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Traffic Engineering: Course Outline

1. Traffic Engineering Elements(a) Vehicle(b) Driver(c) Way(d) Terminal(e) Control

2. Traffic Characterization(a) Speed, Flow, Density, Occupancy(b) Fundamental relation(c) Data collection

3. Fundamental of Uninterrupted Traffic Flow(a) Microscopic and macroscopic flow characteristics(b) Microscopic and macroscopic speed characteristics(c) Microscopic and macroscopic density characteristics(d) Microscopic models (longitudinal control, lateral control, etc.)(e) Macroscopic models (single regime, multiple regime, etc.)(f) Model calibration (digression into basics of regression analysis)(g) Principle of capacity and level-of-service analysis of expressways

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4. Fundamental of Interrupted Traffic Flow(a) Shockwaves(b) Flow at signalized intersections

i. Flow characteristicii. Delay and queue analysisiii. Data collection related issuesiv. Principles of capacity and level-of-service analysis of signalized intersections

(c) Flow at unsignalized intersectionsi. Flow characteristicii. Delay and queue analysisiii. Data collection related issuesiv. Principle of capacity and level-of-service analysis of unsignalized intersections

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5. Design of Traffic Facilities(a) Freeways (expressways)(b) Intersections

i. Unsignalized intersections • Use of static control signs• Channelization• Auxiliary lane lengths• Rotaries

ii. Signalized intersections • Warrants• Types and concepts • Cycle length• Phase lengths• Signal coordination

iii. Interchanges • Warrants• Types

(c) Parking facilities(d) Road signs(e) Street lighting

6. Simulation of Traffic Streams

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Microscopic vs Macroscopic Characteristics of Traffic Flow

Microscopic: Study of the behaviour of individual units in the system.Macroscopic: Study of the behaviour of group of units in the system.

Density ratesDistance headway Density

Average speedsIndividual speedsSpeed

Flow rateTime headwayFlow

Macroscopic MicroscopicTraffic characteristics

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5

• Shape of time headway distribution varied considerably as the traffic flow rate increased due

to increased interaction between vehicles in the traffic stream

• i.e. under low flow very little interaction between vehicles and time headway appears to be

somewhat random

• As the flow approaches to the capacity, almost all the vehicles are interacting and are in car-

following process. In this process all the time headway are approximately constant.

Microscopic Flow Characteristics: Study of Headway Distribution

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Microscopic Flow Characteristics: Study of Headway Distribution

Pertinent observations:• Individual headways are hardly ever less than some

minimum (e.g. 0.5 sec.).• Individual headways (at reasonable flow rates) are

hardly ever greater than some value (e.g. 10 sec.).• Certain observation about the distribution properties:

– mode < median < mean– The distribution varies considerably with flow.– The mean time headway tracks the 67

cumulative percentile curve for the entire flow rate range.

– The ratio of standard deviation to the mean time headway approaches 1 under low flow conditions but decrease continuously as the minute flow rate increase.

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7

No interactions, random arrivalsLarge interactionsIntermediate interactions

Random Arrivals:Generally such arrivals follow the Poisson distribution

Headway Classification

!)()(

ktekP

kt λλ−

=

Now, headway h ≥ t if 0 vehicle arrive in t, then,

0>ttePthP λ−==≥ )0()(

λ1

=tλ is average arrival rate of vehicle, so 1/ λ is the average time headway

tt

ethP−

=≥ )( 0>t

8

• The random (negative exponential) distribution has the inherent characteristics that the small headway are most likely to occur and the probability consistently decreases as time headway increases.

• At higher flow conditions distribution does not match.

• Even for the low flow level, distribution are different for the time headway groups of less than 1 second.

• Standard deviation (SD) for the measured distribution is always less than the SD of the corresponding random distribution

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9

Non Random Arrivals (Pearson Type III Distribution):The poor performance of the exponential distribution at higher volumes led researcher to search for other distributions. One such distribution is the Pearson type III distribution.

[ ] )(1)()(

)( αλαλλ −−−−Γ

= tk etk

tf

)(1)()(

αλαλ −−−−Γ

= tkk

etk

where, α is the shift parameter and k is the shape parameter (k = 1 is Poisson like and k = ∞ is uniform).

for t≥α

It may be noted here that the Pearson type III distribution also function quite well over the range of volume.

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Non Random Arrivals (Composite Models):

The composite models assume that headways follow one particular distribution for free flowing vehicle and another distribution for platooned vehicles; generally:

where,p: proportion of vehicles in free flowing condition.D1: distribution of headway for free flowing vehicles.D2: distribution of headway for platooned vehicles.

• Some people used shifted exponential for D1 and Normal for D2 to obtain P(h ≥ t); • Schuhl have used D1 as exponential distribution and D2 as shifted exponential distribution.• Dawson used shifted exponential for D1 and Erlang for D2 to obtain P(h ≥ t); this he called the

Hyper-Erlang ( or Hyperlang) distribution.

)()1()()(21

thPpthPpthP DD ≥×−+≥×=≥

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Macroscopic Flow Characteristics

Flow rate (or volume) : no. of vehicles passing a point in a given period of time usually expressed as an hourly flow rate

In this we will study the following macroscopic characteristics of flow:

(1) Traffic demand

(2) Service volume

(3) Capacity

(4) Temporal variations (PHF, design volume)

(5) Spatial variations

(6) Modal variations

Traffic Demand:

It is the flow rate at which vehicle would like to be serviced.Traffic demand = measured flow rate , if unsaturated or no congestion in upstream

tq 3600

60 =

if over saturation or congestion is encountered, then flow rate indicates only the flow rate level which can be handled not an indication of existing traffic demand

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Capacity:

This is the absolute maximum hourly flow rate that can be achieved without any regard to level of service.

Service Volume:

This is the maximum hourly flow rate at which persons or vehicles can reasonably be expected to traverse a point or short section of the lane or roadway during a give time period, under prevailing conditions while maintaining a designated level of service.

Temporal Variations:Flow varies within the year, week, day and hour. Examples of such variations are shown in following figures:

AADT: It is the total volume of vehicle traffic in both directions of a highway or road for a year divided by 365 days.

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Single peak and double peak flow pattern in a traffic flow rate variation by time of the day ???

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Relationship between short-term and hourly flows.

(Source: Minnesota Department of Transportation)

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PHF:

In design or analysis of a facility one needs to know the peak demand. However, if one designs a section for the highest minute flow rate then the design would be a massive over deign since for most of the hours it will remain unutilized. If on the other hand one designed the facility based on the hourly flow then possibly for substantial portions of the hours the design would be inadequate. One therefore needs to select a sub interval within an hour which is balance between two extremes; PHF is a factor which is calculated based on this time interval and used to translate hourly flows to peak flow rates within that hour.

{ }T

N

NPHFiTi

HT 60max ×=

; where T is in minutes, NH is hourly flow rate

Hourly flows one then divided by PHFT to get peak T – minute flow rates which one used for design.

PHF15 could vary from 0.25 (which means all the traffic within the hour posses during on 15 min period) to 1.0 (which means each 15 min. period carries the same amount of traffic).

1 2 3 4 5 6 7 8 9 10 11 60

Traf

fic v

olum

e (v

eh/m

in)

Minutes of the hour

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30th Rank of hours

Hou

rly fl

ow

Design Hour Volume:

Similarly, over the year the hourly volume varies significantly. One generally uses the 30th

higher hourly volume as the design hourly volume. Experience has shown that this value is generally around 10% to 12% of the Average Annual Daily Traffic.

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Spatial Variation:

Although there are directional variations, radial variations and network variations of flow, one of the most interesting aspects of spatial variation is the lane volume variation on multilane facilities. The following figures gives an interesting data on this. (This type of variations are important to study because they affect the analysis of ramp site selection, etc.)

Modal Variation:

This relates to studies aimed at studying the distribution of different modes on any given facility. Design implications relates to pavement design, number of lane determinations, etc.

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Flow rate or volume measurement

• Annual average daily traffic (AADT): total annual volume of traffic passing a roadside point over a period of one year, divided by number of days in a year.

• Highest hourly volume (HHV): It is the highest volume to occur in a one hour period for the particular road.

• Average daily traffic (ADT): It is simple the average daily traffic volume calculated from a survey which extends over a number of days.

• Peak hour volume (PHV): It is the maximum traffic count observed in any 60min. Interval during a day.

Choice between manual or automatic techniques depends on following factors:

• Duration of survey

• Nature of survey (straight count vs classified counts

• Available resources i.e. budget constraints, field staffs or equipments

• Climatic factors etc.

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Automatic counting• Axle detectors• Vehicle detectors

Axle detectors:

where NV = number of vehiclesCF = correction factor

APC x CFNV =

2count Axlecountpair axleAPC ==

CF = Total (manual or automatic) vehicle count"axle pair" count

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Vehicle counters• Inductive loop detectors

– Magnetic imaging sensors

Magnetic imaging sensors• Sensitive to the weak earth magnetic field• Measures the distortions in earth’s field caused by a vehicle passing over or

near the sensor.• Can work in all weather conditions• Should be placed such that vehicle passing in the neighbouring lane should

not counted• Does not work if lane discipline is poor.

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Moving observer method:• Low cost method to determine the volume and density of the traffic stream

wpM

B

A

L

woM

apM

aoM

No. of vehicles that overtake the test vehicle when test vehicle is moving with the stream

No. of vehicles that overtake the test vehicle when test vehicle is moving against the streamNo. of vehicles that the test vehicle overtakes when test vehicle is moving with the stream

No. of vehicles that the test vehicle overtakes when test vehicle is moving against the stream

vw

va

Divide the stream into two parts: k1, u1 and k2, u2

assume that u1< vw < u2

wwwo tvvkM )( 22 −=

wwwp tvvkM )( 11 −=

wwwwwwwp

wo

ww tvktvktvktvkMMM 111222 +−−=−=

wwwwwwww tvkktqqtvkktvkvkM )()()()( 2121212211 +−+=+−+=

wwwww tkvqtM −=

0=apM

aaaaaaaao tkvqttvvktvvkM +=+++= )()( 2211

0−+=−= aaaap

ao

aa tkvqtMMM

aw

aa

ww

ttMMq

++

=wwaa tvtv =Q

Along the traffic

Against the traffic

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Microscopic Speed CharacteristicsTwo aspects are of primary importance while studying microscopic speed characteristics:

1. Speed Trajectories

2. Speed Distributions

The importance of speed trajectories under different geometries and traffic phenomenon are

important in designing traffic facilities.

Knowledge of speed distribution are important primarily from simulation stand point.

In the following we discuss theses two topics:

Speed Trajectories:

1. Curves and grades:

The speed on curves is more often than not lesser than the speed on straight stretches. The reason for this is that on curves drivers feel a centrifugal force which causes them to reduce the speed. Again the trajectory followed by drivers may be dependent on a variety of factors:

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(i) The desirable deceleration

(ii) The extent of the transition curve

(iii) The radius and super elevation of the curve

On grades (upgrades) heavier vehicles tends to slow down. Generally, for the grades encountered, there is little or no effect on passenger vehicles, but there is considerable effect on heavy vehicle. Two factors affects the performance of heavy vehicles:

(i) The grades(ii) The length for which the

grade is present

Typically speed trajectories on

upgrades are shown in figure.

