Capacity Analysis

Corinna MulykCorinna Mulyk

CivE 499April 2, 2009

Alberta Transportation

Presentation OutlinePresentation Outline

• What is capacity?What is capacity?• Traffic flow and LOS review

h i i l i d f ? h i i• What is capacity analysis used for?  Why is it important?

• How to improve capacity?

ReferencesReferences

• Canadian Capacity Guide for SignalizedCanadian Capacity Guide for Signalized Intersections

• Highway Capacity Manual 2000• Highway Capacity Manual 2000

CapacityCapacity

• Capacity of a facility = max hourly rate atCapacity of a facility = max. hourly rate at which persons or vehicles reasonably can be expected to traverse a point or a uniformexpected to traverse a point or a uniform section of a lane or roadway during a given time period under prevailing roadway traffictime period under prevailing roadway, traffic & control conditions

CapacityCapacity

• Capacity for a given facility is the flow rate thatCapacity for a given facility is the flow rate that can be achieved repeatedly for peak periods of sufficient demandNOT the absolute max. flow rate observed on the facility

• Units of capacity can be:Units of capacity can be:– Persons per hour– Passenger cars per hourPassenger cars per hour– Vehicles per hour

Traffic FlowTraffic Flow

• Mathematical relationship among flow(q), p g (q),density(k) & space mean speed(vs) –> q=kvs

• Flow ‐> equivalent hourly rate at which vehicles pass a point on a roadway during a time periodpass a point on a roadway during a time period less than 1 hour

• Density ‐> # of vehicles (n) travelling over a unitDensity   # of vehicles (n) travelling over a unit length of roadway (L) at a point in time, k=n/L

• SMS ‐> harmonic mean of speeds of vehicles i i d d i i l f ipassing point on roadway during interval of time, 

also equals average speed over a length of roadway

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Fundamental Diagram of Traffic FlowFundamental Diagram of Traffic Flow

vf vf

MS

MS

Uncongested flow

SM SM Congested flow

kj0Density

0Flow

SMS vs. density SMS vs. flow

Fundamental Diagram of Traffic FlowFundamental Diagram of Traffic FlowOptimal flow or capacity q

Mean free flow speed, ufcapacity,qmax

w (q

)

Optimal speed, vo

Flow

Speed is the slope. v = q/k

Uncongested flow

Congested flow

Density (k)Jam density, kj

ow

Optimal density, ko

Modelling Traffic FlowModelling Traffic Flow

• Greenshields modelGreenshields model• Greenburg model

Greenshields ModelGreenshields Model

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vv f kk

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Nice characteristics of the Greenshields model:

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kk

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q 2

This model works for all k = 0 to k = kj

Greenburg ModelGreenburg Model

kk

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ks

kk jl

kckq jln

Characteristics of the Greenburg model:

jk k k jcvo 1ln o

j

kk

or 1ekk

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kvq ookvq max

This model does not work near k = 0. Do you know why?

Quality & Levels of ServiceQuality & Levels of Service

• Level of service (LOS) ‐> quality measure e e o se ce ( OS) qua ty easu edescribing operational conditions within a traffic stream, in terms of such service measures as:– Speed & travel time– Freedom to maneuverT ffi i t ti– Traffic interruptions

– Comfort– Convenience– Convenience

• Letters designate each level, from A to F.  LOS A ‐> best operating conditions.  LOS F ‐> worstbest ope at g co d t o s. OS o st

Freeway LOSPictorial representation ofvarious freeway conditions• A –free flow• B near free flow other• B –near free flow, other 

users present• C –still near free flow, 

but restricted movements

• D –declining speeds, little space to absorb incidents or other traffic disturbances

• E –near or at capacity• F –breakdown, stop‐

and go oscillationsand‐go oscillations

LOS ALOS A

F fl ti ( )• Free‐flow operation (vf)• Very low density

– Less than 7 pcpkmpl– Average spacing of about 160m between cars

• Low restriction on maneuverability within the traffic

• Physical and psychological comfort

LOS BLOS B

• Reasonable free‐flow condition• Low density

– Less than 11 pcpkmpl– Average spacing of about 100m between cars

• Physical and psychological comfort

LOS CLOS C

• Speed close to V• Speed close to Vf.• More restrictions on maneuverability than level Blevel B.

