Traffic Stream Parameters

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Traffic Stream Parameters
Chapter 5
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Interrupted Versus Uninterrupted flow

• Uninterrupted flow
• No interruptions to traffic stream
• refers to type of facility not quality of flow
• facility is available to the user at all times
  (physically available, doesnt mean quality of
  service)
• types
• freeways (total access control, pure
  uninterrupted flow)
• roadways with long distances in between fixed
  interruptions (i.e. long stretches of rural two
  lane highway or expressway)
• approximately 2 miles between (definition)

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Interrupted flow

• has fixed external interruptions such as traffic
  signals, stop or yield control, etc.
• facility is restricted from user at certain times
  (i.e. during red phase)
• more complex than uninterrupted flow

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Macro versus microscopic

• macroscopic traffic stream parameters describe
  stream as a whole
• Volume
• Speed
• density
• Microscopic traffic stream parameter describe
  behavior of individual vehicles
• Individual vehicle speed
• Headway
• spacing

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Macroscopic Traffic Stream Parameters

• Volume or flow rate
• Speed
• density

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Traffic Flow Elements

• Flow (q)The equivalent hourly rate at which
  vehicles pass a point on 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
• qequivalent hourly flow rate (veh/hour)

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Volume

• number of vehicles, pedestrians, etc. passing a
  point during a specific period of time
• for vehicles, usually expressed as veh/hour (vph)
  or veh/hour/lane (vphpl)
• an indicator of demand, but not a surrogate for
  demand

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• Demand
• number of vehicles, pedestrians, etc. that desire
  to travel between locations during a specific
  period
• Frequently higher than volume during certain peak
  times
• Trips are diverted or not made when there are
  constraints in the system
• difficult to measure actual demand because
  capacity constrains the demand
• Capacity
• maximum number of vehicles that can pass a point
  during a specific period
• A characteristic of the roadway or facility

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Characteristics of Traffic Flow

• Highly variable
• Time of day
• Day of week
• Season
• Road characteristics
• Direction

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Traffic Typically Peaks twice per day
Source www.ecn.purdue.edu/darcy
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Hourly volumes

• Peak hour
• single hour with highest hourly volume used
• Used for design and operations
• Usually directional
• Design peak hour is the hour used for design
• Often estimated from AADT
• DDHV AADT K D
• Where
• DDHV design hour volume
• K proportion of daily traffic occuring
  during the peak hour (proportion of
• AADT occurring during the 30th
  highest peak hour during the year)
• D proportion of peak hour traffic
  traveling in the peak direction of flow
• Best collected in field
• Need to forecast to future condition (20 year
  design)

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Peak Hour

• single hour of the day with the highest hourly
  volume (HHV)
• generally directional
• peak hourly volumes are the basis for highway
  design and many types of operational analysis
• highways designed to serve the peak hour volume
  in the peak direction of flow (design for peak
  hour in both directions)
• PHV (def) maximum number of vehicles that pass
  a point on a highway during a period of 60
  consecutive minutes, PHV for intersections
  similarly typically defined for entire
  intersection.
• Uses func. class. of highways, design of
  geometrics (number of lanes, intersection
  signalization, and channelization), capacity
  analysis, development of traffic operation
  programs, parking regulations.

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Sub-Hourly Volumes

• Volumes fluctuate even within an hour, may cause
  breakdown if not accounted for
• Often look at smaller increments for signal
  timing, etc.
• Adjust volume from smaller intervals to hourly
  volume (vph)
• Peak 10 minutes volume of 1,500 vehicles 6 x
  1500 9,000 vph (this is flow rate not volume,
  volume is the actual count for the hour

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Peak Hour Factor (PHF)

• PHF peak-hour volume __
• 4(peak 15-min volume)
• Flow is not uniform throughout an hour
• HCM considers operating conditions during most
  congestion 15-minute period of the hour to
  determine service level for the hour as a whole