Assumption: Speed at a distance of 0 ft is 0 km/hr.

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2. Passing zones:

Drivers generally follow a pattern of deceleration acceleration during overtaking. Knowledge of such behaviour is important from sight distance considerations and making of no-passing zones.

Speed Distributions:

Generally, normal distribution are used to model speed distribution.

The normal distribution has two parameters µ and σ. These parameters can be estimated from the sample by:

∑=

=−−

=

=N

i

i

Nuus

u

1

22

2

1)( σ

μSample mean,

Sample variance,

setting,

where, ui are individual data points and N is the Total number of data points.

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Digression:

If a frequency distribution is given:

∑=

=g

i

ii

Nufu

1

1

1)(2

1 1

2

2

−⎭⎬⎫

⎩⎨⎧

−=∑ ∑= =

N

ufN

ufg

i

g

iiiii

σ

2

2

2)(

21)( σ

μ

πσ

−−

=iu

i eufNote, N~(µ, σ) the pdf

where ui is the mid point of the group i

In developing a frequency distribution one may use I as the size of the class interval where Iis given by Sturges as

I= Range of observed data / (1+ 3.322 log10N)

where N is the total number of data points.

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Microscopic Speed CharacteristicsCertain concepts related to microscopic speed characteristics are:

(i) Free flow speed (relation to design speed)

(ii) Optimal speed

(iii) Time mean speed

(iv) Space mean speed

(v) Temporal variations

(vi) Spatial variations

(vii) Modal variations

Free Flow Speed, uf :

This is speed at which vehicles (or average speed at which vehicles) travel when driving

independently on the road (or at very low flow condition).

This speed is related to four factors:

(i) The geometry of the road

(ii) The surface conditions

(iii) Driver attitude, and

(iv) Vehicle performance characteristics

Of course there exists a finite value of this speed.

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Optimal Speed, u0 :

This is the speed (stream speed) at which the flow is maximal. As we will see later, there exists a relationship between speed and flow.

Generally this speed is much lower than uf .

Time Mean Speed :

Arithmetic average of the spot speed, ui

Nu

u it∑=

Space Mean Speed :

∑=

i

s

uN

u 111

s

sst u

uuu2σ

+=

Reciprocal of the harmonics mean

As we will see later on all macroscopic relations us should be used rather than ut

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Temporal Variations:

Average speeds at a given location vary with time primarily because flow varies. The speeds

also vary because

(i) Vehicle mix

(ii) Driver mix

(iii) Light varies

(iv) Weather varies

The following points may be noted here:

(i) As flow increases, speeds generally fall (slowly at first and then steeply)

(ii) As the percentage of the heavy vehicles increases, speed falls

(iii) As the percentage of non-commuting driver increases, speed generally falls

(iv) The effect of light and weather are obvious.

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The left lane speeds on and average are 4 mph higher than the average speed, middle lane is approximately equal to the average speed and right lane is about 3 to 4 mph below the average speed.

Longitudinal variations primarily occur due to geometric variations along the road and the presence of traffic control measures. The effect are quite obvious and do not need further elaboration.

Spatial Variations:

Speeds vary transversely and longitudinally across the highway.

Transverse variations are mainly from lane to lane. Generally, (under US conditions) the left lane has the highest average speed and the right most lane has the lowest average speed. These differences are, however, most apparent when flow is low; in congested situation speed is almost same on all the lanes.

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Modal Variations:

Modal variation are not prominent on level or even marginally rolling terrains. However, the difference become apparent on long sustained grades. The differences appear due to vehicle performance limitations.

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• Indirect measurement• Direct measurement

Indirect measurement:• Single detector speed measurement

– Speed is measured based on time taken by the vehicle to pass over an detector, here it is assumed that vehicle length is known

• Dual detector speed measurement:– enoscopes

Speed measurement

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Direct measurement:• Using radar gun:

– Based on doppler effect– In doppler effect, the change in frequency of a signal is proportional to the

speed at which the source is moving towards or away from receiver.– Radar gun emits a microwave signal of a known frequency which is reflected

off a target and picked up by a sensor in the device. The change in frequency of signal is measured and used to estimate the speed of the target relative to receiver.

– Error (%) = 100 (1- cos θ), so error is less than 5% for the angle of incidence upto about 150.

– Drawbacks: • Vehicle must be present in the transmitted beam for a finite period of time (about two seconds)

for a reading to be obtained this can create problem while operating on short range settings depending on the speed of vehicles

• Lower speed (<15 km) cannot be accurately measured

Speed measurement

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• Using laser gun:– Based on measuring time of flight of very short pulses of infrared.– It fires two pulses with a known time apart and based on travel time distances

(or positions) of vehicle at both time are determined.– Change in distance, divided by time interval between pulses, gives the speed of

the target.– In practice, this approach is more complex involving many pulses of light.– Speed measure from laser gun does not effected by vibrating objects– It can measure the speed of even stationary objects.

Speed measurement

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Microscopic Density Characteristics

This basically relates to studies on distance headways and its effect on driving (car-following).

Time headway rather than distance headway is more often used because the greater ease of measuring time headway.

Distance headway can be obtained photographically. However, it is more often obtained by calculation based on time headway.

Distance headway = time headway X speed

There is no point in studying their distributions as one does not use them in studies of any type.

Macroscopic Density Characteristics

Density: no. of vehicle occupying a unit length of road.

Optimum density: It is the density level that exists when the lane of traffic is flowing at capacity.

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Density measurement• By aerial photography

•Much costly and cumbersome

• By input-output study to determine the no. of vehicles in a certain section and divide that by length of section to compute the average density.

•Cost effective

•Need to count the no. of vehicle present in the section intially

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Presence type detector• Determine the duration for which the detectors are occupied by vehicles.• Based on this occupancy time density can be calculated.

Vl

Dl Dl

T = a T = b

Assume a vehicle of average length Vl on an average spends a time t0 .

Average speed0tDVu ll +=

uDVt ll +=0

uDVNNtT ll +== 00

Note here average speed is space mean speed as average is based on average travel time.

If total N vehicle pass over the detector in a time period T and if the sum of the occupancy times of the vehicles is T0

If the fraction of time the detector is occupied,uT

DVNTTOc ll +== 0

TNq = )( ll

ll DVku

DVqOc +=+

=

ll DVOck+

=

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q-k and q-u relations:

The general idea on q-k and q-u relation are:

Flow

Spee

d

q max

u f

u 0

Density

Flow

k j

q max

k 0

The quantity qmax is the capacity of the facility for which the above figure is drown.

However, more recent understanding of the relation acknowledge that it is very difficult to represent the congested regime through a single relationship; there exists a jump around the qmax and that slopes on the u-q curve in the free regime is quite flat.

Flow

Spee

d

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Capacity and Level of Service of Basic Freeway (Expressway) Sections

Basic Freeway Section: Section of the of the roadway where interruption to traffic flow are either absent or inconsequential. A freeway is defined in HCM as “a divided highway facilities having two or more lanes for the exclusive use of traffic in each direction and full control of access and egress”.

Ideal Capacity: Maximum number of passenger-cars that can expected to cross a point or line on an ideal road in a unit interval of time. Ideal road section is one which has ample width (at least 3.5 m wide lanes), wide paved shoulders (al least 1.8 mm wide) and zero gradient.

Level-of-service: Prevailing condition under which driver has to drive.LOS is divided into six classes from LOS (A) to LOS (F).

LOS(A): driving condition is the best; traffic is moving in free flow condition, driver faces absolutely no hindrance from other vehicles on the road, driver is able to choose his/her speed.

LOS (F): Driving condition id the worst, traffic is moving in extremely forced-flow condition, there are frequent stops, driver is absolutely constrained by other vehicles on the road, driving is very taxing, and so forth.

Refer : IRC codes: IRC:64-1990 and IRC:106-1990; Highway Capacity Manual

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Capacity Analysis

Flow

Spee

d

q max

u 0

Flow

Spee

d

Traditional views on u-q relation Modern views on u-q relation

However, more recent understanding of the relation acknowledge that it is very difficult to represent the congested regime through a single relationship; there exists a jump around the qmaxand that slopes on the u-q curve in the free regime is quite flat.

There exists a speed, u0, where flow is maximum or reaches its full capacity.

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Capacity Analysis

Behaviour of driver changes:

• When lane widths are narrow.

• When shoulders are narrow.

• When drivers are unfamiliar with the region. (this difference is visible in weekdays traffic and weekend traffic)

Values of qmax changes when traffic stream has heavy, slow moving vehicles.

Reason for change in behaviour of drivers may be their safety concerns.

• Determine the capacity of road under ideal condition?

• Determine the capacity of road when the actual conditions are different from ideal condition?

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IRC Method/ Old HCM method

Where

ci = ideal capacity in passenger car units per hour

fwl = factor to modify the ideal capacity for a non-ideal lane and shoulder widths (it is less than 1)fhv = factor to modify the ideal capacity due to presence of non-passenger cars (it is generally less

than 1)fp = factor which depends on the proportion of non-commuting driversN = no. of lanes

phvwli ffNfcc =

IRC codes does not provide any value for capacity of the roads, however, it gives the volumes at particular LOS for different type of road classes

fwl factors has been given for only two-lane rural roads, no documentation for multilane facilities. IRC ignores the effect of non-commuters on capacity.

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New HCM method

Step 1: Determine the prevailing conditions of the road in terms of lane width, no. of lanes, shoulder lane and no. of interchanges.

Step 2: Estimate the ideal free-flow speed of the road section based on the type of area the road goes through (i.e. expressway in rural or urban area has different free-flow speeds) .

Free-flow speed values

Capacity values

Flow (pcphpl)

u

New HCM method suggests capacity values based on the free-flow speed in actual driving conditions.

Step 3: Determine the reduction in free-speed due to lane width, shoulder width, no of lanes, no. of interchanges.

Step 4: Sum up all the reduction and subtract the sum from the ideal free-flow speed.

Step 5: Based on free-flow, determine the capacity from above figure in pcphpl.

Effect of vehicle mix and driver population is incorporated in conversion of the existing traffic volume from vehicles/hr to an equivalent no. of passenger cars/hr.

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F

A B C D E

u1

u2

u3

k=k1 k=k2 k=k3 k=k4

k=k5

u

q, (in pcphpl)

Level-of-service, LOS

Level-of-service (LOS) offerred by a particular express-section at a given time is dependent on:

(i) Demand at that time

(ii) Capacity of the road.

To convert the volume, q, in veh/hr to hour peak flow rate f in pcphpl

phv ffNPHFqf

×××=

Calculate the free-flow speed for that road as suggested previously.

From given figure get the LOS corresponding to u and q

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Interrupted Traffic FlowShock Waves

Whenever two streams with different u-k conditions meet a shockwave generated at the meeting point. The wave may travel forward, backward or be stationary.

Before going into the details of determining the velocity of the shock wave, let us try to see what it is through the study of following scenario.

