We know traffic Roundabout Capacity and Performance (Revised June 2001) International Conference on...

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Roundabout Capacity and Performance (Revised June 2001)

Roundabout Capacity and Performance (Revised June 2001)

International Conference on Modern Roundabouts, September 1998, Loveland, Colorado, USAInternational Conference on Modern Roundabouts, September 1998, Loveland, Colorado, USA

Rahmi AkcelikRahmi Akcelik

Presentation schedulePresentation schedule

Research Summary

Roundabout Capacity and Performance Modeling:

ISSUES DISCUSSION

About Australia

About aaSIDRA

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Research SummaryResearch Summary

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Roundabouts: capacity and performanceRoundabouts: capacity and performance

Extensive research and development work

Heavily directional (dominant) origin-destination movements (congestion)

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Roundabout Metering Signals(current research)

Roundabout Metering Signals(current research)

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Research report

ARR 321

Research report

ARR 321 Comparisons of the aaSIDRA, other

Australian and the UK capacity and delay models:

Akçelik, R., Chung, E. and Besley, M. (1998). Roundabouts: Capacity and Performance Analysis. Research Report ARR No. 321. ARRB Transport Research Ltd, Vermont South, Australia (2nd Edition 1999).

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ARR 321ARR 321

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1800

0 300 600 900 1200 1500 1800

Circulating flow rate (pcu/h)

En

try

lan

e c

ap

aci

ty (

veh

/h)

NAASRA

SIDRA (1)

HCM 97 Upper

SIDRA (2)

AUSTROADS

TRL

HCM 97 Lower

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ISSUES


ISSUES

International Conference on Modern Roundabouts, September 1998, Loveland, Colorado, USAInternational Conference on Modern Roundabouts, September 1998, Loveland, Colorado, USA

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Estimating roundabout entry lane capacity and performance measuresEstimating roundabout entry lane capacity and performance measures

Analytical models(notsimulation)

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Capacity and performance modelsCapacity and performance models A good method for predicting capacity and

performance of modern roundabouts should model DRIVER “YIELD” BEHAVIOUR and

ROUNDABOUT GEOMETRY. aaSIDRA model satisfies both criteria using a

gap-acceptance based method to model driver yield behaviour, at the same time allowing for the effects of geometric variables. UK linear regression model used in the

RODEL and ARCADY programs uses only the geometric variables.

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Driver behaviourDriver behaviour

“Yield” means gap-acceptance !(applicable to roundabouts, signals, sign control, freeway merge)

Gap-acceptance model is EMPIRICAL in calibrating driver behaviour parameters:– entry stream characteristics– opposing / circulating stream characteristics

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Roundabout geometryRoundabout geometry

aaSIDRA "parameter sensitivity" facility can be used to obtain graphs of how capacity and a large number of performance parameters (delay, queue length, cost, etc) change with roundabout geometry and driver behaviour (gap-acceptance parameters).

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Modeling the roundabout AS A SERIES OF T-JUNCTIONS is inadequate(heavy and unbalanced demand flows require modeling of origin-destination and queuing effects )

Modeling the roundabout AS A SERIES OF T-JUNCTIONS is inadequate(heavy and unbalanced demand flows require modeling of origin-destination and queuing effects )

Modeling interactions amongst approach flowsModeling interactions amongst approach flows

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Approach lane use characteristics of the traffic streams that constitute the circulating flow

Approach lane use characteristics of the traffic streams that constitute the circulating flow

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0 300 600 900 1200 1500 1800 2100 2400 2700 3000 3300Circulating flow (pcu/h)

Gap

acc

epta

nce

capa

city

(veh

/h)

nc = 2 (Qg)

nc = 2 (Qe)

nc = 1 (Qg)

nc = 1 (Qe)

nc = 1: Di = 40 m

nc = 2: Di = 50 m

pcd = 0.50, pqd = 0.80

Ignoring approach flow interactions cause

overestimation of capacity (underestimation

of delays and queue lengths

Ignoring approach flow interactions cause

overestimation of capacity (underestimation

of delays and queue lengths

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Issue: Analysis detail(level of aggregation)Issue: Analysis detail(level of aggregation)

