TRANSPO ENGG
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Traffic Analysis
Spot Speed
Spot Speed
refers to Instantaneous Speed
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Traffic Analysis
Running Speed
Running Speed
refers to Average Speed
$running\ speed\ =\ \frac{distance\ covered}{time\ elapsed}$
$running\ speed\ =\ \frac{distance\ covered}{time\ elapsed}$
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National Highway Signage
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Traffic Analysis
Space Mean Speed
Space Mean Speed
$\frac{n_t}{u_s}\ =\ \frac{1}{u_1}\ +\frac{1}{u_2}+...+\frac{1}{u_n}$
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Traffic Analysis
Time Mean Speed
Time Mean Speed
$u_t\ =\ \frac{u_1\ +\ \ u_2\ +\ ...u_n\ \ }{n_t}\ $
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Traffic Analysis
Variance of Speed Distribution
Variance of Speed Distribution
$u_t\ =\ u_s\ +\frac{\sigma^2}{u_s}$
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Traffic Analysis
Space Headway
(S.H.)
Space Headway
(S.H.)
$S.H.\ =\ \frac{L_1}{2}+\ clearance\ +\ \frac{L_2}{2}$
$S.H.\ =\ \frac{Length\ of\ Road\ Section}{No.\ of\ Vehicles\ Passing}$
$S.H.\ =\ \frac{Length\ of\ Road\ Section}{No.\ of\ Vehicles\ Passing}$
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Stream of Vehicles in any designated segment
- Queue
- Traffic
- Traffic Density
- Arrival Traffic
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Traffic Analysis
Density
(K)
Density
(K)
(veh/ km or miles) – The number of units or vehicles passing per unit distance.
$Density\ (K)=\ \frac{No.\ of\ Vehicles\ Passing}{Length\ of\ Road\ Section}$
$ (K)=\frac{1}{S.H.\ }$
$Density\ (K)=\ \frac{No.\ of\ Vehicles\ Passing}{Length\ of\ Road\ Section}$
$ (K)=\frac{1}{S.H.\ }$
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Traffic Analysis
Flow Rate or Volume
(q)
Flow Rate or Volume
(q)
(veh/ hr)-the number of vehicles passing per unit time.
$Flow\ (q)=\ \frac{No.\ of\ Vehicles\ Passing}{Time\ Elapsed}\ $
$q=\ \frac{No.\ of\ Vehicles\ Passing}{Headway}$
$q=\ \frac{1}{Time\ Headway}$
$Flow\ (q)=\ \frac{No.\ of\ Vehicles\ Passing}{Time\ Elapsed}\ $
$q=\ \frac{No.\ of\ Vehicles\ Passing}{Headway}$
$q=\ \frac{1}{Time\ Headway}$
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Traffic Analysis
GREENSHIELD'S MODEL
FLOW CAPACITY
GREENSHIELD'S MODEL
FLOW CAPACITY
$q_{cap}=\ \left(\frac{K_j}{2}\right)\left(\frac{u_f}{2}\right)=\frac{{K_j\ u}_f}{4}\ $
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CONCEPT
HEADWAY and TAILWAY
HEADWAY and TAILWAY
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CONCEPT
SPACE HEADWAY
SPACE HEADWAY
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RELATIONSHIP of SPACE MEAN SPEED,
FLOW, and DENSITY
FLOW, and DENSITY
$q\ =\ {K\ u}_s\ $
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Traffic Analysis
Perception-Reaction Time
PEIV
Perception-Emotion-Identification-Volition
Perception-Reaction Time
PEIV
Perception-Emotion-Identification-Volition
as per AASHTO
2.5 s
2.5 s
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Traffic Analysis
GREENSHIELD'S MODEL
MAXIMUM FLOW CAPACITY
GREENSHIELD'S MODEL
MAXIMUM FLOW CAPACITY
$q_{cap}=\ \left(\frac{K_j}{2}\right)\left(\frac{u_f}{2}\right)=\frac{{K_j\ u}_f}{4}$
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Traffic Analysis
MINIMUM TIME HEADWAY
MINIMUM TIME HEADWAY
the elapsed time between the collision of the two consecutive vehicle.