Scenario:

A truck enters a traffic stream (originally traveling at uA, kA ) slows it down to a speed of uB. The truck travels on the road for T seconds and then exits. The vehicles then start speeding up. Let us see this case in greater detail:

Platoon formation due to entry of truck

Incr

easi

ng ti

me

B A

B AB

BB

BB

B

A

AA

AA

A

Truck

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45

Distance-time diagram illustrating the creation and movement of shock waves

Dis

tanc

e

Time

Truck

qA, kA, uA

qB, kB, uB

qC, kC, uC

shockwave 1

shockwave 2

shockwave 3

shockwave 4

shoc

kwav

e 5

46

Speed of shockwaves:

;11 wr uuu −=

;22 wr uuu −=

speed of vehicle in region (A) relative to S

speed of vehicle in region (B) relative to S

In time t the distance by which region (A) crosses S is tur ×1

Similarly in time t the distance by which region (B) crosses S is tur ×2

Number of vehicle from region (B) crossing S is 22 ktur ××∴From conservation of vehicles:

Number of vehicle from region (A) crossing S is 11 ktur ××∴

1122 ktuktu rr ××=××

1122 )()( kuukuu ww −=−or

or )( 121122 kkukuku w −=−

12

12

12

1122

kkqq

kkkukuuw −

−=

−−

=or

shockwave, Sspeed= uw

(A) (B)1k2k

1u2u

at time = 0

(A) (B)1k2k

1u2u

shockwave, Sspeed= uw

at time = 0 + t

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47

If q1 and q2 , and k2 and k1 are nearly equal then in the limit we can write:

dkdquw =

Note that the speed of the is basically the slope of the line joining the two flow and density conditions on a q-k plot.

k

q

q 1

k 1

q 2

k 2

(2)

(1)slope of this line is u w

• Forward moving shock wave

• Stationary shock wave

• Backward moving shock wave

K1< k2q1 > q2Backward moving shock wave

k1 = k2q1 = q2Stationary shock wave

k1 < k2q1 < q2Forward moving shock wave uw = +ve

uw = 0

uw = -ve

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For swAA: qB = 0; qA = q1

kB = 0; kA = k1

For swBB: qB = q1; qA = q2kB = k1; kA = k2

B A

B A

B

BB

BB

B

A

A

A

AA

A

t = 0

1

2 1

123

3 124

q = 0, k = 0

q = q1, k = k1q = q2, k = k2

Platoon formation Truck

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49

Problem session on shockwave:Problem 1:

Traffic is moving on a one way road at q1=1000 vph, k1, density=16 vpkm and a speed (u1) of 62.5 kmph. A truck enters the stream at a speed of (u2)=16 kmph. Due to decreased speed the density behind the truck increases to 75 vpkm. After 10 minutes the truck exits the steam. The platoon then releases itself and starts to flow at capacity (qmax) conditions (qmax=1400 vph, k0=44 vpkm). Determine the speed of all shockwaves, the length of platoon that forms and the time it takes for the platoon to dissipate.

39.3167510007516

12

121 =

−−×

=−−

=kkqqusw km/hr

45.6754412001400

20

22 −=

−−

=−−

=kkqqu m

swkm/hr

29.14164410001400

10

13 =

−−

=−−

=kkqqu m

sw km/hr

16750

1200000

2

24 =

−−

=−−

=kqusw km/hr

82.31440

1400000

05 =

−−

=−−

=kqu m

sw km/hr

Time

Truck

q1=1000 k1=16 u1=62.5

q2=16x75 k2=75 u2=16

qmax=1400 k0=44 u0=1400/44

shockwave 1

shockwave 2

shockwave 3

shockwave 4

shoc

kwav

e 5

Dis

tanc

e

50

To find the maximum length if the one must realize that the platoon grows till the time Shockwave 2 develops.

The rate of growth of the platoon is the | relative speed | between shockwave 1 and shockwave 4.

The platoon grows at the rate of (16-3.39) kmph or 12.61 kmph.

The platoon grows unabated for 10 minutes (the duration for which the truck is there).

Hence maximum length of platoon = kms1.2601061.12 =×

(It contains vehicles)158751.21.2 2 =×=× k

The platoon dissipates at the relative velocity of shockwave 1 and shockwave 2.

Rate of dissipation = 3.39 - (-6.45) = 9.84 kmph

The time it takes the platoon to dissipate = 2.1/9.84 = 0.213 h = 12.8 minutes

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Problem 2:

For the problem 1 plot the location of the front of the platoon and rear of the platoon versus time. Choose appropriate reference frame.

Choosing distance = 0 at the point at which the truck enters and time = 0 as the time at which the truck enter the enters.

Dis

tanc

e (k

m)

Time (min)10.0 22.8

0.565

1.29

2.67

60-6.45

603.39

16

60

00

52

Problem 3:

For the problem 1 plot the length of the platoon versus time.

Leng

th o

fpl

atoo

n (k

m)

Time (min)10.0 22.8

2.1

60

-9.8412.61

60

00

27

53

Flow at Signalized Intersections

Intersection:

An Interruption is a location where three or more roads carrying traffic in different directions cross. The space which is common to all these roads is referred to as the intersection.

•Signalized intersection

•Unsignalized intersection

Flow at a signalized intersection is characterized by repeated stopping/starting of vehicles stream. Each time the light turns yellow vehicle approaching the intersection knows that the red sign is impending and they have to stop. Each time the light turns green, they realize that they cab go and initiate movement procedures.

Type of Signals

• Pre-timed: predefined fixed interval of timing

• Partially actuated

• Fully actuated

54

Flow at Signalized Intersections

Flow Characteristics:

Interruption to traffic flow at a signalize intersection is orderly and deterministic. In this interruption pattern following process become important for analysis:

• Arrival process

• Departure process

• Delay and queue analysis

Arrival process:Arrival process at intersection could be of three kind:

(i) Random arrivals

(ii) Grouped arrivals

(iii) Mixed arrivals

28

55

Random arrival:Such arrival pattern is seen on isolated intersections (i.e. no intersection is present in the vicinity, 3-4 km).In these case inter-arrival times (time headways) are often distributed more or less according to negative

exponential distribution

21)( 21HH eeHhHP λλ −=≤≤ −

!)()(k

etkNPtk

t

λλ −

==

Grouped arrival:Such arrival pattern is seen at intersections which are located close to (say < 2 km) another upstream

intersection.Arrival process seems to be uniform and vehicles can be assumed to arrive at reasonably constant headways.Vehicle released from upstream intersection reached in platoon.

Mixed arrival:Such arrival pattern is seen at intersections which are located at intermediate distances (say from 2-4 km)

another upstream intersection.It is not purely random not purely grouped. Because of large distance many of released vehicles may disperse

from platoon vehicles and come independently.

56

Departure process:If the headway were measured as vehicle entered the intersection an interesting pattern is observed. The first headway would be defined as the time between the initiation of the green signal and the first vehicle’s front bumper crossing the entry line. The second headway would be defined as the time between the first vehicle front bumper crossing the line and the next vehicle front bumper crossing the same line and so on. The pattern typically observed is:

From the above figure two features emerge: (i) the headway stabilizes to a value h referred to as the saturation headway; (ii) the initial headway are larger than h.

t1t2 t3 t4

1 2 3 4 5 6 7 8 9n, the position in the queue

head

way

(bet

wee

n th

enth

and

(n-1

)thve

hicl

e)

h

29

57

Saturation headway represents the maximum number of vehicle that can crass the intersection during the green time.

Initial headways are larger than the hs because of perception reaction time and the extra time taken to accelerate to a reasonable speed (note that later vehicles more or less achieve this speed when they cross the specified point as they start from a distance further upstream from the specified point). In the sense some time is lost due to the fact that initial vehicle takes longer time than hs . Sum of these excess times is referred as start-up lost time, ls

∑∀

−=i

sis hhl )(

The quantity is of the order of 2s. A typical data set from studies is shown in the following:

1 2 3 4 5 6 7 8 9n, the position in the queue

head

wa

y

2

1

3

4Greenshields (1942)

Later studies (1975)

58

This quantity is of the order of 1.2 to 2.8 s. Longer yellow + all red times led to longer clearance lost times.

Clearance lost time (or movement lost time) is the time between the last vehicle from one approach entering the intersection and the initiation of the green signal for conflicting movements, assuming condition in which demand is present to utilize the non-red times in both approaches.

Nearly the end of the departure process some time is also lost. This happens because invariably some part of the amber time remains unutilized because vehicles come to a rest when some part of the amber time is still remaining. This loss of time is referred as movement loss time ( or clearance loss time), lm.

Saturation flow rate is defined as the flow rate from a lane in the intersection assuming that each headway is equal to the saturation flow rate headway (hs) and green exists for the entire time period.

Hence if “hs” is the saturation flow rate headway (or saturation headway) at an intersection in seconds then s,the saturation flow rate is:

shs 3600= s is in vphgpl

30

59

However, “s” is just a theoretical quantity and what is the of prime importance is the capacity. In order to understand how the capacity is related to s consider the following example:

A given lane at a traffic signal has been observed to have the following parameter: hs=2.0 sec./veh, start-up loss time =1.5 sec., and clearance loss time=1.5 sec. The signal provides the lane with 27sec. of green, 3 sec. of yellow and 30 sec. of red during each 60 sec. cycle of the signal.

• In one hour there are cycles.

• Hence total lost time in an hour = 60 (1.5+1.5) = 180 sec.

• Time available for the movement per 60 sec. is 30 sec. Hence, in 3600 sec only 1800 sec. movement is allowed.

• Out of 1800 sec., 180 sec. is lost. Hence, time in which movement take place at 2.0 sec./veh is 1800-180=1620 sec.

• Hence, capacity of the lane is vph.

6060

3600=

8100.2

1620=

60

Delay at signalized intersections:

To study the delay at a signalized intersection let us first look at the arrival and departure process at a signalized intersection:

A(t)

R: Effective redG: Effective greenC: Cycle lengthW(i): Waiting time of the ith vehicleQ(t): Queue length at time t

Q(t)

W(i)

Cumulative arrivals, A(t)

Cumulative departure, D(t)

R G R G R G R

Cycle I Cycle II Cycle III

Veh

icle

s

31

61

Now if we assume that A(t) has a constant slope of “v”; i.e. vehicles arrive at a constant rate of v vehicles/unit time and the maximum rate at which they are discharged is “s” vehicles per unit time and if the number of vehicles that arrive during a cycle are cleared during the green period then one can easily determine the average delay an individual vehicle faces thus:

The modified diagram of A(t) and D(t) in this case is:

R GC

RC

G RC

G

D(t)A(t)Veh

icle

s

Time

62

As per previous diagram, the delay in each cycle is the same. The total delay in a cycle can be determined thus:

Time

Total delay during cycle = ∑=

*

0

i

iiW or in the continuous

approximation

Total delay during cycle = ∫*

0

i

idiW

Or, total delay = Area of Δ abd (1)

Now Wi= - (arrival time of ith vehicle – departure time of ith vehicle)

Arrival time of ith vehicle = [Note slope of A(t) is v]vi

Departure time of ith vehicle =sigC +− )( [note slope of D(t) line in the relevant portion is s]

C

g

i*

Veh

icle

s

vs

d

a b t

Wi

D(t)

A(t)

⎟⎠⎞

⎜⎝⎛ −

+−=sv

svigCWi )(∴ (2)

Now t is the time where A(t) and D(t) line meet; hence

)}({ gCtsvt −−= or)()(

vsgCst

−−

= (3)

32

63

Hence,

Total delay ( ) disv

svigCvt

∫ ⎭⎬⎫

⎩⎨⎧ −

+−=0

)(

2

222

)()(

21)()(

vsgCsv

svsv

vsgCvsgC

−−

××−

+−−

−=

vsgCsv

vsvsgC

−−

−−

−=2

2 )(21)(

{ }svsvvs

gC−

−−

= 2)(2

)( 2

[Note i* = vt ]

)(2)( 2

vsgCvs

−−

=

Now, total number of vehicles that arrive in the cycle is “vC”.