• Queue could be expected on incidents. • Higher density than level B• Higher density than level B

– Less than 16 pcpkmplAverage spacing of about 66m between cars– Average spacing of about 66m between cars

LOS DLOS D

• Speeds decline with increasing flowsSpeeds decline with increasing flows• Limited freedom to maneuver• Higher density than level C• Higher density than level C

– Less than 22 pcpkmpl– Average spacing of about 50m between cars– Average spacing of about 50m between cars

LOS ELOS E

• Little room to maneuver (lane changing)• Immediate queuing in minor incidents.• Higher density than level D

– 28 pcpkmpl28 pcpkmpl

LOS FLOS F

• Breakdown condition• Breakdown condition• Speeds are reduced substantially.• Stoppages may occur for short or long periods of time. 

• In the extreme, speed can drop to zero.

Why are we concerned with LOS?Why are we concerned with LOS?

• LOS is an indication of quality.LOS is an indication of quality. • To set up a minimum standard.• To communicate with the public decision• To communicate with the public, decision                makers and technical people 

• To compare roads• To compare roads. • To determine number of lanes.D t i th h t i ti f d• Determine the characteristics of a road (capacity, speed, delay,…).

Service Flow RatesService Flow Rates

• Maximum flow rate for a facility while maintaining a y gdesignated LOS (except LOS F)

• Each facility has 5 service flow rates (for LOS A ‐> E)– Effectively define flow boundaries between levels of service

• Service flow rate generally based on a 15 min. period.Service flow rate generally based on a 15 min. period.  Hourly service flow rate defined as 4 times the peak 15 min. volume

fl l f d / l• LOS C or D service flow rate typical for design/planning to ensure acceptable operating service for facility users

Max. Service Flow RateMax. Service Flow Rate

Performance MeasuresPerformance Measures

• Reflect operating conditions of a facility givenReflect operating conditions of a facility, given a set of roadway, traffic & control conditions– i e Travel speed & density on freeway delay at– i.e. Travel speed & density on freeway, delay at traffic signal, pedestrian walking speed

• Service measure – one or more performance• Service measure – one or more performance measures that are primary determinant of LOS for each facility typefor each facility type

Saturation FlowSaturation Flow

• Capability to accommodate the vehicular arrival Capab ty to acco odate t e e cu a a aflow by individual intersection lanes

• Highest sustainable departure flow across the g pstop line during the green interval of a traffic signal

• Used to calculate parameters describing how well an intersection operatesD fi d t t hi h hi l iti i• Defined as: rate at which vehicles waiting in a queue during red interval cross the stop line during the green intervalduring the green interval

Capacity & LOS AnalysisCapacity & LOS Analysis

• Facilities classified into 2 categories of flow:Facilities classified into 2 categories of flow:– Uninterrupted flowInterrupted flow– Interrupted flow

Uninterrupted FlowUninterrupted Flow

• No fixed elements (e g traffic signals) externalNo fixed elements (e.g. traffic signals) external to traffic stream that might interrupt flow

• Flow conditions result from:• Flow conditions result from:– Interactions among vehicles in traffic streamI i b hi l d i &– Interactions btw. vehicles and geometric & environmental characteristics of roadway

E F f ili f i• E.g. Freeway facility – causes of congestion that can interrupt flow are internal

Interrupted FlowInterrupted Flow

• Have controlled and uncontrolled accessHave controlled and uncontrolled access points that can interrupt traffic flow

• Access points include traffic signals stop &• Access points include traffic signals, stop & yield signs, and other types of control that stop or slow traffic periodically (e gstop or slow traffic periodically (e.g. roundabout) irrespective of amount of trafficT i ll i d i & bi l fl• Typically transit, pedestrian & bicycle flows considered interrupted flow

Capacity & LOS AnalysisCapacity & LOS Analysis

• Interrupted flow – analysis must account forInterrupted flow  analysis must account for the impact of fixed interruptions (traffic signals stops along bus/transit line)signals, stops along bus/transit line)– E.g. Traffic signal limits time available to various movements in an intersection. Capacity limitedmovements in an intersection.  Capacity limited not only by physical space but also by time available for movements.

Capacity AnalysisCapacity Analysis

• Different capacity analysis required for:Different capacity analysis required for:– Freeways/ExpresswaysTwo lane roads– Two‐lane roads

– Multiple‐lane roadsI t ti– Intersections

– TransitP d i– Pedestrian

Capacity AnalysisCapacity Analysis

• Principle objectives:c p e object es:1. to estimate max. # of persons or vehicles a facility can accommodate with reasonable safety during a 

ifi d ti i dspecified time period• Facilities generally operate poorly at or near capacity, therefore rarely planned to operate in this range

2. estimate max. amount of traffic a facility can accommodate while maintaining its prescribed level of operation (LOS)of operation (LOS)

• Provides tools to assess facilities in order to plan and design improved facilitiesg p

Factors Affecting Capacity & LOSFactors Affecting Capacity & LOS

• Base conditions – standard conditions, must be ,adjusted to fit prevailing conditions on facility– Assume good weather, good pavement conditions, users familiar with facility no impediments to trafficusers familiar with facility, no impediments to traffic flow

– E.x. Level grade, lane width 3.6 m, no heavy vehicles, etcetc.