UK "empirical model" falls in this category

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Lane-by-lane analysisLane-by-lane analysis

aaSIDRA is the only widely-used analytical software that uses the lane-by-lane analysisincluding short lanes

SPATIAL MODEL rather than LINKS or LANE GROUPS

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Basic concepts of traffic analysisBasic concepts of traffic analysis

Issue: Capacity measurement methodIssue: Capacity measurement method

By congestion (saturated conditions only)

By total departures from queue (unsaturated conditions)

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Measuring capacity : unsaturated gap cyclesMeasuring capacity : unsaturated gap cycles

time

queueBack of queue

Queued vehicles

Unqueuedvehicles

“r” “g”

Vehiclearrivals

Unused capacity

Saturated flow Unsaturated flow

s = 3600 /

tu

Opposingstreamvehicles

Entrystreamvehicles

Capacity = s g/c

-

Give-way(yield) / stopline

tb

-

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"g / c" ratio"g / c" ratio

0.000

0.200

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0.800

1.000

0 600 1200 1800 2400 3000Opposing flow rate (pcu/h)

"g /

c" r

atio

Two-lane sign control Critical gap = 4 sFollow-up headway = 2 s

Capacity = s (g/c)

where s = 3600 /

Capacity = s (g/c)

where s = 3600 /

“Empirical” misnomer (use “regression”) HCM 97 Chapter 10 on Roundabouts:

GAP-ACCEPTANCE METHOD UK method for 2-way stop-sign control is also a

REGRESSION MODEL (HCM and aaSIDRA use GAP ACCEPTANCE) !!! Same issues arise !!!

Issue: Linear regression (UK) vs Gap acceptance (US & Australia)Issue: Linear regression (UK) vs Gap acceptance (US & Australia)

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Roundabout Geometry:Compared with the aaSIDRA model, the TRL regression model is OVERSENSITIVE to:

inscribed diameter approach (lane) width and other geometric variables.

This is probably because the TRL database used in 1980s included a large number of sub-standard roundabout designs that existed in the UK historically. This makes the UK model not readily applicable to other countries where modern roundabouts are used.

Roundabout Geometry:Compared with the aaSIDRA model, the TRL regression model is OVERSENSITIVE to:

inscribed diameter approach (lane) width and other geometric variables.

This is probably because the TRL database used in 1980s included a large number of sub-standard roundabout designs that existed in the UK historically. This makes the UK model not readily applicable to other countries where modern roundabouts are used.


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Roundabout Geometry:Modern roundabout designs are more uniform, and therefore, the more recent models based on them are less sensitive to the geometric variables (as in the case of the Australian roundabout model used in aaSIDRA).

German linear regression and gap-acceptance models were found to be sensitive only to the number of entry and circulating lanes!

Roundabout Geometry:Modern roundabout designs are more uniform, and therefore, the more recent models based on them are less sensitive to the geometric variables (as in the case of the Australian roundabout model used in aaSIDRA).

German linear regression and gap-acceptance models were found to be sensitive only to the number of entry and circulating lanes!


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Linearity could be due to measurement method (by approach rather than lane by lane)

A demonstration using aaSIDRA follows >> (similar exercise using real-life & simulation data recommended)

Linearity could be due to measurement method (by approach rather than lane by lane)

A demonstration using aaSIDRA follows >> (similar exercise using real-life & simulation data recommended)


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Capacity models: Linear or Non-linear?Capacity models: Linear or Non-linear?

LANE capacities appear non-linear LANE capacities appear non-linear

y = 1635.8e-0.0009x

R2 = 0.8019

y = 0.0002x2 - 1.0175x + 1529.2

R2 = 0.8073

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Circulating flow rate (pcu/h)

Lan

e c

ap

acit

y (v

eh

/h)

Expon. (Series1)

Poly. (Series1)

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Capacity models: Linear or Non-linear?Capacity models: Linear or Non-linear?APPROACH capacities appear linearbut exponential (non-linear) appears to be betterAPPROACH capacities appear linearbut exponential (non-linear) appears to be better

y = -0.7769x + 2284.3

R2 = 0.3781

y = 2520.8e-0.0007x

R2 = 0.491

y = 0.0001x2 - 1.0848x + 2413.7

R2 = 0.3853

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0 500 1000 1500 2000 2500 3000

