International Conference on Modern Roundabouts,
September 1998, Loveland, Colorado, USA
Roundabout
Capacity and
Performance
(Revised June 2001)
Rahmi Akcelik
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Presentation schedule

Research Summary

Roundabout Capacity and
Performance Modeling:
 ISSUES
 DISCUSSION

About Australia

About aaSIDRA
Research Summary
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Roundabouts:
capacity and performance
 Extensive
research and
development work
 Heavily
directional (dominant)
origin-destination movements
(congestion)
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Roundabout
Metering
Signals
(current research)
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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 321
1 8 00
N AAS R A
1 6 00
S ID R A (1 )
H C M 97 U p p er
1 4 00
E n try la n e c a pa c ity (ve h /h)
S ID R A (2 )
1 2 00
AU S T R O AD S
TR L
1 0 00
H C M 97 L ow er
8 00
6 00
4 00
2 00
0
0
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30 0
600
9 00
1200
C i rcu l a ti n g fl o w ra te (p c u /h )
1 50 0
1800
International Conference on Modern Roundabouts,
September 1998, Loveland, Colorado, USA
Roundabout Capacity and
Performance Modeling:
ISSUES
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Estimating roundabout entry lane
capacity and performance measures
 Analytical
models
(not
simulation)
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Capacity 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 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 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 interactions amongst
approach flows
Modeling the roundabout AS A SERIES
OF T-JUNCTIONS is inadequate
(heavy and unbalanced demand
flows require modeling of origindestination and queuing effects )
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Approach lane use
characteristics of
the traffic streams
that constitute the
circulating flow
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Ignoring approach flow interactions cause
overestimation of capacity (underestimation
of delays and queue lengths
Gap acceptance capacity (veh/h)
1600
1400
nc = 2 (Qg)
1200
nc = 2 (Qe)
1000
nc = 1 (Qg)
nc = 1 (Qe)
800
600
nc = 1: Di = 40 m
400
nc = 2: Di = 50 m
200
pcd = 0.50, pqd = 0.80
0
0
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300
600
900
1200
1500
1800
Circulating flow (pcu/h)
2100
2400
2700
3000
3300
Issue: Analysis detail
(level of aggregation)
more detailed
model of
traffic stream
Individual
vehicles
Microsimulation
models
Drive
cycles
Traffic
flows
Speed-flow
functions
UK "empirical
model" falls in
this category
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aaSIDRA
Most traffic analysis models
Most transport
planning models
Approaches
Lane groups
Individual LANES
more detailed model of road geometry
Lane-by-lane analysis

aaSIDRA is the only
widely-used analytical
software that uses the
lane-by-lane analysis
including short lanes
SPATIAL MODEL rather than
LINKS or LANE GROUPS
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Basic concepts of traffic analysis
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Issue: Capacity measurement method
 By
congestion (saturated
conditions only)
 By total departures from queue
(unsaturated conditions)
Measuring capacity :
unsaturated gap cycles
-
-
tb
Opposing
stream
vehicles
tu
Capacity = s g/c
s = 3600 / 
Unused capacity
Saturated flow
Unsaturated flow
Queued vehicles
time
Give-way
(yield) / stop
line
“r”
Vehicle
arrivals





“g”
Unqueued
vehicles
queue
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Back of queue
Entry
stream
vehicles
"g / c" ratio
1.000
"g / c" ratio
0.800
Capacity =
s (g/c)
Two-lane sign control
Critical gap = 4 s
Follow-up headway = 2 s
0.600
where
s = 3600 / 
0.400
0.200
0.000
0
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600
1200
1800
2400
Opposing flow rate (pcu/h)
3000
Issue: Linear regression (UK) vs
Gap acceptance (US & Australia)