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Peak Hour Factor
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• Example
• Peak 15 minutes flows
• 100 veh/ 15 min
• 125 veh/ 15 min
• 110 veh/ 15 min
• 130 veh/ 15 min
• What is peak hour factor
• PHF (100 125 110 130 ) 0.89
• 4 130

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What does a peak hour factor of 1 mean?
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What does a peak hour factor of 1
mean? Example 15 min flows 100 veh/ 15 min 100
veh/ 15 min 100 veh/ 15 min 100 veh/15 min PHF
(400)/(4100) 1 Flows are constant over hour
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• DHV Peak-Hour Volume
• PHF
• Example
• Peak hour volume 425 vph
• PHF 0.85
• DHV __425 __ 500 vph
• 0.85
• Same as multiplying peak 15 minutes by 4, but we
  usually dont have subhourly volumes so we use
  an appropriate PHF

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Traffic Flow Elements

• Speed (u) Distance traveled by a vehicle during
  a unit of time. For individual vehicle
• u d/t
• Where
• u speed (mph, ft/s)
• d distance traveled (miles or feet)
• t time to traverse distance d (hours or sec)

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Speed

• Second macroscopic flow parameter
• Speed for a traffic stream (average of individual
  speeds)
• Time mean speed
• Space mean speed
• Average speed

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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)

• TMS ?(d/t1)
• n
• where
• d distance traveled (ft)
• n number of observed vehicles
• ti time vehicle i to traverse section

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Speed

• Space mean speed
• average speed of all vehicles occupying a given
  section of highway or lane over some specified
  interval
• Weights the amount of time a vehicles occupies a
  highway section, a vehicle at 25 mph occupies
  twice as much time as a vehicle at 50 mph

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Space mean speed

• us ___nd___
• ?ti
• Where
• n number of observed vehicles
• l distance traversed (ft)
• di time for ith vehicle to traverse the
  section

TMS always gt SMS
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Space vs. Time Mean Speed Example

• For a 100-foot section, the following were
  measured

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Time Mean Speed
TMS ?(d/t1) n
(ft/sec)
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Space vs. Time Mean Speed Example

• Calculate space mean speed.

us ______________(500 ft) ( 10 )
_____________________ 5.0 5.6
5.6 4.8 6.1 5.3 5.9 5.2 4. 5
5.0 us 94.3 ft/sec lt ut (always)
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• Note that space mean speed and time mean speed in
  this context refer to constant speed
• Average link speed is something else
• Distance to traverse entire link including
  acceleration, deceleration, queuing, etc

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Density (k)

• Concentration
• Number of vehicles traveling over a unit length
  of highway at an instant in time
• measures quality of traffic flow (how close
  vehicles are) relates to ability to maneuver and
  psychological comfort level
• Usually veh/mile or vpmpl

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Density (k)

• 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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Density distance between successive vehicles
D 5280/dd Where D
density (vehi/mi/ln) dd average spacing
between vehicles in the lane (miles)
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Density

• D 5280/dd
• If average spacing 45 feet, what is density?
• Assume over l lane over 1 mile
• D __5280 (ft/mile)___ 117.33 veh/mile/ln
• 45 ft

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Headway time interval between vehicles V
3600 ha where v rate of flow,
veh/hr/ln ha average headway in lane
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Headway V 3600 ha If volume 1200
veh/h/lane, what is headway?
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V 3600 ha If volume 1200
veh/h/lane, what is headway? ha 3600/1200 3
sec if you sat by the side of the road, you
would find that on average a vehicle passed you
every 3 seconds.
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Is this the same as a gap?
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Is this the same as a gap? Somewhat but gaps
are actual spaces Gap (g) Gap is very similar to
headway, except that it is a measure of the time
that elapses between the departure of the first
vehicle and the arrival of the second at the
designated test point. Gap is a measure of the
time between the rear bumper of the first vehicle
and the front bumper of the second vehicle, where
headway focuses on front-to-front times. Gap is
usually reported in units of seconds. (Uof
Idaho)
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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)

h t2 tf
tf
t2
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Gap

• The time between the back of a vehicle and the
  front of the following vehicle (sec)

h t2 tb
tb
t2
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Space Headway (d)