Circulating flow (pcu/h)

Ap

pro

ach

cap

acit

y (

veh

/h)

as s

imp

le s

um

of

lan

e c

ap

acit

ies

Linear (Series1)

Expon. (Series1)

Poly. (Series1)

A demonstration of regression vs mathematical model: capacity of cylindrical containers

A demonstration of regression vs mathematical model: capacity of cylindrical containers

D

h

h, D parameters generated randomly (200 data points)h, D parameters generated randomly (200 data points)

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Height, h (cm)

Bas

e di

amet

er,

D (

cm)

Regression on h & D << the “empirical” approachRegression on h & D << the “empirical” approach

y = 2.5759x

R2 = 0.1715

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Height, h (cm)

Cap

acity

(L)

y = 3.0845x

R2 = 0.5091

y = 0.0454x2 - 0.4079x

R2 = 0.6126

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Base diameter, D (cm)

Cap

acity

(L)

Mathematical model: << the aaSIDRA approachMathematical model: << the aaSIDRA approach

D

h

C = h Awhere A = (D/2)2

is the base area

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aaSIDRA performance model for intersections(more general form of the HCM two-term delay models)

P = P1 + P2

aaSIDRA performance model for intersections(more general form of the HCM two-term delay models)

P = P1 + P2

Performance P1 P2

measure (non-overflow term)

(overflow term)

Delay

Queue length

Effective stop rate

Queue clearance time NA

Proportion queued NA

Queue move-up rate NA

Gap-acceptance model is needed to estimate performance statistics(not just CAPACITY)

Gap-acceptance model is needed to estimate performance statistics(not just CAPACITY)

Why gap acceptance model?Why gap acceptance model?

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Issue: Cycle-average queue vs average back of queueIssue: Cycle-average queue vs average back of queue

T1

T2

time

queue

Back of queue

Nb = Nr + Ng

Queue at end of red

Nr

Queue at start red

Ni = 0

Queuedvehicles

Ns

Unqueuedvehiclecount

Nu

Unsaturated cycle: T2 < T3

T0

R G

Back of queue count

Ng

New arrivals

T3

tb tu

l

-

T1' T3'

l

- h >

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Issue: Need for delay model comparisonsIssue: Need for delay model comparisons

HCM 94/97 aaSIDRA HCM 94/97 aaSIDRA

y = 0.5486x + 6.6815R2 = 0.4186

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0 10 20 30 40 50 60Simulated delay (sec)

HC

M 9

4 d

elay

(s)

y = 0.6343x + 3.4477R2 = 0.6581

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0 10 20 30 40 50 60Simulated delay (s)

SID

RA

del

ay (s

)

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Issue: Modeling of flares / short lanesIssue: Modeling of flares / short lanes

Short lane capacity is flow dependent

aaSIDRA model uses back of queue and predicts excess flow into adjacent lane

Issue: Lane utilisationIssue: Lane utilisation

Lane under-utilisation is best modeled using a lane-by lane method as in aaSIDRA

This helps with design of lane disciplines

Lane under-utilisation is best modeled using a lane-by lane method as in aaSIDRA

This helps with design of lane disciplines

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Roundabout case: Melbourne

ITE 67th Ann. Meeting

Roundabout case: Melbourne

ITE 67th Ann. Meeting

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Roundabout case: Canberra See ARR 321 Roundabout case: Canberra See ARR 321

About AustraliaAbout Australia

Sydney - population 4 mSydney - population 4 m

Melbourne - population 4 mMelbourne - population 4 m

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aaSIDRAaaTraffic Signalised & unsignalised Intersection

Design and Research Aid

aaSIDRAaaTraffic Signalised & unsignalised Intersection

Design and Research Aid

Introducing_aaSIDRA (PowerPoint presentation)

SIDRA_and_UK_Roundabout Models.pdf(Acrobat file)

Further info available from http://www.akcelik.com.au/downloads.htm

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“it is still an

unending story”

“it is still an

unending story”

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