgments and abilities of individual drivers come into play, vehicles in the traffic stream do not and cannot behave uniformly. Further, no two similar traffic streams will behave alike, even under equivalent circumstances, as driver behavior varies with local characteristics and driving habits. Traffic streams, however, can be described in quantitative terms with the use of some key parameters like volume, speed and density.
  • 3. Traffic Streams Traffic facilities are broadly separated into two principal categories: 1. Uninterrupted flow facilities, and 2. Interrupted flow facilities Uninterrupted Flow Facilities are those on which no external factors cause periodic interruption to the traffic stream. Example: Freeway Interrupted Flow Facilities are those having external devices that periodically interrupt traffic flow. Example: Urban Roadways. The principal devices creating interrupted flow are primarily traffic signal and also STOPand YIELD signs, etc.
  • 4. Traffic Streams 4 Uninterrupted and Interrupted Flow are terms that describe the facility and not the quality of flow. A congested freeway where traffic is almost coming to a halt is still classified as uninterrupted 単ow facility, because the reason for congestion is internal to the traPic stream. Awell-timed signaling system on an arterial may result in almost uninterrupted traffic flow, but still is classified as interrupted flow facility.
  • 5. Traffic Stream Parameters 5 TraPic Stream Parameters fall into two broad categories: Nacrozcopic parameters, and Nicrozcopicparameterz. Macroscopicparameters characterizethe traPic stream as a whole Microscopic parameterscharacterizethe behavior of individual vehicles in the traPic stream with respect to each other.
  • 6. Traffic Stream Parameters 6 Macroscopicflow traffic in the aggregate. overall speeds, traffic flows, densities, etc. Microscopic flow traffic at the level of the individual vehicle observe the paiticular behaviors of drivers, and of individual vehicles in the traffic stream. vehicle headways & lane-chan9ing behavior (merging, diverging, weaving, passing, etc.) critical 0 microscopic level.
  • 7. Traffic Strea Pa meters 7 A traPic stream may be described macroscopically by three parameters: 1. Volume or Rate of Flow 2. Speed 3. Density
  • 8. Traffic Strea 8 Pa meters Volume and Flow Pa/wme is defined as the number of vehicles that pass a point on a highway, or a given lane or direction of a highway, during a specified time interval. Usually expressed as vehicles per unit time, for example, vehicles per hour or vph. Aate a///owis the equivalent hourly rate at which vehicles pass a point on a highway lane during a time period less than 1 hour.
  • 9. Traffic Stream Parameters 9 Volume and Rate of Flow are two diPerent measures. Volume is the actual number of vehicles observed or predicted to be passing a point during a given time interval. Rate of flow represents the number of vehicles passing a point during a time interval less than 1 hour, but expressed as an equivalent hourly rate.
  • 10. Traffic Stream Parameters 10 Avolume of 200 vehicles observed in a 10-minute period implies a rate of flow of (200 x 60)/10 = 1200 veh/hr. Note that 1200 vehicles do not pass the point of observation during the study hour, but they do pass the point at that rate for 10 minutes.
  • 11. Traffic Strea Pa meters 11 . The maximum number of vehicles per unit time that a particular transportation facility may accommodate (veh/h).
  • 12. Traffic Strea 12 Pa meters Acommon time interval for volumes is a day. Daily volumes are frequently used as the basis for highway planningand general observations of trends. TraPic volume projections are often based on measured daily volumes.
  • 13. Traffic Stream Parameters 13 Dai"ly Volumes and Their Uae (ontd..) There are four commonly used daily volume parameters: Average AnnualDaily Traffic (AADT): is the average 24-hr traffic volume at a given location over a full 365-day year. Average Annual Weekday Tracce {AAWT): is the average 24-hr traffic volume occurring on weekdays over afull 365-day year. 3 . AverageDai/y Traffic {NDT): is an average 24-hr volume at a given location for some period of time less than a year, but more than one day. Average Weekday TraTlic AWT): is an average 24-hr traffic volume occurring on weekdays for some period less than oneyear.