Average delay = Total delay/ Total number of vehiclesvCvs

gCsv 1)(2)( 2

×−−

=

Average delay Cs

vsgC

×−−

=)(2

)( 2(4)

64

However, equation (4) is generally written as:

Average delayCs

ssvCgC

×⎟⎠⎞

⎜⎝⎛ −

⎟⎠⎞

⎜⎝⎛ −

=12

12

2

Average delay (UD)⎟⎠⎞

⎜⎝⎛ −

⎟⎠⎞

⎜⎝⎛ −

=

sv

CgC

12

12

(5)

The average delay in equation (4) is generally termed as “uniform delay” (UD) as it is based on the assumption of uniform arrival.Note that in equation (4) v is the volume and s is the saturation flow rate.

Note that the equation (4) can be easily obtained by using 0.5 x base x height to calculation of area of the Δabd and then dividing it by “vC” – the total number of vehicle that arrive during the cycle length.

i*

a b(C-g)

Note vsgCvsvti

−−

==)(* (see previous figure)

Hence, area)(2)()()(

21 2

vsgCvs

vsgCvsgC

−−

=−−

−=

d

33

65

Compare equation (6) with equation (4).

The problem with the equation (4) and (6) is that, never, in reality vehicles arrive uniformly. There is always some stochastic variation which cause queues from one cycle to overflow into the next. This results in much larger delays especially when chances of such spill over is large. That is, when (or ) is large

gsvC

sCgv

)/(

∴ Average delayCs

vsgC

vCvsgCvs

×−−

=×−−

=)(2

)(1)(2)( 22

(6)

66

Let us study how one could estimate delay if over saturation (i.e. ) exists for a finite period of time T. It must be understood here that the over saturation is not due to stochastic disturbances but due to a hike in demand for a certain period of time. So the following analysis is completely deterministic.

Consider the following case:

Cgsv >

Time

v1

v2

v

0 T τ

Arr

ival

flow

34

67

Time0 Cg

s

T τ

ZA(t)

D(t)

yv

v2

v1

vehi

cles

In this case arrival /departure diagram would look like the following:

During 0 to τ the signal is over saturated. Let us estimate the average delay during this time. The total delay during this time will be the area shaded with dots + the area shaded with lines.

68

Now, total delay due to area shaded with lines cab easily obtained by assuming the dashed line as an arrival pattern and using the uniform delay equations.

The slope of the dashed line can be obtained by looking at any one of the small triangles.

Say if slope is σ, then sgC =σ

or sCg

=σ

Then by substituting “σ” in place of “v” in Equation 5 one would obtain on an average how much time a vehicle has to wait due to the part of the figure shaded with lines.

∴ Average delay (due to “uniform” component), ADuniform

( )

⎥⎦

⎤⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−

−=

sCgs

CgC/12

/1 2

( )gCCgC

−=⎟⎠⎞

⎜⎝⎛ −=

211

2

which is half of the red light period

(7)

To compare the average delay in the over saturation case, one has to add the average delay due to the over saturation component to the average delay due to the uniform component.

35

69

Now average delay due to over saturation component, ADosc can be obtained (note in this discussion “wait” refers to the “waiting due to the over saturation”).

Consider the vehicle that arrives at T. This vehicle has to wait for “Z” units of time (see the previous figure).

The vehicle that arrives at time = 0 has to wait 0 units of time.

The waiting time of vehicles between 0 and T the “wait” increases linearly (since “wait” is the difference between two straight lines – the A(t) line and dashed line.

Therefore average “waiting” time of vehicles arriving during 0 to T is Z

21

Now look at the vehicles which arrive between 0 and τ.

The wait time decreases from “Z” (for the vehicle that arrived at T) to 0 (for the vehicle arrive at τ).

T

“wai

t”tim

e

Z

T

“wai

t”tim

e

ZTherefore average “waiting” time of vehicles arriving during T and τ is Z

21

70

Hence, one can say that the average waiting time for all vehicle arriving during 0 to τ is Z21

Now =Zy Slope of the dashed line, σ

∴⎭⎬⎫

⎩⎨⎧

=

CgsyZ

sCg

=σNote

But ⎟⎠⎞

⎜⎝⎛ −=−=

CgsvTT

CgsvTy

∴ ⎟⎟⎠

⎞⎜⎜⎝

⎛−=

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛ −

= 1cap

vT

Cgs

CgsvT

Z whereCgscap =

∴ ⎟⎟⎠

⎞⎜⎜⎝

⎛−== 1

221

capvTZADosc (8)

Hence, average delay in the present case,

oscunifromos ADADAD +=

( )⎟⎟⎠

⎞⎜⎜⎝

⎛−+

−= 1

22/1

capvTCgCADos

36

71

Average delay, d =⎟⎠⎞

⎜⎝⎛ +

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛−

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎟⎟⎠

⎞⎜⎜⎝

⎛

+

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⎟⎠⎞

⎜⎝⎛ −

⎟⎠⎞

⎜⎝⎛ −

Cg

capv

vcap

capvv

capv

sv

CgC 52

31

2

22

65.01212

1(9)

Under the following assumptions, the delay for such stochastic arrivals have been obtained by “Webster”.

Assumptions:

(i) The number of arrivals in a given time interval has Poisson distribution and that the distribution does not change with time.

(ii) The departure headways are uniform.

(iii) ; i.e. the system is not saturated,

(iv) The system has been running long enough to have settled into a steady state.

Under there assumptions “Webster” developed a delay equation which is given as equation (7). This is the best known delay equation.

sCgv ⎟⎠⎞

⎜⎝⎛<

In reality, however more often than not arrival is not deterministic, it is stochastic as discussed earlier. One it is assumed that arrival is stochastic the previously given relation for average delay cannot be used.

72

The first term of “Webster” equation is derived Equation 4 and the second term can be obtained analytically through steady state queuing analysis and is often referred “overflow delay” or “random delay”. The third is a correction term obtained using simulation studies and generally effect a 5 to 15% reduction in the estimates of d obtained by summing the first two terms. Hence, as an approximation the third term is often omitted and the sum of the first two term is multiplied by 0.90.

There, however, exists a problem with the Webster and Webster – like models which assumes steady state conditions. They invariably over estimated the delay when v is close to

. This over-estimation is due to the fact that it assumes steady state operation which would imply that v is close to for sufficiently long period so that steady state is reached. If, in reality, such a thing happens then the delay estimates from Webster like equations would hold not be too bad. However, this high demand never exists for that long period that steady state reached. Hence, the discrepancy between mathematically obtained results and real world results.

Cgs /

Also note that Webster equation for obtaining cycle length is based on optimizing d from Equation 9.

Cgs /

37

73

Discussion:

There exists a problem with “overflow” conditions and its delay computations either through second part of the Webster’s equation or through ADosc in Equation 8. The problem with the Webster’s equation is that “steady state” is never reached while in Equation 8 the conditions assumed are fully deterministic implying that even if average is slightly less than 1 then over saturation does not exist. This implication is unrealistic because conditions are never deterministic. Hence, neither of them are good enough. In reality, the “overflow”delay should lie between the estimates obtained from Webster’s “overflow” or “random”delay components and ADosc . For ratios reasonably lesser than 1 Webster’s estimates should be followed whereas for somewhat greater than 1. ADosc should be followed. The dashed line in the following figure shows how the overflow delay estimate should look like in a real-life situation.

capv

capv cap

v

There are various versions or equations which try to estimate the dashed line behaviour. However we shall not discuss them in this class. The interested reader may refer to Mcshane and Roess (Traffic Engineering) or Hurdle’s (TRR 971) paper.

74

Example:

On an approach to a signalized intersection, the effective green time and the effective red time are 30 s each. The arrival rate of vehicle on this approach is 360 vph between 0 -120 s, 1800 vph for 120 – 240 s, and 0 vph for 240 – 420 s. The saturation flow rate for this approach is 1440 vphgpl. The approach under consideration has one lane. Assume that at time = 0 s the light for the approach has just turn red.

Q1. Plot the arrival rate of the vehicle versus time.

Q2. Assuming the arrival and departure process to be continuous, plot the cumulative number of arrival and departure versus time.

Plot of arrival rate of vehicle versus time Plot of cumulative number of arrivals and departure of vehicle versus time.

38

75

Q3. Determine the average delay to the vehicles arriving between 0 – 120 s, 120 – 240 s and 0 – 240 s.

Cycle length, C= effective red time + effective green time = 30+30 = 60 s.

Arrival rate, v, in between 0 – 120 s is 360 vph (i.e intersection is operating under unsaturated condition because s = 1440 vphgpl). Further, the arrival is deterministic and uniform. So average delay can calculated using following equation

Average delay (UD) between 0 – 120 s s

sv

CgC

10

144036012

6030160

12

122

=⎟⎠⎞

⎜⎝⎛ −

⎟⎠⎞

⎜⎝⎛ −

=⎟⎠⎞

⎜⎝⎛ −

⎟⎠⎞

⎜⎝⎛ −

=

Average delay between 0 – 120 s can be directly obtained from figure given in next slide.

Average delay = Area of Triangle I or II/ No. of arrivals in a cycle s106

4305.0=

××=

Between 120 – 240 s the intersection is operating under oversaturated conditions. The arrival is deterministic and uniform. Average delay can be calculated using following equation

( ) scapvTgCADos 1051

7201800

2120

230601

22=⎟

⎠⎞

⎜⎝⎛ −+

−=⎟⎟

⎠

⎞⎜⎜⎝

⎛−+

−=

Note vph72060144030

=×

==Cgscap

76

Average delay between 120 – 240 s can be also obtained from following figure:

Average delay= (Area of Triangle III + 5x Area of Triangle IV)/No. of arrivals from 120-240 s

s10560

30125.05601805.0=

×××+××=

Average delay to all vehicle between 0-240 s can be obtained dividing the total delay (faced by all vehicle) by the number of vehicle.

Average delay snn

dndn 2.896012

105601012

21

2211 =+

×+×=

++

=

39

77

Q4. Determine the delay to the fourth and the sixtieth vehicles that arrive at the intersection.

The arrival rate of vehicle from 0-120 s is 360 vph or 0.1 vps. Assuming that fourth vehicle arrives before the expiry of 120 s, the time of arrival of the fourth vehicle is 4/0.1 = 40 s.

Departure rate of vehicles is 1440/3600=0.4 vps. The time of departure of the fourth vehicle, assuming that fourth vehicle gets discharged during first green, is 30+4/0.4=40 s.

