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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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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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Roundabout Capacity and Performance Modeling:
ISSUES
Roundabout Capacity and Performance Modeling:
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
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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.
Issue: Linear regression (UK) vs Gap acceptance (US & Australia)Issue: Linear regression (UK) vs Gap acceptance (US & Australia)
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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!
Issue: Linear regression (UK) vs Gap acceptance (US & Australia)Issue: Linear regression (UK) vs Gap acceptance (US & Australia)
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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)
Issue: Linear regression (UK) vs Gap acceptance (US & Australia)Issue: Linear regression (UK) vs Gap acceptance (US & Australia)
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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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Lan
e c
ap
acit
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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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Circulating flow (pcu/h)
Ap
pro
ach
cap
acit
y (
veh
/h)
as s
imp
le s
um
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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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acity
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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”