Must be greater than PRT (2.5s)
$time\ headway\ \left(s/veh\right)\ =\ \frac{3600\ \left(s/hr\right)}{capacity\ \left(v/hr\right)}$
Must be greater than PRT (2.5s)
$time\ headway\ \left(s/veh\right)\ =\ \frac{3600\ \left(s/hr\right)}{capacity\ \left(v/hr\right)}$
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Traffic Analysis
PEAK HOUR FACTOR
(PHF)
PEAK HOUR FACTOR
(PHF)
It indicates how consistent traffic volume is during the peak hour.
$PHF\ =\ \frac{PHV}{\left(\frac{60}{time\ range}\right)\ V_{(max\ vol.)}}$
$PHF\ =\ \frac{PHV}{DHV}$
$PHF\ =\ \frac{PHV}{\left(\frac{60}{time\ range}\right)\ V_{(max\ vol.)}}$
$PHF\ =\ \frac{PHV}{DHV}$
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Traffic Analysis
PEAK HOUR VOLUME
(PHV)
PEAK HOUR VOLUME
(PHV)
the total volume of vehicles per hour
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Traffic Analysis
DESIGN HOURLY VOLUME
(DHV)
DESIGN HOURLY VOLUME
(DHV)
$DHV= \dfrac{60}{t} \left(V_{max.\ vol.}\right)$
the maximum volume of vehicles per hour
the maximum volume of vehicles per hour
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CONCEPT
COMPARISON
of
SPACE MEAN SPEED
and
TIME MEAN SPEED
COMPARISON
of
SPACE MEAN SPEED
and
TIME MEAN SPEED
${\ u}_s\ <\ {\ u}_t\ $
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CONCEPT
SPEED-DENSITY MODEL
SPEED-DENSITY MODEL
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CONCEPT
FLOW-DENSITY MODEL
FLOW-DENSITY MODEL
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CONCEPT
FLOW-SPEED MODEL
FLOW-SPEED MODEL
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Accident Analysis
Determine
Conflict Points
Determine
Conflict Points
Conflict Points- The points in an intersection where crashes can happen.
The conflicts may happen as any kind of the maneuvers.
The conflicts may happen as any kind of the maneuvers.
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Accident Analysis
Sample
Intersections
Sample
Intersections
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Accident Analysis
Sample
Interchange
Sample
Interchange
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Accident Analysis
CONCEPT
Channelization
CONCEPT
Channelization
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The use of secondary roads or definite paths of travel in intersection
to facilitate orderly movements traffic from main traffic streams
to facilitate orderly movements traffic from main traffic streams
- Flyover
- Intersection
- Channelization
- Interchange
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Accident Analysis
ACCIDENT RATE per
MILLION ENTERING VEHICLES
(MEV)
ACCIDENT RATE per
MILLION ENTERING VEHICLES
(MEV)
$\frac{accident\ rate}{1,\ 000,\ 000}=\ \frac{no.\ \ of\ accidents\ }{ADT\bullet365\bullet\ (no.\ \ of\ yrs)}$
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Accident Analysis
ACCIDENT RATE per
HUNDRED MILLION VEHICLES MILES
(HMVM)
ACCIDENT RATE per
HUNDRED MILLION VEHICLES MILES
(HMVM)
$\frac{accident\ rate}{100,\ 000,\ 000}=\ \frac{no.\ \ of\ accidents\ }{ADT\bullet365\bullet\ (no.\ \ of\ yrs)\ \left(span\right)}$
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Accident Analysis
RATE of ALL ACCIDENTS
RATE of ALL ACCIDENTS
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Accident Analysis
RATE of FATAL ONLY
RATE of FATAL ONLY
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Accident Analysis
RATE of INJURY ONLY
RATE of INJURY ONLY
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Accident Analysis
SEVERITY RATIO
SEVERITY RATIO
$S.R.=\ \frac{fatal\ +\ injuries}{fatal\ +\ injuries\ +damage\ \ }$
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Crash Prevention Measure
Crash Reduction Factor
(CRF)
Crash Reduction Factor
(CRF)
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The cumulation of units that will be going through some sort of service
- Queue
- Traffic Intensity
- Service Rate
- Arrival Rate
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The inflow of traffic in a highway service,
such as toll booths or checkpoints.
such as toll booths or checkpoints.
$Arrival\ Rate\ (\lambda)$
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The outflow of traffic in a highway service,
such as toll booths or checkpoints.
such as toll booths or checkpoints.