• The distance between the front of a vehicle and
  the front of the following vehicle (ft)

(d)
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Gap (distance)

• The distance between the back of a vehicle and
  the front of the following vehicle (ft)

(d)
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Daily Volume

• Uses
• General planning
• Pavement performance
• Crash rates
• Annual average daily traffic (AADT) average
  volume counted for 24 hours over 365 days
• Average daily traffic (ADT) average 24-hour
  volume at a given location that is counted for
  some period gt 1 day and lt 365)
• usually extrapolated to represent traffic over
  the year
• Classification counts fleet mix

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Note AADT and AAWT only have one value for a
year, they are shown continuously for comparison
purposes From McShane, Roess, and Prassas, page
62 (1998)
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Traffic Demand (cont.)

• Exhibit 2-28 relationship between HHV and percent
  of ADT in peak hour (referred to as K-factor)

Source A Policy on Geometric Design of Highways
and Streets (The Green Book). Washington, DC.
American Association of State Highway and
Transportation Officials, 2001 4th Ed.
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Design Hourly Volume

• DHV is a representation of peak hour traffic,
  usually for the future, or horizon year
• K-factor represents proportion of daily traffic
  occuring during the peak hour
• K-factor __DHV x 100
• AADT
• K 8 to 12 urban, 12 to 18 rural

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From McShane, Roess, Prassas (1998) page 63
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Design Hourly Volume (Example)

• If AADT is 3500 vpd and the 30th highest hourly
  volume for the year is 420 vph what is the
  K-factor for that facility?
• K-factor __DHV x 100
• AADT
• K-factor __420 x 100 12
• 3500

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Question Whats the impact of choosing
different K factor for design?
If AADT is 3500 vpd, how will the design volume
differ for k-factor 8 vs. 12? DHV
K-factor x AADT
100 DHVk8 8 x 3500 280 vph
100 DHVk12 12 x 3500 420 vph
(diff of 140 100 veh)
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Traffic Demand (cont.)

• D directional distribution one way volume in
  peak direction (expressed as a percentage of
  two-way traffic) Rural 55 to 80
• Can also adjust for how traffic is distributed
  between lanes (e.g., 3 lanes, highest/outside
  lane may be 40 of total directional flow)

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Directional Distribution (example)
If traffic is directionally split 60/40, what is
directional distribution of traffic for previous
example (Design hourly volume 420
veh/hr)? Directional Design Hourly Volume (DDHV)
0.6 x 420 252 veh/hr
Notice we use 0.6 not 0.4!!
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Traffic Demand

• Design Hourly Volume (DHV) future hourly volume
  (both directions) used for design - typically
  30th HHV (highest hourly volume) in the design
  year
• Why 30th HHV?
• Breakpoint of 2-28
• Compromise too high is wasteful, too low poor
  operation
• Approximately median weekly peak hour volume (top
  highest week peak hours)
• (30th HHV exceed 29 times in year)

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Design Volume

• Usually hourly volume
• Which hour?
• Average hourly volume inadequate design
• Maximum peak hour not economical
• Hourly volume used for design should not be
  exceeded very often or by very much
• Usually use 30th highest hourly volume of the
  year
• On rural roads 30 HHV is 15 of ADT
• Tends to be constant year to year

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Traffic Demand (cont.)