  • 14. Traffic Stream Parametem 14 Weekdays Table 3-7 Illustration of Daily Volume fbrameters of Days MamhIy Weekday AWT 5/2 t 9,455 JJ,D00 8,409 9,091 J0,y3g JD,45S 11,304 J2r381 ADT Month (days) fdays) veh) gveht fvpd) 13,710 14,643 12,419 j3,333 J4,5T.6 16,667 18,710 1B,38Z Jan 22 3T 425,000 2O8;000 Feb. 20 28 410,00D 22q,gg0 Rav 31 38>,ooo J85,OOO 4 0} 22 2 T 30 31 400,000 450,000 2000DO 21 5,000 ul Aug. # JJ 31 31 S8O,00O szo,ooo 26O,DQO 260,000 P Oct. Nov. . Dec. 2* 22 21 22 3 31 30 3 490,000 420,000 4J5,0O0 400,000 205,000 jg0,0gg 2O0,00O z o,ooo 9,318 8,636 9,523 9,545 J6,333 13,548 13,833 T2,9O3 Year 260 365 5,44S,OOD 2,583,000 J563,000/26O = 9,93S vpd AADT = $,445,000/365 = 14,91 8 vpd
  • 15. Traffic Stream Parameters 15 Hourl Volumes and Their Use While daily volumes are useful in highway planning, they cannot be used alone for design or operational analysis purposes. Traffic volume varies considerably during the course of a 24-hr day. The single hour of the day that has the highest hourly volume is referred to as the peak hour. Traffic volume within this hour is of greatest interest to traffic engineers in design or operational analysis.
  • 16. Traffic Strea Pa meters 16 Sub-hourl Volumes and Rates of Flow The variation within a given hour is also of considerable interest for traffic design and analysis. The quality of traffic flow is often related to short-term fluctuations in traffic demand. A facility may have capacity adequate to serve the peak- hour demand, but short-term peaks of flow within the peak hour may exceed capacity, thereby creating a breakdown.
  • 17. Traffic Stream Parametem 17 Sub-hourl Volumes and Rates of Flow Table 3-9 Illustration of Hourly Volume and Rate of Flow 2 Volume fdr Time Cot 2/O.25 eate of Flow for 1 interval Time interval Time Interval (velt) {yp}s) S:OOS: l5 P.M. 5:155.30 P.M. 1000 4I O O 4OOO too S:3O5:45 r.ter. I2oo 4eoo 5:456:00 P.M. 900 3600 5:OO6:00 r.M. 4200 Vph hourly volume
  • 18. Traffic Stream Parameters 18 Sub-hourl Volumes and Rates of Flow contd.. The relationship between hourly volume and the maximum rate of flow within the hour is defined by the Peak Hour Factor (PHF). PHF hourly volume U maximum rateof flow 4xVJ 5 where, V = hourly volume minute volume within the h::t '高 = maximum 15-
  • 19. Traffic Strea Pa meters 19 Sub-hourly Volumes and Rates of Flow [contd..) The maximum value of PHF is 1.00, which occurs when the volume in each 15-min period is equal. The minimum value is 0.25, which occurs when the entire hourly volume occurs in one 15-min interval. The normal range of values is between 0.70 and 0.98, with lower values signifying a greater degree of variation in flow during the peak hour.
  • 20. Traffic Strea Pa meters 20 eed Speed is the second principal parameter describing the state of a given traffic stream. In a moving traffic stream, each vehicle travels at a diPerent speed. Thus, the traffic stream doesnot have asingle characteristic speed but rather a distribution of individual vehicle speeds. From the distribution of vehicle speeds, a number of average or typical values may be used to characterize the traffic stream asa whole.
  • 21. Traffic Strea 21 Pa meters eed contd.. Average or mean speeds can be computed in two different ways: Time Mean Speed (TLS) is defined as the average speed of all vehicles passing a point on a highway over some specified time period. :fipace Mean Speed(ENE) is defined as the average speed of all vehicles occupying a given section of a highway over some specified time period. Time mean speed is a point measure, while space mean speed is a measure relating to a length of highway or lane.