$Departure\ $
or
$Service\ Rate\ (\mu)$
or
$Service\ Rate\ (\mu)$
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The ratio between the arrival and departure rate. This is also the probability that the service is occupied at any moment.
$Traffic\ Intensity\ (I)$
$I=\ \frac{\lambda}{\mu}$
$I=\ \frac{\lambda}{\mu}$
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Queues where the intensity is greater than 1.0
$I\ >\ 1.0$
$I\ >\ 1.0$
Oversaturated Queues
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Queues where the intensity is equal to 1.0
$I\ =\ 1.0$
$I\ =\ 1.0$
Saturated Queues
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Queues where the intensity is less than 1.0
$I\ <\ 1.0$
$I\ <\ 1.0$
Undersaturated Queues
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Traffic Flow Models
Poisson's Distribution
Poisson's Distribution
models the flow of vehicles in a segment (observed uniformity of units)
$P\left(x=n\right)\ =\ \frac{e^{-\lambda} \bullet \lambda^n}{n!}$
$P\left(x=n\right)\ =\ \frac{e^{-\lambda} \bullet \lambda^n}{n!}$
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Traffic Flow Models
Poisson's Distribution Sample
Poisson's Distribution Sample
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Traffic Flow Models
Exponential Distribution
Exponential Distribution
models the time headway of vehicles in a segment (observed uniformity of units).
$P\left(T>\ t\right)\ =\ e^{-\lambda\ t}$
$P\left(T>\ t\right)\ =\ e^{-\lambda\ t}$
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Traffic Flow Models
Exponential Distribution Sample
Exponential Distribution Sample
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Traffic Flow Models
Queue Modeling Notations
Queue Modeling Notations
$\left\langle\begin{matrix}Arrival\ \\Time\ \\\end{matrix}\middle|\begin{matrix}Departure\ \\Time\ \\\end{matrix}\middle|\begin{matrix}No.\ of\ \\Lanes\\\end{matrix}\right\rangle$
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Traffic Flow Models
Queue Modeling Concept
Queue Modeling Concept
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Traffic Flow Models
M/D/1 MODELING
Number or Length of Vehicles
in a Queue
M/D/1 MODELING
Number or Length of Vehicles
in a Queue
common unit is veh
$m\ =\ \frac{I^2}{2\ \left(1-I\right)}$
$m=\ n\ I$
$m\ =\ \frac{I^2}{2\ \left(1-I\right)}$
$m=\ n\ I$
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Traffic Flow Models
M/D/1 MODELING
Total Number or Length of
Vehicles in a Service
M/D/1 MODELING
Total Number or Length of
Vehicles in a Service
common unit is veh
$n\ =\ \frac{I}{2\ \left(1-I\right)}$
$n\ =\ \frac{I}{2\ \left(1-I\right)}$
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Traffic Flow Models
M/D/1 MODELING
Average Waiting Time
of vehicle
M/D/1 MODELING
Average Waiting Time
of vehicle
common unit is min/ veh
$w\ =\ \frac{I}{2\mu\ \left(1-I\right)}$
$w\ =\ \frac{I}{2\mu\ \left(1-I\right)}$
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Traffic Flow Models
M/D/1 MODELING
Total Delay
M/D/1 MODELING
Total Delay
common unit is min/ veh
$t\ =w\ +\ \frac{1}{\mu}\ $
$t\ =\frac{2\ -I}{2\mu\ \left(1-I\right)}$
$t\ =w\ +\ \frac{1}{\mu}\ $
$t\ =\frac{2\ -I}{2\mu\ \left(1-I\right)}$
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Traffic Flow Models
M/M/1 MODELING
Number or Length of Vehicles
in a Queue
M/M/1 MODELING
Number or Length of Vehicles
in a Queue
common unit is veh
$m\ =\ \frac{I^2}{\left(1-I\right)}$
$m=\ n\ I$
$m\ =\ \frac{I^2}{\left(1-I\right)}$
$m=\ n\ I$
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Traffic Flow Models
M/M/1 MODELING
Total Number or Length of
Vehicles in a Service
M/M/1 MODELING
Total Number or Length of
Vehicles in a Service
common unit is veh
$n\ =\ \frac{I}{\ \left(1-I\right)}$
$n\ =\ \frac{I}{\ \left(1-I\right)}$
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Traffic Flow Models
M/M/1 MODELING
Average Waiting Time
of vehicle
M/M/1 MODELING
Average Waiting Time
of vehicle
common unit is min/ veh
$w\ =\ \frac{\lambda}{\mu\ \left(\mu-\lambda\right)}$
$w\ =\ \frac{\lambda}{\mu\ \left(\mu-\lambda\right)}$
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Traffic Flow Models
M/M/1 MODELING
Total Delay
M/M/1 MODELING
Total Delay
common unit is min/ veh
$t\ =\frac{1\ }{\mu-\lambda}$
$t\ =\frac{1\ }{\mu-\lambda}$
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The distance required for a driver to stop a vehicle after seeing an object in the vehicle's path without hitting
the object. This distance is the sum of the distance travelled during perception reaction-time (lag distance) and during braking (braking distance).