“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)
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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Issue: Linear regression (UK) vs
Gap acceptance (US & Australia)
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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Issue: Linear regression (UK) vs
Gap acceptance (US & Australia)
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?
LANE capacities appear non-linear
Lane capacity (veh/h)
2000
1800
Expon. (Series1)
1600
Poly. (Series1)
y = 1635.8e-0.0009x
R2 = 0.8019
1400
y = 0.0002x2 - 1.0175x + 1529.2
1200
R2 = 0.8073
1000
800
600
400
200
0
0
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500
1000
1500
2000
Circulating flow rate (pcu/h)
2500
3000
Capacity models: Linear or Non-linear?
APPROACH capacities appear linear
but exponential (non-linear) appears to be better
Approach capacity (veh/h)
as simple sum of lane capacities
5000
Linear (Series1)
4500
y = 2520.8e-0.0007x
R2 = 0.491
Expon. (Series1)
4000
Poly. (Series1)
3500
2
y = 0.0001x - 1.0848x + 2413.7
R2 = 0.3853
3000
2500
2000
y = -0.7769x + 2284.3
1500
R = 0.3781
2
1000
500
0
0
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500
1000
1500
2000
Circulating flow (pcu/h)
2500
3000
A demonstration of regression vs
mathematical model:
capacity of cylindrical containers
h
D
h, D parameters generated randomly
(200 data points)
Base diameter, D (cm)
100
80
60
40
20
0
0
20
40
60
Height, h (cm)
80
100
Regression on h & D << the “empirical” approach
800
y = 2.5759x
R2 = 0.1715
600
500
400
300
200
100
0
0
20
40
60
80
100
800
Height, h (cm)
120
y = 3.0845x
R2 = 0.5091
700
600
Capacity (L)
Capacity (L)
700
y = 0.0454x 2 - 0.4079x
R2 = 0.6126
500
400
300
200
100
0
0
20
40
60
Base diameter, D (cm)
80
100
120
Mathematical model:
<< the aaSIDRA approach
C=hA
where A =  (D/2)2
is the base area
h
D
aaSIDRA performance model for intersections
(more general form of the HCM two-term delay models)
P = P1 + P2
Performance
measure
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Delay
Queue length
Effective stop rate
Queue clearance time
Proportion queued
Queue move-up rate
P1
P2
(non-overflow (overflow term)
term)





NA



NA
NA

Why gap acceptance model?
Gap-acceptance model is
needed to estimate
performance statistics
(not just CAPACITY)
Issue: Cycle-average queue vs average
back of queue
h>
-

l
T0
T2
l
T3
G
R
Unqueued
vehicle
count
Nu
New
arrivals
Queue at end
of red
Nr
queue
Unsaturated cycle: T2 < T3
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Queued
vehicles
Ns
T1
time
Queue at start
red
Ni = 0
T3'
tu
T1'
tb
-
Back of
queue
count
Ng
Back of
queue
Nb = Nr + Ng
Issue: Need for delay model comparisons
HCM 94/97
aaSIDRA
60
60
y = 0.5486x + 6.6815
R2 = 0.4186
40
30
20
40
30
20
10
10
0
0
0
10
y = 0.6343x + 3.4477
R2 = 0.6581
50
SIDRA delay (s)
HCM 94 delay (s)
50
20
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30
40
Simulated delay (sec)
50
60
0
10
20
30
Simulated delay (s)
40
50
60
Issue: Modeling of flares / short lanes

Short lane capacity is flow dependent

aaSIDRA model uses back of queue and
predicts excess flow into adjacent lane
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Issue: Lane utilisation
Lane under-utilisation is
best modeled using a
lane-by lane method
as in aaSIDRA
This helps with design of
lane disciplines
Roundabout
case:
Melbourne
ITE 67th
Ann.
Meeting
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Roundabout case: Canberra
See ARR 321
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About Australia
Sydney - population 4 m
Melbourne - population 4 m
aaSIDRA
aaTraffic Signalised & unsignalised Intersection
Design and Research Aid
Further info available from
http://www.akcelik.com.au/downloads.htm


Introducing_aaSIDRA
(PowerPoint presentation)
SIDRA_and_UK_Roundabout Models.pdf
(Acrobat file)
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“it is still an
unending story”
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