  • 22. Traffic Strea 52 Pa meters eed contd.. SIWS where, d is the distance traversed, n is the number of travel times observed and 7,is the travel time for /-th vehicle.
  • 23. 1 JOOO 18.0 7OOO/18 US.6 2 1OOO 20.O 1OOOWO SO.0 3 OOO z2.O 1OOO22 - 45.S 4 ]OOO ]9.O 1 OOO/19 : 52.6 S 6 IOOO ]ODO 2O. OOCL"20 1OOOWO - 5 0. O SO.O Toto贈s Aer8ee 6000 i I 9z6 119.O 1s.a 3O3.T/6 303.z = 50.6 Traffic Stream Parametem 23 eed contd.. Table S-IO Comyutatiarj of Time M e a n Spee anc4 Space M e a n Spee<l D i s t a n c e T r a v e l T i m e Speed or 6OOO119 - TO.4 lps
  • 24. Traffic Strea Pa meters 24 Relationship between time mean speed and space mean speed Time mean speed is greater to equal to space mean speed The two speeds have the following relationship: Vs
  • 25. Traffic Strea 25 Pa meters eed contd.. They are two forms of space mean speed. The Average Travel Speed computation uses total average travel time while Average Running Speed computation uses the average running time. Running time is defined as the time during which the vehicle is in motion while traversing a given highway segment.
  • 26. Traffic Strea 26 Pa meters eed contd.. Example Consider the case of a 1-mile section of a roadway. On the average, it takes a vehicle 3 minutes to traverse the section, 1 minute of which is stopped time experienced at signalized intersections. AverageTrave 1Speed ' mph 2()mph 60 Avera geEtinning
  • 27. Traffic Strea 27 Pa meters eed contd.. Operating Speed is defined as the maximum safe speed at which a vehicle can be conducted in a given traffic stream, without exceeding the design speed of the highway segment. Operating speed is difficult to measure. It requires that a test car be driven through the traPic stream in a manner consistent with the definition. Asmaximum safe speed" is a judgmental matter, consistent measurements among test-car drivers are not often achieved.
  • 28. Traffic Strea Pa 28 meters Densi Density, the third measure of traPic stream conditions, is defined as the number of vehicles occupying a given length of highway or lane. Usually expressed as vehicles per mile (vpm) or vehicles per mile per lane (vpmpl). Density is difficult to measure directly, as an elevated point is required.
  • 29. Traffic Strea 29 Pa meters Densi coctd... It can, however, be computed from speed and flow rate using the relationship as follows: Where, q = flow rate (vph) v, = space mean speed (mph), and k = density (vpm).
  • 30. Traffic Strea Pa meters ac" a and Time Headwa Spacing and Time Headway are microsco ic measures, because they apply to individual pairs of vehicles within the traffic stream. /pac7ny is defined as the distance between successive vehicles in a traffic lane, measured from some common reference point on the vehicles, such as the front bumpers or front wheels. Spacing 0 given point ,o
  • 31. Traffic Strea Pa meters 31 ac" a and Time Headwa Fime 6ea#rrayis the time between successive vehicles as they pass a point along the lane, also measured between common reference points on the vehicles. Particular location
  • 32. Traffic Strea 32 Pa meters Clearance (ft) = (spac財ng)(average vehic/e /ength) Gap (sec) = (headwdfi)(time eqciva/ence of the averape vehicfe fenpth)
  • 33. Traffic Strea Pa meters contd.. ac!n and Time Headwa Average values of Spacing and Time Headway are related to the macroscoic arameters as follows: da k=5280, 3600 9' where, k = density (vpmpl), vs = 多Iverage speed (ft/sec), q = rate of 単ow (vphpl), dv' average spacing (ft), and ha = average time headway (sec).