the object. This distance is the sum of the distance travelled during perception reaction-time (lag distance) and during braking (braking distance).
- Stopping Sight Distance
- Braking Distance
- Horizontal Sight Distance
- Full Braking Distance
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STOPPING SIGHT DISTANCE
(SSD)
Concept
Level Terrain
(SSD)
Concept
Level Terrain
$SSD=vt+\ \frac{v^2}{2gf}$
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STOPPING SIGHT DISTANCE
(SSD)
Concept
Level Terrain
(SSD)
Concept
Level Terrain
$SSD=vt+\ \frac{v^2}{2gf }$
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STOPPING SIGHT DISTANCE
(SSD)
Concept
Uphill Terrain
(SSD)
Concept
Uphill Terrain
$SSD=vt+\ \frac{v^2}{2g\left(f+G\right)}$
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STOPPING SIGHT DISTANCE
(SSD)
Concept
Downhill Terrain
(SSD)
Concept
Downhill Terrain
$SSD=vt+\ \frac{v^2}{2g\left(f-G\right)}$
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INTERMEDIATE SIGHT DISTANCE
(ISD)
(ISD)
$ISD=2\ (SSD)$
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The distance required for a driver to complete a passing maneuver
without colliding an opposing vehicle and cutting off the passed vehicle
without colliding an opposing vehicle and cutting off the passed vehicle
- Stopping Sight Distance
- Braking Distance
- Overtaking Sight Distance
- Passing Sight Distance
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Sight Distance in
HORIZONTAL Curves
$S<L\ $
HORIZONTAL Curves
$S<L\ $
$M=\ \frac{S^2}{8R}$
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Sight Distance in
HORIZONTAL Curves
$S>L\ $
HORIZONTAL Curves
$S>L\ $
$M=\ \frac{L\ \left(2S-L\right)}{8R}$
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Sight Distance in
VERTICAL SUMMIT Curves
$S<L\ $
VERTICAL SUMMIT Curves
$S<L\ $
$L=\ \frac{{AS}^2}{200\ \left(\sqrt{h_1}+\sqrt{h_2}\right)^2}$
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Sight Distance in
VERTICAL SUMMIT Curves
$S>L\ $
VERTICAL SUMMIT Curves
$S>L\ $
$\ \ L=2S-\frac{200\ \left(\sqrt{h_1}+\sqrt{h_2}\right)^2}{A}$
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Sight Distance in
VERTICAL SUMMIT Curves
California Standard
Appearance Criterion
VERTICAL SUMMIT Curves
California Standard
Appearance Criterion
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Length of Curve in
VERTICAL SAG Curves
Design Velocity of Vertical
Curves for Comfort
VERTICAL SAG Curves
Design Velocity of Vertical
Curves for Comfort
$L=\frac{A\ v_{(kph)}^2}{395}$
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HeadLight Sight Distance in
VERTICAL SAG Curves
$S<L\ $
VERTICAL SAG Curves
$S<L\ $
$L=\ \frac{{\rm AS}^2}{120+3.5S}$
$L=\ \frac{{\rm AS}^2}{200\ \left(h_1+S\tan{\beta}\right)}$
$L=\ \frac{{\rm AS}^2}{200\ \left(h_1+S\tan{\beta}\right)}$
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HeadLight Sight Distance in
VERTICAL SAG Curves
$S>L\ $
VERTICAL SAG Curves
$S>L\ $
$L=2S-\frac{120+3.5S}{A}$
$L=2S-\frac{200\ \left(h_1+S\tan{\beta}\right)}{A}$
$L=2S-\frac{200\ \left(h_1+S\tan{\beta}\right)}{A}$
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Underpass Sight Distance in
VERTICAL SAG Curves
$S<L\ $