Therefore the delay to fourth vehicle is = departure time – arrival time = 40 – 40 = 0 sThe same observation can be made from above figure. The delay to the sixtieth vehicle can also be read from figure as 144 s.

Q5. Determine the maximum delay faced by a vehicle on this approach.

See in figure, maximum delay is 180 s

Q6. Determine the maximum queue length on this approach. At what time does the queue length first become equal to the maximum.

As can be seen from figure, the maximum queue length is 36 vehicles. At time = 240 s, the queue length first becomes equal to 36 vehicle.

78

Q7. Determine the percentage of time for which there exists a queue on this approach.

Q8. Determine the average queue length between 120 and 420 s.

As can be seen from figure, there is no queue from 40 – 60 s and from 100 – 120 s. For the rest of the time, there is a queue at the intersection. Hence, the % of time for which there is no queue is (40/420)100 = 9.52 %.Hence, the % of time when there exist a queue is 100 – 9.52 = 90.48 %.

Average queue length = (Area of Triangle III + 5xArea of Triangle IV)/(total time from 120–420 s)

21300

30125.05601805.0

=

×××+××=

vehicles

40

79

Data collection on average delay:

Cumulative departure

Average delay is equal to area divided by total number of arrivals.

Total area between cumulative arrivals and departure plots

∫∑ ==tn

dttqnd )()(

arrivalsofnumber Total

)( delay Average

∫= t

dttq

R G R G R G RCycle 1 Cycle 2 Cycle 3

Cum

ulat

ive

arriv

als /

depa

rture

sTime

qi.

Cumulative arrival

P

Vtotal

total

m

ii

V

qI ∑=

××= 1

9.0 delay Average

I

80

Data collection on saturation flow rate:

The saturation flow rate is reciprocal of the saturation headway.

Measure the time between 4th vehicle and last vehicle crosses the intersection.

Determine the number of vehicles in the queue.

4 headway timesaturation ,4,

−−

=L

TT iiL L = last vehicle in the queue

Capacity analysis:

CGsc i

ii ×=ci capacity of lane i

Gi Green time for lane i

si Saturation flow on lane i

Saturation flow depends on (i) no. of lanes in the lane group and width of lanes or alternatively the width of lane group, (ii) gradient of the lane, (iii) percentage of turning traffic, (iv) vehicle mix, (v) number of parking manoeuvers, and (vu) number of bus stoppings.

41

81

Level of service:

Level of service of different lanes at signalized intersection should be determined through a measure which directly gives the level of discomfort of drivers using these lanes at the intersection.

Level of service is measured as average delay to vehicles of different lanes.

>80.0F

55.1 to 80.0E

35.1 to 55.0D

20.1 to 35.0C

10.1 to 20.0B

<= 10.0A

Control delay per vehicle, sec.Level of service

HCM level of service

82

Warrants for Signalization

Various warrant conditions are defined for signalization. Detailed standards exists. However, in this class, we are only going to look at the warrant conditions without going into details.

Warrant 1: Minimum vehicle volume

If vehicular volumes are “high” for a “reasonable period” of the day is “most” of the approaches then signalization is warranted.

Warrant 2: Interruption of continuous traffic

Even if volumes on certain approaches are low if the volume on other approaches are “quite high” then also signalization is justified.

Warrant 3: Minimum pedestrian volume

If the volume on certain approaches one quite high and the pedestrian volumes wanting to cross those approaches are also high than signalize.

42

83

Warrant 4: Safety consideration or Accident experience

If at an intersection accident of the type which can be corrected through signalization occur quite frequently then signalize.

Warrant 5: Combination of warrants

Some times none of warrants may be satisfied fully, however, if two or more of warrants 1, 2, and 3 are satisfied to a reasonable extent then a signalization may be warranted.

Although there other conditions which can also justify the use of signals like:

•A minor intersection between two intersections

•Flow pattern on an intersection is highly peaked with high volume observed only for 4 to 5 hours of a day.

84

Terminology:Cycle: one complete sequence of signal indications

Cycle Length: total time for signal to complete one cycle

Phase: part of cycle allocated to any combination of traffic movements receiving the right of way

Interval: period of time during which all the signal indications remain constant.

Change interval: the “yellow” and/or “all-red” intervals which occurs at the end of a phase to provide for clearance of the intersection before conflicting movements are released.

Green Time: time within a given phase during which the green indication is shown

Lost time: time during which the intersection is not effectively used

Effective green time: time during which a given phase is affectively available for stable moving platoons of vehicles in the permitted movements. It is equal to the green time plus the change interval minus the lost for designated phase.

43

85

Design of Signal Phases and Timing

In this section, three topics are discussed. Namely,

(i) Signal Phasing : the selection of what phases should be present during a cycle.

(ii) Cycle length : determination of cycle length.

(iii) Phase length : Green and Inter – green time allocation – what % of the cycle time should be given to each of the phases as green and inter – green period.

Signal Phasing

Phasing is the sequence by which the various movements both vehicles and pedestrians are being served at a signalized intersection. The objective of phasing is the minimization of the potential hazards arising from the conflicts of vehicular and pedestrian movements, while maintaining the efficiency of flow through the intersection.

Greater the number of phases, better separated are the conflicting flows.

However, increasing the number of phases hinders efficiency while improving safety.Safety improves (with large number of phases) because conflicts are eliminated, however, efficiency falls because delays increase due to:

(i) more lost times (in start-up and unused yellow times), and

(ii) minimum phase duration requirements.

86

There exists no algorithm by which phasing may be selected. It is purely an art based on certain guidelines.

A. Keep the phasing scheme as simple as possible (like start with simple two phase system)

B. Increase the number of phases if pedestrian or turning volumes is high.

The following diagram illustrates three most basic phasing scheme: (i) Two phase operations, (ii) Three phase operations, and (iii) Four phase operations.

Vehicular traffic

Pedestrian traffic

Vehicular traffic

Phase A

Pedestrian traffic

Phase B

TWO PHASE OPERATION

44

87

However, say if pedestrian volume is large then:

Sometimes the right-turning volume from one road may be large and this may require aseparate phase.

Pedestrian not allowed

Vehicular traffic

Phase A

Vehicular traffic

Phase B

THREE PHASE OPERATION

Pedestrian not allowed

All red

Phase C

Pedestrian traffic

Vehicular traffic

Phase A Phase B

THREE PHASE OPERATION

Pedestrian traffic

Phase C

Dotted arrow indicates permitted movements

88

If turning volume in either direction is heavy then a four phase operation may be warranted.

In all the above phasing schemes, note that if a right-turn is protected then no pedestrian movement is allowed during the protected phase.

The four phase scheme shown above or the second of the two three – phase scheme shown here works best if a turning lane exists.

FOUR PHASE OPERATION

Phase A(Protected turn)

Phase B(Permitted turn)

Phase C(Protected turn)

Phase D(Prohibited turn)

45

89

Cycle Length Determination

A cycle is a complete sequence of signal indications; cycle length is the duration in which the whole set of phases at a signalized intersection takes place once.

The appropriate cycle length is generally obtained using Webster’s equation. This equation yields results close to an optimal cycle length, however, we shall not go into the details of its derivation. We shall simple state it here. The details will be stated while discussing the delay equations at an intersection.

V3

V2

V1

Ave

rage

del

ay p

er v

ehic

leTime length

Least delay point (optimum cycle length)Vol on approach

V1> V2> V3

• Cycle length’s effect is not monotonous

• there exists a cycle length for which delay to vehicles is the least

• Sensitivity of cycle length near optimum cycle length is very small

• On both side of optimum cycle length sensitivity is different with respect to cycle length

General nature of avg. delay per vehicle versus cycle length variations for different approach volumes derived from the plots developed by Webster

90

∑=

−

+= p

i

icrsV

LC

1)/(1

55.1

Optimum cycle length C as suggested by Webster is:

C: Optimal cycle length, in seconds

L: Lost time during a cycle. Sum of the start-up lost time and the clearance lost times.

p: total number of phases in the cycle

: critical flow ratio for phase i

V: volume of a particular movement

s: saturation flow for movement

icrsV )/(

∑=

++=p

i

ir

im

is lllL

1

)( ls: startup time loss

lm: movement time loss or clearance lost time

lr: all red time loss

46

91

335

250

725 7651670

Saturation flows:Th = 1800 vphgplTh, LT = 1700 vphgplTh, RT = 1650 vphgpl

Phase B

Phase A

To obtain the critical movements in each phase one proceeds in the following manner:

Phase A:

Phase B:

{ } 20.015.0,20.0max1700250,

1650335max ==

⎭⎬⎫

⎩⎨⎧

Hence the Th, RT movement from west is critical.

{ } 46.045.0,46.0,44.0max1700765,

18001670,

1650725max ==

⎭⎬⎫

⎩⎨⎧

Hence the Th movements are critical.

Determination of critical movements ( or Determination of )icrsV )/(

92

If for the above problem, lost time per phase is given as 4 s then one could determine

( ) sC 50)46.020.0(1

5425.1=

+−+×

=

two phase signal

A point worth mentioning here is that empirical research show that cycle lengths within a ± 30% from the “optimal” length estimated using Webster’s formula perform close to the optimal.

Generally cycle lengths are provided in multiples of 5 s. That is 40 or 50 or 55 etc. seconds.

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93

Phase length : Green Allocations / Amber Allocation

Step 1: For each phase compute the yellow / amber time requirement using dilemma zone calculations. For the same phase generally the same amber duration is provided. However, for different phases different amber times can be given.

Step 2: The (cycle time - ∑(amber time + all red) ) is allocated as green in proportion to the critical flow ratios in every phase.

Step 3: Check whether the allocated green times meet the requirement from the pedestrian standpoints. If it is does not meet the requirement then increase the cycle time in steps of 5 s till the requirements are met.

The requirement is obtained as follows:

where Tp is in seconds and W is width if the intersection in meters; assuming the pedestrian walking speed is 1.2 m/s (or 4 ft/s).

2.17 WTp +=

94

Let us look at the previous example again. Assume lane width is 3.66 m. Also assume that 3 s of amber time is provided per phase.

10 s

16 s

10 s

16 s

10 s

16 s

Tp

- Amber time

ok7+(4x3.66)/1.2 =19 s3≈ 1649x (0.20/0.66)60 – (2x3) = 54A

ok7+(2x3.66)/1.2 =13 s3≈ 3849x (0.46/0.66)60 – (2x3) = 54B

not ok7+(4x3.66)/1.2 =19 s3≈ 1549x (0.20/0.66)55 – (2x3) = 49A

ok7+(2x3.66)/1.2 =13 s3≈ 3449x (0.46/0.66)55 – (2x3) = 49B

Increase C to 60 s

Increase C to 55 s

ok7+(2x3.66)/1.2 =13 s3≈ 3144x (0.46/0.66)50 – (2x3) = 44B

not ok7+(4x3.66)/1.2 =19 s3≈ 1344x (0.20/0.66)50 – (2x3) = 44A

Tp ok?TpAmber

GreenAllocationCycle length –(∑(Amber + all

red))

Phase

During Phase A pedestrians have to cross 4 lanes.Tp = 7+(4x3.66)/1.2 = 19 s

During Phase B pedestrians have to cross 2 lanes.Tp = 7+(2x3.66)/1.2 = 13 s 338Phase B

316Phase A

Amber timeGreen time

Cycle Length = 60 s All red time = 0 s

48

95

Amber Time Determination (Dilemma Zone Analysis)

• Consider the scenario where a vehicle moving at speed limit decides to stop when the light turns amber.