  • 34. Traffic Strea Pa meters 34 Lane occupancy: measure used in freeway surveillance. Ratio of the time that vehicles are present at a detection station in a traPic lane compared to the observation time. dirt cti高n .f travel I. Lengih ot vehicle C. I9istancc between lotps tif detector
  • 35. Traflic Strea Pa 35 meters Lane occupancy LO total time vehicle detectoris occupied totalobservation time T Time that the vehicle used to travel 1+6: t0 + C f. - Length of vehicle C - Distance between uops of detector
  • 36. TraWic Strea 36 Pa meters ane occupancy Assume k vehicles are evenly spread out on 1 mile highway at speed v, mile/hr Density = kvehicle/mile is: (Br束)/v, Therefore: LO X (L +C) k k = LO z6280 m i l e s Total time needed to have all vehicles pass the detector (vehicle/mile)
  • 37. Speed, Flow Relationship 37 Density Assume We have 損= ABk q /rr=W 6k2 i -- A 8k A > 0.B > 0 Density, 贈 (veh/mi) 束 pv A Ap v B B B 2B ' ' Density, k (veh/mi) (b)
  • 38. Properties of speed-density curve 38 The product of the x-y coordinates of the point Pis the 単ow associated with Max flow occurs at: 属 - A2Bk 0 - 3k k, k represenls the , and densitv k k' k A 2//
  • 39. Properties of speed-flow curve 39 The slope of the line connecting any point on the curve and the origin is the inverse of the density Nax flow occurred at: as 0 t A
  • 40. Properties of flow-density curve 40 The slope of the line connecting any point on the curve and the origin is the space mean speed
  • 41. General properties for a traffic flow model 41 Need to satisfy four boundary conditions Flow is zero at zero density Flow is zero at maximum density Mean free-flow speed occurs at zero density Flow-density curves are convex (i.e. there is a point of max flow)
  • 42. Connections beMeen speed, 42 density and flow A: almost zero density, free-flow speed, vey low volume B: increased density, reduced speed, increased volume C: increased density, reduced speed, max volume D: jam density, min speed (crawling), vey low volume Density. k D Flow. q 0 Density, k
  • 43. Traffic Strea Pa meters 43 Since a given flow may occur under two completely diPerent operating conditions (stable and unstable), volume or rate of flow cannot be used as a measure describing the operational quality of the traffic stream. Speed and density, however, are good measures of the quality of operations, as both uniquely describe the state of the traPic stream.
  • 44. Macroscopic Models of Traffic Flow 44 The two most commonly used macroscopic models are: The Greenshields Model The Greenberg Model
  • 45. Macroscopic Models of Traffic Flow t単 !tn.! liretds Mot≒n.1 45 The general model connecting speed, flow, and density discussed so far is a linear model proposed by Greenshield in 1935. He suggested that the speed and density were linearly related as follows:
  • 46. Macroscopic Models of Traffic Flow !e'n.' liie ldc Mc高≒o.I 46 It can be shown that: The maximum fiow (i.e., capacity) occurs when the speed of the traffic stream is half of the free-flow speed: * f " 2 The maximum flow (i.e., capacit:y) occurs when the density is half of the jam density: k The maximum flow, q a,:
  • 47. Macroscopic Models of Traffic Flow !e'損beroz I i I座 47 Greenbergdeveloped a model in 1959, taking speed, flow and density measurements in the Lincoln Tunnel. Used a fluid-flow analogy concept. The model is of the following form:
  • 48. Macroscopic Models of Traffic Flow !e'nberoz I i f損 48 It can be shown that: The maximum flow occurs when speed The maximum flow occurs when density (k) is related with jam density (ki) as follows: Then, the maximum flow (q ax) iS the product of the density (k) and speed (vs) at maximum flow.
  • 49. Macroscopic Models of Traffic Flow 贈1 f,r I" / Modelx 49 The Greeshields Model can be used for light or heavy traffic conditions. The Greenberg Nodel is useful only for heavy traPic conditions.