Chapter 5 1

Chapter 5: Traffic Stream CharacteristicsChapter 5: Traffic Stream Characteristics

Explain the difference between Explain the difference between uninterrupted flow and interrupted flowuninterrupted flow and interrupted flow

Explain the three principal traffic-stream Explain the three principal traffic-stream parameters and how to obtain themparameters and how to obtain them

Explain the relationship among the three Explain the relationship among the three macroscopic principal traffic-stream macroscopic principal traffic-stream parametersparameters

Chapter objectives: By the end of these chapters the student will be able to:

Chapter 5 2

5.1 Types of traffic facilities5.1 Types of traffic facilities

Uninterrupted Uninterrupted flow facilityflow facility

No external factors to cause periodic No external factors to cause periodic interruption of flow.interruption of flow. Traffic flow is a product of interaction Traffic flow is a product of interaction between vehicles and geometric and between vehicles and geometric and environmentenvironment

E.g.E.g. Basic sections of a freewayBasic sections of a freeway

Interrupted flow Interrupted flow facilityfacility

Have external devices that Have external devices that periodically interrupt traffic flowperiodically interrupt traffic flow Constant stopping and restarting Constant stopping and restarting neededneeded

E.g. Urban streets and arterialsE.g. Urban streets and arterials

Remember it does not mean the quality of operation.

Chapter 5 3

5.2 Traffic stream parameters5.2 Traffic stream parameters

Macroscopic parametersMacroscopic parameters Microscopic parametersMicroscopic parameters

Volume or flow rate, Volume or flow rate, vv or or qq = 1/ = 1/hh

Headway (or time Headway (or time headway), headway), hh

Speed, S or vSpeed, S or v Speeds of individual Speeds of individual vehicles, svehicles, s

Density, k or D = 1/Density, k or D = 1/dd Spacing (or distance Spacing (or distance headway), headway), dd

Chapter 5 4

5.2.1 Volume and flow rate5.2.1 Volume and flow rate

Can you define these?

AADT

AAWT

ADT

AWT

DDHV = AADT * K * D

What’s the difference between “Volume” and “Flow (or Flow rate)”?

Sub-hourly volume and flow rate

Define PHF = (peak hourly volume) / (max. rate of flow for that hour)

PHF = V/(4 * V15)

What does this tell you?

v = V/PHF

= peak flow rate for the 15-minute peak period

(Review Tables 5.1 and 5.2 & 5.3 queuing)

Illustration of Daily Volume ParametersIllustration of Daily Volume Parameters

Chapter 5 5

Volume, Flow Rate, and QueuingVolume, Flow Rate, and Queuing

Chapter 5 6

If capacity is 4,200 vph, then the 15-min capacity volume is 4,200/4 = 1,050.

Chapter 5

5.2.2 Speed and travel time5.2.2 Speed and travel time

Time mean and space mean speed: Know the difference?

Time mean Time mean speed (TMS)speed (TMS)

Average speed of all vehicles Average speed of all vehicles passing a pointpassing a point over some specified time periodover some specified time period

TMS = ∑ (d/tTMS = ∑ (d/tii)/n)/n

Space mean Space mean speed (SMS)speed (SMS)

Average speed of all vehicles Average speed of all vehicles occupying a given occupying a given sectionsection over some specified time period or over some specified time period or harmonic mean of individual speeds.harmonic mean of individual speeds.

SMS = d/(∑(tSMS = d/(∑(tii)/n) = nd/∑(t)/n) = nd/∑(tii))

(See page 112 and Table 5.5)

sft

n

nnSMS

sftn

nnTMS

/7.583

)2*0.440.88

/0.662

)0.440.88

Illustrative Computation of TMS and SMSIllustrative Computation of TMS and SMS

Chapter 5 8

Chapter 5 9

Speed typesSpeed types

Do you know the difference among these speeds?

Average travel speed

Average running speed

Operating speed = Max safe speed , without exceeding the design speed of the highway segment

Percentile speed = a speed below which the stated percent of vehicles in the traffic stream travel

Chapter 5 10

5.2.3 Density and occupancy5.2.3 Density and occupancy

Definition: the number of vehicles occupying a given length of highway or lane (vpm, vpmpl, v/km, v/km/lane)

Relationship among v, S, D:

v = S * D

Flow rate = Speed * Density

Unit length (1 mile or 1 km)

Chapter 5 11

Speed

ELpt

Speed

Lpt v )()('

Occupancy as a surrogate parameter for density

Density is difficult to measure. So, we use “occupancy” as a surrogate measure for density. This can be obtained by traffic detectors of any kind.

Occupancy: the percent of the roadway (in terms of time) that is covered (occupied) by vehicles.

Apparent occupancy

Actual occupancy

Speed

ELLpt v

)(

This is the occupancy measured at a point.

Chapter 5 12

Flow rate, speed and occupancy are given; Flow rate, speed and occupancy are given; estimate densityestimate density

ELL

miftOD

v

app

5280

mi

veh

hourmi

hourveh

S

q

Speed

rateFlowD

_

Typically occupancies given by the detectors are apparent occupancies.

dv

app

LL

miftOD

5280

But if average flow rate and average speed for a certain time period are given, density can be computed as:

(Eq.5-7)

Chapter 5 13

Derivation of the Density-Occupancy Derivation of the Density-Occupancy RelationshipRelationship

ELLOD

ELLD

ELL

S

q

S

ELL

T

N

T

TO

S

ELLN

S

ELLNT

S

ELLt

tNhrT

t

ELL

t

ELLmphS

Vapp

V

V

SMS

SMS

Voapp

SMS

V

SMS

Vo

SMS

Vp

po

p

V

p

VSMS

52805280

5280

5280

1

5280

5280

3600

3600

1

5280

3600

3600

5280

3600

3600/

5280/)(

)(

)()(

Estimate SMS using detector data

Compute total time occupied (not occupancy) by N vehicles detected in time period T

Solve the first equation for average time occupied by each vehicle

Plug in the 3rd eq into 2nd eq

Compute the occupancy Oapp. N/T turned out to be flow rate, q. Also q/SMS is density by definition. Now the relation between occupancy, Oapp, and density, D, was established.

Solve for D. Voila, you get Eq. 5.7)

Chapter 5 14

5.2.4 Connection between macroscopic and 5.2.4 Connection between macroscopic and microscopic measuresmicroscopic measures

These are in English units.

D (Density) = 5280 / da where da is average spacing

v (Flow rate) = 3600 / ha where ha is average headway

S (Average speed) = da / ha

Spacing or Space headway

Headway or Time headway

15

5.3 Relationships among flow rate, 5.3 Relationships among flow rate, speed, and densityspeed, and density

Flo

w (

v)

Density (D)

Do you remember whose flow model is used for this?

S = Sf –(Sf/Dj)*D

v = S*D

16

5.3 Relationships among flow rate, 5.3 Relationships among flow rate, speed, and densityspeed, and density

Flo

w (

v)

Density (D)

Optimal flow or capacity

Optimal (critical) density

Jam density

Mean free speed

Optimal speed

Speed is the slope. S = v/D

Do you remember whose flow model is used for this?

S = Sf –(Sf/Dj)*D

Uncongested flow Congested

flow

Unstable flow area