The distance required to come to stop, xs

cbs d

vvx2

20

0 += δ

where, v0 is the speed limit (or design speed), δb in the reaction time for breaking, dc is the comfortable deceleration rate.

Note that any vehicle whose distance from stop line is less than xs when the light turns amber will not be able to stop.

• Consider the scenario where a vehicle moving at speed limit decides to cross the intersection when the light turns amber.

The distance required to be crossed during an amber time of τ , is

The distance required to crossed = xg + W + L

where xg is the position of vehicle when light turns yellow, W is the width of intersection and L length of vehicle.

96

In this time a vehicle can travel

2)()(

2

00ac

aaavv δτδτδ −

+−+=

2)( 2

0acav δττ −

+=or

Since, v0 is the speed limit it is assumed the ac , the comfortable acceleration rate, should not be operative as no body will accelerate. Hence, distance traveled is only v0τ

∴ LWxv g ++≥τ0

or LWvxg −−≤ τ0

That is, xg can at most be equal to v0τ – W - L

Any vehicle farther than xg will not be able to cross the intersection during amber duration.

Time available for crossing would be τ .

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97

xg and xs give rise to the following scenario

xs

xgCan not go

Can not stop

Can go or can stop (Option Zone)

xs

xgCan not go

Can not stop

Can not go and can not stop (Dilemma Zone)

(a) (b)

Now clearly in situation (b) where xg < xs should be avoided. Note xg is the only term which is function of τ.

Hence, at least xg = xs ; let this happen when τ = τ min

In this case,

cb d

vvLWv2

20

0min0 +=−− δτ

0

0min 2 v

LWdv

cb

+++= δτ

98

Signal Coordination

The fact that certain vehicles can avoid stopping at an intersection presents the opportunity to coordinate a series of permitted signals to allow platoons of vehicles to clear all the signals without intersection. This scheme works best when the signals being coordinated have the same cycle length. Of course, the phase lengths may be different in each signal

The criterion based on which signals are coordinated is referred to as the through band.Signals are coordinated so as to maximize this through band. Notice the width is in units of time and hence the width divided by the average time headway gives an idea of how many vehicles can move without being stopped.

However, for a given coordination, the through bands in both direction may not be equal. If they are equal then the design is called a balanced design otherwise it is referred to as preferential design.

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99

All the signals should have the same cycle length.

Benefits in signal coordination:• Minimize the number of stops and delay faced by vehicles

• Maximing through band width

• Signal can be set to encourage certain speeds, preferred speed

• Vehicle can sent through in successive intersections in moving platoons; in well formed platoon, the time headway is somewhat shorter than can be achieved when they start from the stop.

100

Offset: Difference between green initiation times, measured in terms of the downstream green initiation relative to the upstream green initiation.

or amount by which the signals at the intersection are staggered with respect to the first intersection are referred to as the offsets

Bandwidth: “Windows” of green time through which the platoons of vehicles can move. Expressed in terms of time

Efficiency of a Bandwidth: it is defined as the ratio of the bandwidth to the cycle length, expressed as a percentage

%100length cycle

bandwidth efficiency ×=

Maximum bandwidth possible for a given movement is always equal to the minimum green time for that movement among all the intersection.

Type of signal coordination which has a very good bandwidth in one direction and very poor bandwidth in opposing direction, is called preferential coordination.

On the other hand, if there is a balance between the through-bands in both the direction then the design is called balance design.

All the signals being coordinated should have the same cycle length otherwise coordination cannot be achieved over a long period of time. However, signals may have different phase lengths.

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101

The following diagram shows how the through band may be obtained. The diagram is for an arterial with three signals and velocity of travel “u” and cycle length of C.

offset

G1 Y1 R1 G1 Y1 R1

G2 Y2 R1 G2 Y2 R1

C

C

C

G3 Y3 R3 G3 Y3

Firs

t veh

icle

Last

veh

icle

Last

veh

icle

Firs

t veh

icle

Signal (1)

Signal (2)

Signal (3)

Time

Through band

Offset = 2 units

Offset = 1 units

Offset = 0 units

102

In the scenario shown on the previous figure, the design is definitely preferential as the through band in the north – to – south direction has zero width. However, it is not the best preferential design as the through band in the south – to – north direction could be further increased by increasing the offset of Signal (2). This is shown in the following figure:

Firs

t veh

icle

Last

veh

icle

Last

veh

icle

Firs

t veh

icle

Dis

tanc

e

52

103

The previous examples are of preferential design. The following figure shows an example of balance design. Note that, in this case, it can not be readily said whether the through band is of maximum width possible under balanced design.

Dis

tanc

e

104

Problem: The fixed time signals at the intersections of a one-way street have been coordinated. The relevant data on these intersections are given below:

15201040535C

6104025550B

0035540A

Distance from A (m)Offset (s)Red (s)Amber (s)Green (s)Intersection

The operating speed on the street is 48 km/h (or 13.33 m/s). Determine the (a) bandwidth and the (b) offset pattern which will improve the bandwidth?

(a) s 80 redambergreen length cycle =++=

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105

Actuated signals and detection

• Actuated signals require “actuation” by a vehicle or pedestrian in order for certain phases or traffic movements to be services.

• Actuation is achieved by vehicle detection devices and pedestrian push buttons.• The timing of such signals is controlled by traffic demand at actuated signal intersections;

cycle and green times may vary from cycle to cycle depending upon the sequence and number of detector actuations.

• If the traffic demand pattern is very regular (traffic volume level, then there is no any extra benefit in providing actuated signal

See the variability in traffic demand in given figure: • Traffic peaks sharply in the morning on weekdays and settles down to some significant level

after the morning rush• Saturday and Sunday patterns are different from weekdays as well as from each other.

106

Type of actuated control:• Semiactuated control• Actuated control

Semiactuated signals have detection on some or all movements except the main line. Non detected phase is controlled on a pretimed basis. Cycle length is allowed to change by varying the detected phase length.

Sufficient green time for the mainline is not guaranteed without additional delay to the other movements. Once the mainline’s minimum green time has been served, the non-coordinated phases can be served when a call arrives. Without the presence of a conflicting call the signal normally will rest in the mainline phase.

The underlying promise in semiactuated control is that there is a main street that should have the green as much as possible and a side street that should be given only enough green to service the relatively low and somewhat unpredictable traffic.

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107

Concept and timing of the semiactuated signal

Side street detector is used to identify the arrival of a vehicle; the controller is notified; if the main street has had “enough” green, the side street is given the green for just enough time to guarantee that its vehicles are processed. Again the green is given to main street.

Implicit assumptions:

• Side street traffic is always the minor flow

• All side street vehicles will probability be stooped

• There is no pattern inside street vehicle arrival which can be better served by regular scheduled period of green.

Situations where the use of semi actuated signal is useful:

• Main street is major road and side street off peak demand is low and quite random (like residential street)

• Main street is an major road and side street demand peaks for short term due to a local traffic generator (like factory, schools, etc)

• Signal is installed in response to a warrant unrelated to traffic volume, such as pedestrian volume, accident warrants, etc..

There is no absolute rule for when actuated versus pre-timed signal may be used..

108

Fully actuated signal provides detection on all roads. Cycle and all phase lengths are allowed to correspond to traffic flows. It reduces side street delay in period of low mainline demand. Give example: when a vehicle arrives just after the call opportunity.. Then it has to wait till next opportunity of call..

Concept:

When the competing demands are equally important, and that there is no structured arrival patterns on any approach which should be taken the advantage off.

Suitable for isolated intersections at which demand level varies significantly

At low volume avoid unnecessary stopping.

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109

Flow at Unsignalized Intersections

Flow at unsignalized intersections are generally guided by the hierarchical position of the movement specified either by rules of driving or through static signs like – stop and yield,

• At any unsignalized intersection there are various types of movements, like (i) through movement on major street, (ii) right turn movement from major street, (iii) left turn movement from major street, (iv) through movement on minor street, and so forth.

• Each of these movements has a place in the hierarchy specifying their claim on the right-of-way at the common intersecting space.

• For example, in general, first in the hierarchy is the through movement on the major street and slightly lower down is the right turn from major street.

• Now if in a situation there is a vehicle on the right turn movement and another on the conflicting through movement, then the latter will use the intersection and the former has to wait till the latter clears the intersection.

• If some movement is still lower down the hierarchy (like the right turn from minor street) then a vehicle on that movement has to wait till the vehicles on movements higher up in the hierarchy has cleared the intersection.

• As can be seen, the departure process is purely stochastic and extremely complex to model.

110

Unsignalized intersections work very efficiently if the total conflicting volume is not very high

• For example, if at the intersection of a major street with minor street, the traffic to and from the minor street is low then the intersection works quite well irrespective of the volume on the major street.

• If, however, conflicting movements have reasonable volumes then unsignalized intersections become inefficient and tend to cause large delays to the low priority (i.e., lower in the hierarchy) movements. This is when signalization becomes imperative.

Arrival process

• The arrival process of vehicles obviously do not depend on the type of intersection at which they arrive.

• Hence they are like those at the signalized intersections and no separate discussion is therefore provided here.

56

111

Departure process

• Departure process from unsignalized intersections are quite different from those at signalized intersections.

• The departure process of a movement is determined by the hierarchical position of the movement and the type of control ('STOP' or 'YIELD') on the movement.

• If a movement is at the top of the hierarchy and is not controlled (or 'YIELD' controlled) then vehicles on the movement always have right of way at the intersection and their flow is not interrupted.

• However, for the majority of the movements, their position is not at the top of the hierarchy and are often 'STOP'' controlled.

• For these movements, the departure process is quite complex and is therefore explained here through an example.

112

• Two through vehicles (marked T1 and T2) and two right-turning vehicles (marked R1 and R2) on the left-to-right stream are shown. Numerous vehicles on the right-to-left stream are also shown.

• Consider the arrival and departure processes for the left-to-right stream at a proper location on the road (say the stop line).

• Vehicles arrive at this point as has been described earlier. The departure process for the two types of vehicles shown, however, is different.

• The through vehicles represent those vehicles which always have the right of way. Hence for these vehicles the arrival time at the stop line is always equal to the departure time from the stop line. The right turning vehicles represent those vehicles which are lower in the hierarchy and have to wait for gaps in the opposing stream to complete their manoeuver. For example, vehicle R1 waits at the stop line and evaluates each of the gaps in the opposing stream.

Fig.: A snapshot of an unsignalized T intersection.

57

113

• Only when a gap is greater than some value (at which the driver is comfortable) does the driver of the vehicle accept the gap and makes the right turn.

• In the figure shown this could be Gap III. Hence, vehicles which have to look for gaps in the opposing stream (or streams), sometimes have to wait at the stop line before departing.

• Since the arrival of gaps is a stochastic process, the departure process of vehicles (or the waiting time at the stop line), is also a stochastic process.