VERTICAL SAG Curves
$S<L\ $
$L=\ \frac{{AS}^2}{800C}$
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Underpass Sight Distance in
VERTICAL SAG Curves
$S>L\ $
VERTICAL SAG Curves
$S>L\ $
$L=2S-\ \frac{800C}{A}$
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Vertical Curve
RADIUS of CURVATURE
RADIUS of CURVATURE
$r=\ \frac{L}{\left|g_1\right|+\left|g_2\right|}$
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PAVEMENT DESIGN
RIGID PAVEMENT
WITHOUT DOWELS
RIGID PAVEMENT
WITHOUT DOWELS
$t=\ \sqrt{\frac{3W}{f}}$
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PAVEMENT DESIGN
RIGID PAVEMENT
WITH DOWELS @
SHOULDER EDGE
RIGID PAVEMENT
WITH DOWELS @
SHOULDER EDGE
$t=\ \sqrt{\frac{3W}{2f}}$
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PAVEMENT DESIGN
RIGID PAVEMENT
WITH DOWELS @
MIDDLE/CENTER EDGE
RIGID PAVEMENT
WITH DOWELS @
MIDDLE/CENTER EDGE
$t=\ \sqrt{\frac{3W}{4f}}$
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PAVEMENT DESIGN
RIGID PAVEMENT
SPACING of DOWELS
SAMPLE
RIGID PAVEMENT
SPACING of DOWELS
SAMPLE
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PAVEMENT DESIGN
FLEXIBLE PAVEMENT
FINDING THE THICKNESS
FLEXIBLE PAVEMENT
FINDING THE THICKNESS
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PAVEMENT DESIGN
FINDING THE THICKNESS
using
CALIFORNIA BEARING RATIO
FINDING THE THICKNESS
using
CALIFORNIA BEARING RATIO
$t=\ \sqrt W\ \left(\frac{1.75}{CBR}-\frac{1}{P\ \pi}\right)^{0.5}$
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PAVEMENT DESIGN
FINDING THE THICKNESS
using
PLATE BEARING TEST
FINDING THE THICKNESS
using
PLATE BEARING TEST
$t=K\log{\left(\frac{P}{S}\right)}$
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STIFFNESS FACTOR of PAVEMENT
$ST=\ \sqrt{\frac{E_b}{E_p}}$
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TRAFFIC INDEX RATIO
$TI\ =1.35\ \left(EWL\right)^{0.11}$
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SHRINKAGE FACTOR
$S.F. =\dfrac{∆H}{H_0}=\dfrac{∆e}{1+e_0}$
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MODULUS of SUBGRADE REACTION
$S.R.\ =\ \frac{stress}{deflection}$
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FINESS MODULUS
$F.M.\ =\ \frac{\sum CVR}{m_T}$
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CENTRIFUGAL RATIO
or
IMPACT FACTOR
or
IMPACT FACTOR
$CR\ =\ \frac{CF}{W}\ =\ \frac{v^2}{g\ R}$
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CENTRIFUGAL FORCE
$CF\ =\ \frac{{W\ v}^2}{g\ R}$
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BRAKING TIME
$t_b\ =\ \frac{v}{g\ \left(f\ \pm\ G\right)}$
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ASPHALT MIX
Absolute Specific Gravity of Mix
Absolute Specific Gravity of Mix
$\frac{100}{G_{b-mix}}=\ \sum\frac{P_{materials}}{G_{materials}}$
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$G_{b-mix}=\ \frac{P_1+P_2+P_3}{\frac{P_1+P_2+P_3}{G_1+G_2+G_3}}$
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$G_{b-mix}=\ \frac{P_1+P_2+P_3}{\frac{P_1+P_2+P_3}{G_1+G_2+G_3}}$
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ASPHALT MIX
Percent air voids in aggregates
/ mineral aggregates
Percent air voids in aggregates
/ mineral aggregates
$V_{MA}=\ 1-\frac{G_c}{G_b}\ P_{agg}$