• Prevailing conditions– Roadway conditionsRoadway conditions– Traffic conditions– Control conditions

Base Roadway Conditionsd l lUn‐interrupted Flow Facilities

• 3.6 meter lane width3.6 meter lane width• 1.8 meter from edge of lane to obstructions• Free Flow Speed 100 km/h• Free Flow Speed 100 km/h• Only Passenger CarsL l T i• Level Terrain

• No “NO PASSING” zones• No “ Impediments” such as traffic control or turning vehicles

Base Roadway Conditionsd lInterrupted Flow

• 3.6 meter lane width3.6 meter lane width• Level Grade• No curb parking on approaches• No curb parking on approaches• Only Passenger CarsN l l TRANSIT BUS t• No local TRANSIT BUS stops

• Not Located in Central Business District• No “Pedestrians”

Prevailing Roadway ConditionsPrevailing Roadway Conditions

• Geometric & other elementsGeometric & other elements– # of lanesType of facility & its development environment– Type of facility & its development environment

– Lane widthsSh ld idth l t l l– Shoulder width, lateral clearances

– Design speedH i l & i l li– Horizontal & vertical alignments

– Availability of exclusive turn lanes at intersections

Prevailing Traffic ConditionsPrevailing Traffic Conditions

• Vehicle typee c e type– Entry of vehicles other than passenger cars affects # of vehicles that can be served

– Heavy vehicles (trucks, RVs, buses) are larger/take up more space & have poorer operating capabilities, particularly acceleration, deceleration, maintaining p y , , gspeed on upgrades

• Lane or directional distribution– Percentage of traffic utilizing each lane or direction of travel. Optimal conditions when amount of traffic is about the same in each direction or laneabout the same in each direction or lane

Prevailing Control ConditionsPrevailing Control Conditions

• Control conditions affecting operations:g p– Type of control in use– Signal phasingAll ti f ti– Allocation of green time

– Cycle length– Relationship with adjacent control measurese a o s p adjace co o easu es

• Other considerations:– Restriction of curb parking– Turn restrictions– Lane use controls– One‐way streets– One‐way streets

Levels of AnalysisLevels of Analysis

• OperationalOperational• Design

l i• Planning

Levels of AnalysisLevels of Analysis

• OperationalOperational– Current or anticipated conditions– Evaluate need for minor, low‐cost improvements thatEvaluate need for minor, low cost improvements that can be implemented quickly

– Help decide between operating condition alternatives when doing a comparison (signal timing & phasing, application of traffic control devices, addition of HOV or bike lanes etc )or bike lanes, etc.)

– Inputs can be based on field measurementsTo answer: when in near term is facility likely to fail?– To answer: when, in near term, is facility likely to fail?

Levels of AnalysisLevels of Analysis

• DesignDesign– Establish detailed physical features (basic # of lanes need for auxiliary lanes etc ) that will allowlanes, need for auxiliary lanes, etc.) that will allow new or modified facility to operate at desired LOS

– Mid to long‐term implementationMid to long term implementation

Levels of AnalysisLevels of Analysis

• PlanningPlanning– Strategic issues, planning studies, i.e. possible highway system configurationhighway system configuration

– Long‐term implementation time frame

Freeway CapacityFreeway Capacity

• Is the maximum 15‐min. flow that can beIs the maximum 15 min. flow that can be accommodated by a uniform freeway segment under prevailing traffic and roadway conditions in one direction.

• The value of capacity for freeways with ideal traffic and road conditions is 2400 pcphpl.