Critical Gap

The minimum value of the adequate gap is referred to as the critical gap.

In deterministic view of things it is assumed that driver accept a gap whenever the gap is greater than critical gap. However, in reality, it is not true and critical gap is only idealization of the observation that driver does not chose gaps which are “small” and choose gaps which are “large”.

In the analysis of unsignalized intersection assumes that a critical gap exits.

114

Two of the important features which should be looked into at an unsignalized intersection are:

(i) Delay to vehicles, and

(ii) Queue of vehicles.

Flow characteristics at an unsignalized intersection:

• Various type of vehicles arrives at the intersection; vehicles differ from one another in time they spend at the stop line (service time)

• For vehicles which are at the top of the hierarchy, service time is zero and deterministic; for other types of vehicles service time is indeterminist and follow different distribution.

• Q formed at the stop is “first-in-first-out”; Q may contain more than one type of vehicle depending on the number of lanes on the approach under consideration (if separate lane for tuning movement vehicles has been provided then only the tuning movement of vehicles left there)

For analyzing any stochastic queueing system:

• Determine arrival and service time distribution: arrival distribution can be assumed to be Poisson (if other intersections are not present in the neighbourhood) or determinic (when other intersection is present in closeby) or a comination of two.

• Service time distribution depends: on number of gaps a vehicle reject before accepting a gap and the distribution of the gap

58

115

Analysis of queue distribution and the delay to vehicles is even more complex.

Complexity arises primarily due to complex and different service time distributions of the various types of vehicles.

Indian code does not provide any relation which can be used to determine delay at unsignalized intersections under Indian traffic condition. HCM 1985 does provide relations to determine queue lengths and delay based on highly empirical consideration.

The factors which affect delay and queue length are:

(i) Conflicting volume : The flow rate of the opposing stream

(ii) Movement type: vehicle in movement with lower in hierarchy generally face higher delay that vehicles with higher hierarchy.

(iii) The flow rate of the stream in which vehicles arrive and want to cross/merge into the opposing stream

(iv) Speed of conflicting movement: this increases the critical gap..

(v) The critical gap increase if the no. of acceptable gap in the conflicting movement reduces.

116

Data collection:

Two type of data are generally collected at un signalized intersections:

•Average delay

•Critical gap

Average delay: data is collected in the same way as in unsignalized intersection. Only difference is that the cumulative departure does not follow any fixed pattern

R G R G R G RCycle 1 Cycle 2 Cycle 3

Cum

ulat

ive

arriv

als /

depa

rture

s

Time

qi.

Cumulative arrival

P

Vtotal

Cumulative departure

total

m

ii

V

qI ∑=

××= 1

9.0 delay Average

IAverage delay: data on critical gap is difficult to obtain in field. Reason for it is that driver rejects a lot of gap but accept only one. From this fact one say that critical gap for the person is greater than the largest rejected gap and smaller than the accepted gap. So one can get the range.

Some time former may be greater than later due to difference in driver behaviour.

59

117

Drew suggested following procedure to determine the critical gap:

• Observed an unsignaized intersection and obtain data on many driver in respect to the largest gap rejected and the smallest gap accepted.

• Divide the time scale into small intervals (say 0.5 s duration) and determine for every class t the no. of such gap accepted and no of such gap rejected.

• Plot the cumulative curves on the same graph of “number of gaps” vs “t”

• Report the value of t where these plots intersect as the critical gap. This value of t represents that gap size for which the number of gaps smaller than t which have been accepted.

118

Capacity and Level of service

Capacity analysis:

Meaningful to talk about the capacities of different movements, lane, approaches to the unsignalized intersection not about whole intersection.

Capacity depends on:

Gap availability: vehicles moves by accepting gap in conflicting movement;

• more the number of conflicting stream lower the gap availablity;

• higher the flow in conflicting movement, lower the gap availability

• Greater the size of critical gap; lower the no. of acceptable gaps

Therefore, total the no. of gap available for use by a traffic streams depends on the number and volume of conflicting streams and size of critical gap.

Hierarchical position: not all gaps available for use can be used by vehicles of a movements

Gap accessibility: lane may be shared by more than on e movements,

60

119

Level of service:

• Level of service is determined based on average delay to a vehicle on that intersection. i.e. like in signalized intersection.

120

Interchanges

Warrants for Interchanges

Warrant 1: Design designation warrant

If a road is fully access controlled, like an expressway, then all the intersections on that road should be grade-separated.

Warrant 2: Volume warrantIf the volume at an intersection is so high the capacity provided by an at-grade intersection will be insufficient then interchanges should be used.

Warrant 3: Accident related warrantIf an intersection has a disproportionate rate of serious accidents, and if analysis of the intersection suggest that the accident hazards can not be reduced by possible and inexpensive traffic control measures, then an interchange should be provided at the intersection.

Warrant 3: Topography warrantIn some cases the topography of the area may be such that the only feasible, or sometimes cheaper, alternative s an interchange; in such cases, in interchanges is definitely justified.

Interchanges: the grade separated intersection where conflict in traffic flow is resolved by duplicated the intersecting space at various heights, also called flyovers in India

Ramps: roads connecting to intersection roads

61

121

Design for Interchanges

The design features specific to interchanges alone is that of the layout of the ramps. Following are some layouts which are commonly used:

(i) Trumpet interchange

(ii) Diamond Interchange

(iii) Partial clover-leaf interchange

(iv) Full clover-leaf interchange

122

Trumpet interchange

Where a major roads terminates to other major roads

62

123

Diamond Interchange

124

63

125

Partial clover-leaf Interchange

When on one road minor conflict movement can be tolerated

126

Clover-leaf Interchange

All the conflicting movement has been separated

64

127

Conflict points and conflict zone

128

Channelization

• Facilitate safe and orderly movement • Separate or regulate conflicting movements • Define paths of travel • Use traffic islands or pavement markings • for both vehicles and pedestrians

Done with medians, islands, road islands, road markings, etc.

65

129

1. Discourage or prohibit undesirable/wrong-way movements

• Prevent right turn movement from the minor street

• Design channelization to discourage wrong way movements

Principles of Channelization

130

2. Define desirable path for vehicles: Prevent right turn movement from the minor street

• With clear definition of proper path – by pavement marking

66

131

3. Channelization to promote desirable speeds and delineate desirable paths

132

4. Remove stopped/decelerating vehicles

4. Separate the points of conflict where possible

• Provide exclusive turning lane

• Channelized left turn

67

133

7. Channelization to streamline flows (rotary intersection)

6. Facilitate the movements of high-priority traffic flow

134

8. Design approaches to intersect at near right angles and merge at flat angles

• Roadway alignment which cross as close to 90 degree, minimizes the exposure of vehicles to potential conflicts and reduce the severity of conflict

• Skewed crossing provide awkward sight angle and increase the distance traversed at intersection (in signal designing, need more amber time to clear the traffic)

68

135

Parking

In case of roadway transportation, parking is terminal.

Provision of parking is an essential consequence of the movement of people and goods into and within urban areas.

(terminal is a location where vehicle of a mode stop for various reasons including boarding, alighting of passenger, loading or unloading of goods, resting when not in use, refueling, maintenance, etc.)

Since parking is terminal or destination of a trip, the availability and price of parking effects:

• attractiveness of destination

• Mode of transportation

• Encourage or discourage the short term parking

On – street: On-street parking facilities are basically the spaces near the sides of the roads where vehicles are allowed to park.

Off – street: Off-street parking facilities are parking spaces away from the main thoroughfare and connected to it through a service road. These spaces, unlike the on-street parking spaces, are developed solely for the purpose of parking

136

On-Street Parking:

Issues related to on-street parking:

• Whether requirement for on-street parking exists in a particular location

• Whether the capacity of roadway is enough (after the on-street parking is provided) to cater to the traffic on road,

• Whether on-street parking will increase safety hazards substantially?

• What kind of on-street parking should be provided?

Requirement for on-street parking:

• Given the land use in an area, one can determine the parking space required for that area

• If, adequate, off-street parking is not available in the vicinity, then on-street parking is requirement exists

• On-street parking requirement= total parking requirement – off-street parking space available

• It may pointed out, if on-street parking space is available then driver may be biased towards the on-street parking as it offer less walking distance to the intended destination

69

137

Effect of on-street parking on capacity and safety:

• On-street parking adversely effect the capacity and safety

• Reasons for reduction for capacity:

•Reduction of carriage width available for traffic

•Parking maneuvers on the road caused frequent interruptions to the traffic.

(IRC code does not speak about it, while HCM& AASHTO talks about it)

• On-street parking increase the frequency of accidents

138

Parallel on-street parking

• Vehicle occupied less carriage width when parked parallel

• But over a length of road less no. of vehicle can be parked in comparison of angle parked

• Parallel parking involves difficult driving maneuvers (specially when parked between two parked vehicles) and hence caused interruption on the thoroughfare

• Vehicle of large length can be easily parked

3 to 3.6 mBy AASHTO

On-street parking

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139

Angle on-street parking

• Vehicle occupied more carriage width when parked at an angle

• But over a length of road more no. of vehicle can be parked in comparison of parallel parked vehicles

• Driving maneuvers is less complicated

• It has been observed that angle parking caused more accidents than parallel parking. This is possibly due to the fact that drivers are sometimes blinded by other parked vehicle while backing out on to the road from a parked position.

• Large vehicle length can cause special problem in angle parking

It is generally suggested that parallel parking should be the first considered and only in special cases angle parking should be used.

If, however space is available, the carriage width is large then angle parking may be a better choice since more vehicles can be parked over a smaller length.

140

Off-street parkingOff-street parking facilities are facilities built solely for the purpose of parking.

Type of off-street parking facilities based on design – open paved surface, multistoried parking, park-and ride facility, etc.

Each of these must concentrate to provide the space for:

• Allow easy and independent parking

• Allow easy vehicle circulation

• Utilized the space most effectively

• Special requirement, if any, like elevator for drivers on multistoried parking

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141

Parking duration: length of time a vehicle remains in one parking space

Long term parking: parking with a duration of three or more hours

Parking accumulation: the total number of vehicles parked in a specific area at a specific time

Parking load: area under parking accumulation curve.. Generally represented in veh-hour

Parking demand: no. of vehicles desiring to park at a specific location or in a general area. It is expressed in no. of vehicles during peak-parking hours

Parking volume: no of vehicles that park in a study area during a specific length of time

Turnover : no. of vehicle utilizing the same space/stall over a given period of time

Occupancy: ration of no. of spaces occupied divided by total no. of spces available, expressed in %

142

Method for collecting data for parking:

• Ins and out survey

• Fixed period survey

• License plate survey

Ins and out:

• All the vehicles present in the parking space are counted at the beginning

• The vehicles entering and exiting from the area is counted

• At the end, another count of all the vehicles present in the area is conducted to cross check.

This survey give – parking accumulation and occupancy

Does no give – average parking duration, turnover

To determine the parking demand

In case of existing parking:

72

143

Fixed period survey:

• All the vehicles present in the parking space are counted at the beginning

• Count all the vehicles present in the area after a fixed interval

One can missed short term parking

This survey give – parking accumulation and occupancy

Does no give – average parking duration, turnover

License plate survey:

Gives most accurate and realistic data collection

• All the vehicle’s license plate no., present in the parking space, are note down at the beginning

• Note down the license plate no. of vehicle present in the area after a fixed interval

One can missed short term parking

This survey give – parking accumulation , occupancy, average parking duration, turnover

Quite expensive and laborious.