• T percentage of heavy vehicles during design
  hour (Iowa interstate 35 plus)
• Affects capacity, ability to pass on two-lane
  rural roads, etc.
• Larger, occupy more space
• Should determine during design hour (truck
  patterns may not be same as passenger vehicles)

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Relationship between flow, speed, and density
V S x D Where V rate of flow, veh/hr or
veh/h/lane S space mean speed, mph D
density, veh/mi or veh/mi/lane Must apply to the
same section of road usually used to estimate
density, hardest to get in field, why?
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Relationship between flow, speed, and density
Example flow rate on arterial is 983
veh/hr/lane and speed is 46 mph, what is
density? D V/S 1,283 veh/hr/ln 21.4
veh/mile/ln
46 mph
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Flow-Density Example

• If the spacing between vehicles is 500 feet what
  is the density?
• d 1/k
• k 1/d 1 veh/500 feet

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Flow-Density Example

• If the spacing between vehicles is 500 feet what
  is the density?
• d 1/k
• k 1/d 1 veh/500 feet
• 0.002 vehicles/foot 10.6
  veh/mile

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Flow-Density Example

• 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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Relationship between flow, speed, and density
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Relationship between flow, speed, and density
When density 0 Flow 0
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Relationship between flow, speed, and density
As density increases, flow increases to max value
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Relationship between flow, speed, and density
At maximum flow (density ke) further increases in
density will result in reduction of flow
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At max density (kj), flow 0 because all
vehicles are stopped
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Maximum speed (space mean speed) occurs as flow
tends to zero or density tends to zero Mean free
speed (uf)
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At qa, ua lt uf
qa
Increase in flow results in a decrease in speed
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Maximum flow
At some point, additional vehicles results in
decrease in number of vehicles moving past a
point (congestion), decrease in flow and speed
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Maximum speed occurs when density 0
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As density increases, speed decreases
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Maximum density occurs when speed 0 (cars
parked)
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Relationship between flow, speed, and density

• Fundamental diagram of traffic flow on
  uninterrupted facilities
• Actual form depends on prevailing traffic and
  roadway conditions on the roadway under study and
  on the length of the segment
• zero flow occurs at two points
• when there are no cars on the facility, density
  and flow rate are zero, speed is whatever the
  first driver would select, this is freeflow speed
  (sf)
• when density becomes so high that all vehicles
  are forced to stop (speed zero), flow rate is
  also zero because there is no movement (vehicles
  cannot pass a point), density is jam density
  (Dj)
• between 2 extreme points, as density increases
  from zero, flow rate also increases (more
  vehicles on the roadway) and speed declines
  (interaction of other vehicles)

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Relationship between flow, speed, and density

• low decline in speed at low and medium densities
• as density continues to increase, speed decreases
  significantly before capacity is reached
• capacity occurs at the optimum speed (uo) and
  optimum density (Do)
• any flow other than capacity can occur under 2
  different conditions
• high speed and low density
• high density and low speed
• Level of service related to speed, density, and
  flow (will discuss later)
• Other descriptions of these interrelationships
  have been modeled by Greenberg, Underwood,
  Northwestern, and Edie (plus) logarithmic, two
  regimes

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Mathematical Relationships for Traffic Flow

• Greenshields model
• Earliest works
• Linear relationship between speed and density
• uf _uf k
• kj
• Flow
• q uf k uf k2
• kj
• Maximum flow
• qmax kjuf
• 4

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Mathematical Relationships for Traffic Flow

• Greenberg model
• Used analogy of fluid flow to develop
  relationships for traffic flow
• Useful only for dense traffic conditions

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Traffic Flow Models

• Greenberg Model
• Assumes a fluid flow theory for speed and density

For maximum flow
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Traffic Flow Models

• Greenshields Model
• Assumes a linear relationship between speed and
  density

For maximum flow
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TimeSpace Diagram

• Portrays trajectory of individual vehicles in
  motion
• Distance (y axis)
• Time (x axis)

Image source http//www.webs1.uidaho.edu/niatt_la
bmanual/Chapters/trafficflowtheory/theoryandconcep
ts/TimeSpaceDiagram.htm
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Homework

• Do Problems
• 5.1
• 5.4
• 5.6
• 5.7
• Due Wed Sept 16th
• Note that we have two weeks no late homework!!