LOS Criteria for Basic Freeway Sections ( k /h) bl(110 km/h)‐ Table 6‐1

LOSk

(pc/km/l)Speedkm/h

qpcphpl

q/c(p / / ) / p p p

AB

711

110110

7701210

0.330.51B

CD

111622

11010897

121017402135

0.510.740 91D

EF

2228-

9784-

21352350

-

0.911.00

-F

Example l d– Freeway lanes required

• Use LOS knowledge to determine the number of glanes required in each direction on an urban freeway if:– 3000 vph (each direction)3000 vph (each direction)– 12% trucks– 8% busesLOS C– LOS C

– PHF = 0.8– Design speed 110 km/h– 3.6 m lanes– Adequate lateral clearance– 4.1% grade over 900 m4.1% grade over 900 m– Interchanges 400 m apart

Freeway Example ‐ EquationsFreeway Example   Equations

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min15 highest the for pcphplv

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RVsandbuses/trucksofproportionPandP

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direction one in slane of numberN,factor hourpeakPHF

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RVs and buses/truck for PCEsE and E

RVsandbuses/trucksof proportionPandP

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factor population driverffactor vehicle heavyf

p

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Freeway Example ‐ SolutionFreeway Example  Solution

• Step 1: Determine heavy vehicle factorStep 1: Determine heavy vehicle factorfHV = 1/(1+PT(ET‐1))   ‐> no RVs so PR= 0fHV = 1/(1+0.2(2.5‐1) = 0.77HV /( ( )

• Step 2: Solve for vp , assuming drivers are familiar with the freeway (fp = 1)y ( p )vp = V/(PHF*N*fHV*fp)vp = 3000/(0.8*N*0.77*1) = 4870/Np ( )

N=2 ‐> vp = 2435 pcplph, N=3 ‐> vp = 1623 pcplph, p p

N=4 ‐> vp = 1218 pcplph

Freeway Example ‐ SolutionFreeway Example  Solution

• Step 3: Determine FFSStep 3: Determine FFS

f 0 f 0 f 0 (f h t ) FFS 110 k /hfLW = 0, fLC = 0, fID = 0 (from charts), FFSi = 110 km/hN=2 ‐> FFS= 102.7 km/h, N=3 ‐> FFS=105.2 km/h, N 4 > FFS 107 6 km/hN=4 ‐> FFS= 107.6 km/h

Freeway Example ‐ SolutionFreeway Example  Solution

• Step 4: Determine densityStep 4: Determine densityk = vp/FFS

N=2 ‐> k = 23.7 pc/km/lN=3 ‐> k = 15.4 pc/km/lp / /N=4 ‐> k = 11.3 pc/km/l

Max. density for LOS C is 16 pc/km/l, so N=3.Repeat procedure for down grade.

Example – Analysis of l dSignalized Intersection

• Flow type: interruptedyp p• Service Measure: control delay• Capacity evaluated in terms of demand flow rate 

( / )to capacity ratio (v/c ratio), LOS evaluated on basis of control delay per vehicle (seconds per vehicle)vehicle)

• Control delay = portion of total delay attributed to signal operation, includes initial deceleration d l i d d l fi ldelay, queue move‐up time, stopped delay, final acceleration delay

• Each lane group analyzed separatelyEach lane group analyzed separately

LOS Criteria for Signalized IntersectionsLOS Criteria for Signalized Intersections

• HCM Exhibit 16‐2HCM Exhibit 16 2

Example – Analysis of l dSignalized Intersection

• Determine capacity and LOSDetermine capacity and LOS– Capacity – based on saturation flow rate

• Determine signal phasing required to service all lane g p g qgroups, evaluate warrants for protected movements (i.e., left turns), turn lanes

• Optimize green times to provide necessary LOS for each direction of traffic or lane group– On highways, preference may be given to serving highway traffic over side‐street traffic.

Use of Software for AnalysisUse of Software for Analysis

• SynchroSynchro– The application allows the user to model current or future traffic at an intersection or on a networkor future traffic at an intersection or on a network

– Input prevailing conditions, volumes, traffic signal timing/phasingtiming/phasing

– Performs the analysis and provides output for the LOS, delay, v/c ratio, etc., y, / ,

Synchro SampleSynchro Sample

Improving Capacity at l dSignalized Intersections

• Short‐termS o t te– Adjustment to traffic signal timing or phasing– Coordinating with adjacent traffic signals to improve plattooning

– Prohibiting turning movementsI t di t t• Intermediate‐term– Addition of turning or through lanesChannelization– Channelization

• Long‐term– Grade separationGrade separation

Capacity –hTwo Lane, Two Way Highways

• 3200 pcph is ideal capacity for both directions3200 pcph is ideal capacity for both directions (max. 1700 pcph per direction)

Capacity Improvements h– Two Lane Highways

• Eliminating AccessesEliminating Accesses• Eliminating No Passing Zones

d i ili• Introducing Auxiliary Lanes– Climbing Lanes– Passing Lanes

Questions?Questions?