144

In case of new parking design:

73

145

User Information Surveys:

Individual users can provide valuable information which is not attainable with license plate surveys.

• Parking interviews

• Postcard studies

Parking Interviews:

• driver are interviewed right in the parking lot

• Information about origin and destination, trip purpose, and trip frequency

Postcard Studies:

• Postage paid postcard request the same information as in parking interviews

• Return rates average about 35%

Biasness

• overestimate their parking need to encourage the surveyors to recommend additional parking.

• they file false reports that they feel are more socially acceptable

146

Parking Facility Design Process:

• Goal of parking design to maximize the no. of spaces provided which allowing vehicles to park with only one distinct maneuver

• Step by step procedure is not simple. Parking design requires balancing a variety of concerns like- you might decide on a nice layout for parking but have not provided the space for disable persons

List of maneuvers in parking:

• Vehicle enter from street (space provided by entry driveway)

• Vehicle searches for a parking stall (space provided for circulation/ or access aisle)

• Vehicle enters the stall (space provided access aisle)

• Vehicle is parked (stall design to accommodate the vehicle length and width)

• Pedestrian access the building or destination

• Vehicle exits the parking stall (space provided by access aisles)

• Vehicle searches for exit (space provided by access and circulation aisle)

• Vehicle enters the street network (space provided by the exit driveways)

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Entrance considerations:

• During high demand time many vehicle wants to enter in the parking facility roughly at the same time

• Which force vehicles to wait out side of entrance

Internal considerations:

• Vehicle searching for stall requires space for maneuvering

• Two type of parking operation: (i) self parking, (ii) attendant parking

• tollbooth and other restrictions require space for waiting vehicles

Parking stall layout considerations:

• Parking stall should be flexible enough for future expansions

• Stall and aisle dimensions should be compatible with the type of operation planned

•Critical dimensions are width and length of stall, width of aisle, angle of parking and radius of turns

Aisle and stall combination is called as modules.

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As the parking angle reduces the aisle width is also reduces.

Arrangement of parking stalls: (a) 900 parking stalls with two-way aisles, (b) 600 drive-through parking stalls with one-way aisle, (c) 600 parking stalls with two-way aisles, and (d) 450

herringbone stalls with one-way aisles.

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Various examples of vehicle circulation: (a) one-way circulation, (b) one-way circulation, (c) two-way circulation, (d) one-way ramp circulation with adjacent parking for multistoreyed garages, and (e) clearway, external spiral ramp circulation for multistoreyed parking garages.

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Design of parking lots

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Design of off-street facilities:

Elements of good design:

• Elements of customer service, convenience, and safety with min. to street traffic flow

• Accessibility, ease of entering, circulating, parking, unparking, and exiting are important factors

• Good dimensions and internal circulation are more important than a few additional spaces.

• Better sight distances, maneuverability, traffic flow, parking ease and circulation

Site characteristics:

• Site dimension, topography and adjacent street profiles affect the design

• Relation with surrounding system will affect the location of entry and exit points and internal circulation pattern

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Access location:

• External factors such as traffic controls and volume on adjacent streets must be considered

Layout alternatives:

• Layout of parking lot seeks to strike a balance among maximizing capacity, maneuverability and circulation.

Advantage of 90 degree parking

• Most common and understandable

• Sometimes better fitted into buildings

• Generally most efficient if site is sufficiently large

• Uses two-way movement (can allow short and dead end aisle)

• Allows unparking in either direction (minimize the travel distances)

• No need to aisle directional sign or marking

• Required wide aisle which help in pedestrian walking on aisle

• Fewer total aisle

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Several advantage and disadvantages of angle parking:

• Easiest in which to park

• Can be adopted to any width of site by varying angle

• Requires slightly deeper stall

• Unused triangle space at the end of parking aisle

• Generally to avoid long travel, additional cross aisle for one way travel are required

• Generally aisle are one way

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A joint development of a general purpose office building with a 200,000 ft2 gross building area and a movie theater complex with 1500 seats is planned. The facilities will be served by a common parking lot. Estimates the number of stall required and assess whether the efficiency improves with shared use of parking lots as appose to separate parking lots for each of the developemnts. Also estimates the efficiency as the degree of stall utilization over 1 week. Lot utilization on weekdays and sundays is specified in the following table.

Given that

Office building (weekdays) ln(P) = 0.93 ln (X)+1.253 (X in terms of 1000 ft2)

Movie theaters (weekdays) P= 0.32 X - 174.0

Movie Theaters (weekend) P= 0.50 X – 322.0

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At the corner of Missouri Boulevard and McCarty Street

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Traffic signs

• Proper road signs aid the drivers in reaching their destinations safely and efficiently.• Properly designed road signs improves by:

– Instructing drivers on safe speeds (i.e. signs like curve ahead)– Informing drivers on impending changes in road geometry (i.e. narrow bridge ahead)– Reducing the driver confusion through clear signs on allowable traffic movement pattern

(like no entry, no U turn)

• Road signs (static like painted signs and dynamic signs like electronic message signs) have three design elements:

– The text of sign– The lettering, letter sizes and colour combination of the sign– The placement of sign

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The text of the sign:

• In general, road signs should not use text and should convey the relevant message through pictograms and shape of the road signs.

• Because text has to be read (which requires time) whereas pictograms and shapes convey the message faster and require much less attentions of the driver towards the sign

• However, certain signs like speed limit signs, directional signs, definition plates needs to use text

• Design guideline for text in a sign (if no codal suggestion exists):– Text should be brief and to the point – a driver should not required to spend more than a

second or two to read the sign

Lettering, Letter sizes and colour

• Main concern while deciding the colour is the VISIBILITY and CLARITY.• IRC specifies the rage of letter sizes that should be used in signs• The letter height should be so chosen that the design driver is able to read the sign from the a

distance as required by the placement of the sign. Letter size is depend on where the sign is placed.

• Like a person of normal vision can see a letter of height 8.5 mm from approximately 6 m distance

• As the distance increases the letter size should be increases proportionally.

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Placement:

Lateral placement:• Signs are placed generally places slightly away from the main roadway at about right angles

(93- 95 degree) to the direction of travel.• Lateral offset distance should not too less to pose a hazard to traffic not should be too far.• Sign should be placed in the cone of 10 degree.• When sign cannot be posted on the side , it can be provided overhead.

Longitudinal Placement:• Longitudinal position of sign – the distance of the sign from the feature or point of action that

the sign indicate• Position must take into account two factors – safety and clarity

– Should not place much ahead of feature

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Q1. On a freeway a sharp horizontal curve exists. Te speed limit on the curve is 40 kmph. The speed limit on the expressway is 75 kmph. A sign is to be posted, warning driver drivers of the impending curve and advising them to slow down to the speed limit. Determine the longitudinal placement of sign and the letter size for the sign. Assume that the perception-reaction time is 1.5 s, the coefficient of friction is 0.3, the road has 0% grade, and a design driver has 6/9 vision. Also assume that the perception-reaction time includes the time taken to read the sign.

IRC specifies that letter size on expressways should not be greater than 25 cm and greater than 8 cm.

Sol. : Assume letter size is h. sign can be read by a 6/6 vision person from a distance of 6h/8.5 m.

Then a 6/9 person can see this sign from = hh 4705.05.8

696

=×

Now for a driver to reduce the speed safely from 75 kmph (20.83 m/s) to 40 kmph (11.11 m/s) the distance required, d

m 84)03(.81.92

11.1183.205.183.20)(2

2222

=+×

−+×=

+

−+=

Gfgvv

tvdr

firi

Therefore, the total distance required between the point at which the sign become ligible to the driver to the start of curve should be 84 m. If x is the distance (in m) between the sign and the start of curve, then

hxxh4705.084

844705.0−=

=+

This relation gives the designer the choice to choose the letter height, h, based on x.

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So , if assume the letter height is 250 mm (25 cm), then x = -33.625 m

This shows that sign should be placed after the 33.625 m from the start of the curve.

However, it cannot be allowed since (i) visibility may be restricted because the road is bending and (ii) it is not a sound practice to place a sign concerning the driver restrictions on curve and that too after that curve has started. This implies that x should not be allowed to become negative.

Generally the letter heights on such road should not be less than 80 mm. So if 80 mm is used

Then x = 46.36 m before the curve.

Now check whether the sign is legible to the driver for period at least equal to the time taken to read the sign.

If assumed that within 1.5 s perception-reaction time, 1 s is required to read the sign. Then sign should be legible from the a distance of about 20.83 m. Sign is legible from a distance of 0.4705 h = 0.4705x80= 37.64 m. So it is ok.

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Traffic signs divided logically into a number of broad types or categories:

• Mandatory sign: announce and enable traffic regulation, like speed limits, banned movements, etc.

• Cautionary signs: provided advanced warning of some features such as low bridge, left hand curve, etc.

• Informatory signs: provide information to the drivers

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Mandatory Signs: announce and enable traffic regulation, like speed limits, banned movements, etc.

Left turn prohibitedRight turn prohibitedPedestrians prohibited Hand carts directionTongas direction

Bullock carts directionBullock carts and handcarts directionHorns prohibitedCycles prohibitedTrucks prohibited

All vehicles prohibitedVehicles prohibited in both directionOne way signs-vehicles prohibited in one direction Straight Prohibitedor no

entry

Speed limit No stopping or standingNo Parking Overtaking prohibited U- turn prohibited

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Compulsory ahead Compulsory ahead or turn left

Compulsory ahead or turn right

Compulsory turn right aheadCompulsory turn left

Compulsory keep leftCompulsory sound hornCompulsory cycle trackRestriction ends signCompulsory bus stop

Axle load limitLoad limit Length limit Height limit Width limit

Give way Stop

Mandatory Signs Contd..:

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Cautionary Signs: provided advanced warning of some features such as low bridge, left hand curve, etc.

Pedestrian Crossing Cycle CrossingLoose GravelSlippery Road Narrow Bridge

Road wideness ahead Narrow road ahead Steep descent Steep ascent Left reverse bend

Right reverse bend Left hair pin bendRight hair pin bendLeft hand curve Right hand curve

FerryFalling Rocks CattleMen at Work School Ahead

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Hump or rough road Dangerous dip Roundabout Major road ahead Major road ahead

Staggered Intersection Staggered Intersection T-IntersectionY-IntersectionY-Intersection

Y-IntersectionSide Road Left Side Road Right Gap in MedianCross Road

50-100 meters 200 meters 50-100 meters 200 meters Barrier ahead

Cautionary Signs Contd..:

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Informatory Signs

First-aid post Eating place Resting place

Hospital Petrol pump Public telephone

First aid post Place identification sign Direction sign

Destination sign Re-assurance sign Advanced direction sign

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Parking lot Auto rickshaws Parking lot Taxis Parking lot Cycles

Parking lot Scooters and motorcycle Parking both sides Park this Side

Informatory Signs Contd..: