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REPRINT
Opposed turns at signalised
intersections: The Australian method
R. AKÇELIK
REFERENCE:
AKÇELIK, R. (1989). Opposed turns at signalised intersections: The Australian
method. ITE Journal 59(6), pp 21-27.
NOTE:
This paper is related to the intersection analysis methodology used in the SIDRA
INTERSECTION software. Since the publication of this paper, many related aspects of the
traffic model have been further developed in later versions of SIDRA INTERSECTION.
Though some aspects of this paper may be outdated, this reprint is provided as a record of
important aspects of the SIDRA INTERSECTION software, and in order to promote software
assessment and further research.
© Akcelik and Associates Pty Ltd / www.sidrasolutions.com
PO Box 1075G, Greythorn Victoria 3104, Australia
Email: [email protected]
OpposedTurnsql Signqlized
Interseclions:
TheAustrqliqn
Method
BYRAHMIAKQELIK
I he 1985 Highwuy Capacity Manual
I ( H C V ) ' b r o u g h rt h e U . S . a n d A u s tralian methodologies' " for signalized
intersections closer together. An important element in this methodology is the
techniquesused for the estimationof opposed (permissive) turn saturation
flows. Although the basic modeling philosophies of the HCM and Australian
methodsare similar, there are significant
differences in the proccdures used and
therefore in the results from the two
methods. In particular, the latest methodology employed in the SIDRA
softwaret? has eliminated the use of opposed turn adjustment factors for lane
groups and adopted an explicit and direct method of modeling individual
lanes. The purpose of this paper is to
hring thesenew methodsto the attention
of the U.S. researcherssince it is understood that efforts are being made to
improve the 1985HCM method. The intention is also to dispel any misunderstanding about the Australian opposed
turn models that may have resulted from
statementsin some U.S. papers.
A 1987paper by Roessexplainingthe
development of procedures for the analy s i s o f s i g n a l i z e d i n t e r s e c t i o n si n t h e
HCM includcs the following statement:
Thc most dramaticchangefrom sourcemat e r i a l si n v o l v e dp e r m i t t c do r o p p o s e dl e f t
turns.Previousmaterialsdcvclopedin Australia. Englandand the United Stateshave
alwaysassumedthat permittedleft turnsfilter
throughthe opposingflow at a calibratedrate
for the entire periodof the greenphase.s
After explaining the HCM model, the
paper goes on to state that this model
was adopted
after it was clear that no simpler methodology
would climinate the overprediction of leftturn capacity,which results from assuming filtration for the entire green phase.
The only Australian
reference in the pa-
per is the ARRB ResearchReport ARR
No. 123.' However, the statement also
relatesto the early Australian modeler'r'rl
since it forms the basis of the opposed
turn model in ARR No. 123. In both
c a s e s ,t h e s t a t e m e n t i s n o t v a l i d : t h e
Australian methods have never assumed
that permitted (opposed) turns filter
through the opposing flow for the entire
length of the green period.
It is hoped that this article will explain
the similarities and differencesbetween
the HCM and the Australian opposed
turn models and dispel any misunderstanding that may have resulted from
earlier statementsby others. The discussion is relevant to opposed turn modeling in general and will be useful towards
explaining the HCM option in the
SIDRA program.r'" In this discussion,
various limitations of the HCM model
will also be pointed out.
The discussionin this article is limited
to the case of a singleopposed (permitted) green period only. The treatment of
the more complicated caseof "protected
plus permitted phasing" (two green periods per cycle) in the HCM has further
limitations, as pointed out in earlier papers using an example from the HCM.'o
A recent U.S. paper analyzedthe same
example and recommended some revi-
s i o n o f H C M . ' ' T h e m o d e l i n go f o p posedturnswith protectedand permitted phasingis fully implemented
in the
SIDRA program in a generalway that
a p p l i e st o b o t h e x c l u s i v ea n d s h a r e d
lanes.IForan exampleof thesharedlane
case,seeFigure6 in cited reference7.1
The Bosic Model
The basic opposed turn model used in
Australia is shown in Figure l. Strictly
speaking, the model applies to the case
of opposed turns in an exclusivelane,
but it is also useful to explain the basis
of the model for opposed turns in a
shared lane. The following model assumptionsare seen in Figure l:
. Opposed turns cannot filter during interval I (blocked-no gap acceptance), which correspondsto the saturated part of the opposing movement
green period,
. Opposed turns can only filter during
interval 2 (departures by gap acceptance), which is the unsaturated part
of the opposing movement green period, and
. The departures after the green period
are included in interval 3.
The notation in Figure I is as ftrllows:
('
:
:
cycle time.
opposing movement effective
rcd and green times.
q, s = opposingmovementarrival and
saturation flow rates,
:
saturated
and unsaturatedpor9,, 9,,
tions of the opposing moveti I
.JUNE{989 . 2,I
ITEJOURNAL
ment green period (9. + g" :
s,.
nt
8),
: opposed turn saturation flow
during g,,, and
: number of vehiclesthat depart
after the end of green period.
All traditional capacity models employ
the simplifying assumption shown in Figure 1 as "Approximate Model l" in order to be able to derive opposed turn
equivalents (or adjustment factors) for
u s e i n t h e p r e d i c t i o n o f c a p a c i t i e so f
shared lanes and lane groups with opposed turns. The basis of this approximation is the use of an average saturation flow, s.,, which applies for the whole
of the opposed turn green period (with
no changein the capacityestimate):
.r,. :
(.r,,9,, + n)/g
(l)
This assumption was used in the early
Australian model"'r and retained in
ARR No. 123' for shared lanes only. For
opposed turns in exclusive lanes, "Approximate Model 2" shown in Figure I
was introduced in ARR No. 123 as a
more accurate model, which treats interval l as part of the lost time-i.e., as
effectivelyred. Essentially,the same opposed-turncapacityis obtained from thc
two approximate models shown in Figure l. However, Model 2 predicts queue
lengths and delays better, which has advantagesfor predicting short lane capacities also. This model was subsequently
extendedto shared lanes in the SIDRA
program.'
Opposing
movemenl
departurepattern
The reason for the earlier reported
statement*that in the Australian method
"permitted left turns filter through the
opposing flow . . . for the entire period
of green phase" may be related to the
assumption of the "Approximate Model
l" shown in Figure l. However. this assumption is also used in the derivation
of the HCM opposed-turn adjustment
factors, as will be explained below. It
shouldbe noted that an evenearlier U.S.
paper incorrectly presentedthe early
Australian model as if the model predicted the "left-turn" capacity as s,.g/c
( 1 2 0 0f i n t h a t p a p e r ' s E q u a t i o n 2 i s
equivalentto s,,in the original model).'r
It may be that this is the basis of the
statementthat permitted left turns filter
through the opposing flow for the entire
period of green phase in the Australian
Method.* On the other hand, another
U.S. paper had stated the early Australian model correctly, and found very favorable results in a field evaluation of the
model.'o
OpposedTurnsin o
Shoredlone
Opposedturn
departurepaltern
Departures
by
gap acceptance
Deoarturesafter
lhe greenperiod
S,
Approximate Model 1
So9=Sr9r+nt
Approxlmate Model 2
sugo=sugu+nf
Startloss
o
End gain
Figure l. Basicopposedturn model. Souncn: Appendix F in cited reference2.
.JUNE1989
22 . ITEJOURNAT
For shared lanes, the capacity characteristics of opposed turns and other traffic
need to be mixed. The term "opposed
turn" usually applies to left turns in the
United States(driving on the right) and
right turns in Australia (driving on the
left). Generally,the term "opposed
turn" also applies to left turns in Australia. or to right turns in the United
States(turning from a slip lane or turning on red), or giving way to opposing
right turns according to the Victoria and
New Zealand rule. Again, generally
speaking,opposed turns in shared lanes
may mix with through, left-, or rightturning traffic, as the case may be. Although the following discussion applies
generally,it will be presented in terms of
"opposed left turns" and "through"
traffic in shared lanes since the HCM
model is expressed specifically in these
terms.
The assumptionsinvolved in deriving
the HCM equations for shared lanes
with opposed left turns and through traffic can be seen in Figure 2. Importantly.
the model divides interval I (when opposing traffic is at saturation) into two
parts:
. During the first part of interval l. a
number of through vehiclescan depart
before the first left-turning vehicle arrives at thc stop line and blocks the
lane. The length of this period is g, and
the number of through vehicles that
can depart is .1, : .srgr. where sr. is
through traffic saturation flow
. During the rest of intcrval 1 (g, - g,),
no through or lcft-turning traffic can
depart (the HCM notation for g, is g.,).
In interval 2, opposed left turns and
through traffic depart at a mixcd saturation flow rate of .r,. The total number
of departuresis S, - s,g,,.In interval 3,
S. vehiclesdepart, which is cquivalentto
n, in Figurc I for the numbcr of departures after the end of thc green period.
The HCM givesthe following left-rurn
factor. 1,,,,for a single excltrsiveor shured
lane (HCM Equation 9-16):
rrl
r
rrn '- &g * 8 g, . 1
ll+p, 1E,-l'11
)
+ = (l+ p,)
(2)
f' =
lu{x)
t+txl-,,
(1)
wherc p, is the proportion of through
vehiclcs in thc sharcd lane (p, : I p, ). ancl y,,is the opposing flow rate
(vch/h).
For an cxclusivcleft-turn lanc, p, :
'l'hcrcfore.
1.0 and g, :
0.
Equation 2
can be rcwritten as
t " , , I,\-El,( + ' o| )
r"'
(' ' .' s )
An analysisof Ecluations2 to .5 shows
that the HCM opposcd-turn model employs thc basic assumptionof the traditional "Approximate Modcl l" shown in
Figurc l-that is, it usesan averagesaturation flow rate throughout thc opposcd grccn period. This is explaincd
below (rcfer to Figurc 2). For the purpose of this discussion,the HCM saturation flow equation (HCM Equation 98) can be writtcn as
s : .s,Nf,f, ,
(6)
whcre
where gr. 9,,, and g are as explained
above,p,. is the proportion of left turners
in the lane (p, : rl,.lq where q, and q
are the left-turn and total flow rates),
and E,. is a through-car equivalent for
left turns (which appliesduring g,,period
only). The HCM ftrrmulas tirr g, and Er.
g, = 2Pt 6-o1'r,7
(3)
.s, - ideal saturation flow per lane (s,,
in the tlCM notation). usually
Iti00 through car units per hour
( t c u / h) ,
f , : thc product of acljustmentfactors
used to allow for the effccts of
l a n e w i c l t h ,g r a d c , a r e a t y p e .
b u s e s ,a d j a c e n tp a r k i n g . h c a v y
vchiclesa
. nd right turns
(-.f",f,,f ,,,,f ,,f,,,f,,,),
N
:
l, , :
number of lanes in the lane
group, and
adjustment factor for left turns in
thc lane group.
For a single lane, N : I and f,, : f,,,,
where f,, is given by Equation 2 or 5.
Putting f. : 1.0 for ideal conditions.thc
saturation flow for a single lane case is
r : s,.f"
An important aspectof the derivationof
lcft-turn factorsgiven in the HCM is that
all through-traffic ffows are assumed to
have ideal saturation flows: s,. : J, :
IU(X)tcu/h : 0.5 tcu/s (1, : 1.0). Thus.
s : 0.51,,,is obtained from Equation 7
as a basis for single-laneopposed-turn
saturationflow
Derivolionot lhe HCM
Equolions
The derivation of the HCM adiustment
factor for opposed left turns in a single
lane. 1,, (Equation 2), and its extension
to the case of opposed turns in a lane
group, f, , (HCM Equation 9-17), are
discusscdhere in referenceto capacities
in various intervalsshown in Fieure 2.
Interval la
Thc averagenumber of through vehicles
per cyclc that can depart before being
blocked by the first left turner to queue
i n t h c l a n e i s S , : s , . 6 , .P u t t i n g . i r : s ,
- 0.-5vch/s and using g, from Equation
. s' ,- l J ( l - l ' l ' - , )
t),
s " 9 = S r 9 , + s y9 r * S "
S,=s1 g1
(7)
(tr)
The generalform of Equation 8 usess,g.
insteadof 0.5 9,. which is the maximum
number of through vehiclesthat can depart during B, (s, : s, : 0.-5veh/s in
Equation 8). as discussedin more detail
laterin this article.
Interval 2
"
91
-f- I
1b
9"- 91
The shared lane saturation flow. s,, during interval 2 (of length g,,)can be found
by mixing the through and opposed leftturn saturation flows (.r, and .r,). Using
the method described in Akgelik'. this
can be expressedas
q/s,:
Figure 2. The opposed turn model for shared lanes (the HCM model approximation
is indicated by the shaded area).
q,,/s, I
qrls,
(9)
lls, : p,.ls,, + p,/s,
(9a)
where q, r7,. and q/ are the flow rates
.JUNE1989. 23
ITEJOURNAL
ftrr total. lcft-turn. and through traffic,
and p, an<Jp , are the proportions of leftturn and through traffic in the lane.
The left-turn saturation flow can be
cxpressedin terms of through traffic saturation flow. .1,, and through car equivalent for lcft turns, E,, as
s,.:
sr/E,
(10)
In interval 2, s,. : s,.where .r,.is the filter
(opposed) turn saturation flow. Using
thc ideal saturationflow for through traffic (.s, : s,),
E, : s,ls,,
(11)
is tirund. Comparing Equations 4 and ll.
it is seen that the HCM method usess,
: 1tt00vch/h and
s,, :
l4(X) -
v.,
(12)
where y.,is the opposing flow in veh/h.
Puttings, : s,lE, ands, : .r,in Equapg
t:
tion9andsubstitutin
| - p,,the
averagesaturation flow during interval 2
is found as
s':
s,
ri/r;
-t
(lr)
Thercforc,the numbcrof vchiclesthat
can departduring9,,is foundas
riod is a function of the proportion of
left turners in the lane, as given by
S.:l+p,
Thus. the HCM model assumesthat ^!
changcs betwcen I for thc casc of a fcw
lcft turners in the lane and 2 for the case
of an exclusiveleft-turn lane.
Average Saturation Flow for the
Entire Green Period
For the shared lanc, the total capacity
(number of departures) per cycle is the
sum of capacitiesin intervals la, 2, and
3 (no capacityin interval lb):
S :
s'8"
| + p , ( E ,- l )
E,quation2 implicsthat the numberof
afterthe endof the greenpedcpartures
(16)
f,,, : sts,g
: (.t/ + .S, + S.)/.r,9 (17)
( 14)
Interval 3
Sr + .S" + ,S,.
where Sr, S,, and S,.are given by Equations 8, 14, and l-5. As shown in Figure
2, an average saturation flow. s,,. ftrr the
entire grccn period, g, to yield the same
shared lane capacity as S can be found
from .s,,8 : S. The avcrage shared lane
s a t u r a t i o n f l o w c a n b e e x p r e s s e di n
terms of through traffic saturation flow
as.r,, : 1,,,s,.Using the ideal saturation
flow for through traffic. s, : .r,,and putting s., : Sig where S is as in Equation
16, the left-turn adjustment factor for a
single lane is found as
.S, : s,9,,
-
(15)
usingS,,S,, and5',.from Equationstt. 14,
and 15 and settingsr : 0.-5veh/s.the
HCM formulafor f,,,givenby Equation
2 is found. In other words. the HCM
methodusesan averagesaturationflow
of
(l7a)
. s ,:, 0 . 5/ , ,
whichappliesto thc cntircgrecnperiod.
o
Rahmi Akgelik is
a principal research scientist al
Australian
the
Road Research
Board. He is a
Memher of ITE,
tlrc Institution of Engineers (Australia),
'fRB
Tiaffc Signal Systems Committee,
and ITE Tbchnical Committee 5B'27Left-Turn Lane Storage Length Design
(lriteria. AkE'elik is the author ry' Traffic
Signals:Capacity and Timing Analysis,
one of the best-selling ARRB publicarions. He is also the author of the SIDRA
pa<'kagc, which is nom' in use by about
120 orpanizations in l8 <'ountric.s.
. JUNE1989
24 . ITEJOURNAL
OpposedTurnsin a Lane Group
For opposcd turns in a lane group, the
HCM mcthod makcs a further approximation. Tb dcrive thc opposed left-turn
adjustmcnt facbr, f,.,. for a lane group
of N lanes. it assumesthat all lanes except the shared lane has the ideal saturation flow s,. and hence a capacity of
(N - l) s,g. The capacityof the shared
lane is .r,[,,9(from Equation 17). Thereforc. thc total capacity per cycle for the
lane group is
S' - (N- l)ss + .rl,,s
(lt3)
Tb dcrive.f, ,, averagethe total capacity
per cycle (S') ovcr thc entire green period (L):
s'
: :_ = (N_ | * f,,,)s, (t9)
.s,,,
o
where .r',,is the average saturation flow
for a lane group of N lanes.
Puttingf : I in Equation 6 for ideal
conditions,.s : s,N/,., is obtained. Putting.s : .r',, the HCM adjustmentfactor
for opposcd left turns in a lane group of
N lancs is found as
,,, + (N_ l)
f , _
Jt I
(20)
N
ln othcr words, the HCM opposed leftturn adjustment factor is based on the
use of an average lane group saturation
flow of
. s , , :, 0 . 5 / , , N
(20a)
which appliesto the entire green period.
Comporison wifh lhe
Recenf Ausfrolion Model
The opposcd turn model in the early
Australian modelrr used an E^, factor
that was derived in a similar way to the
explanation given above. The only improvement in the HCM modcl over this
early Australian model is the capacityin
interval | (departures being blocked).
This aspectof the HCM model is further
discusscdbelow.
'fhe
opposed turn adjustment factor
En, method was adopted in ARR No.
123.' but its use was limited to shared
lanes only. A lost time method was introduced in ARR No. 123 for opposed
turns in exclusive lanes (approximate
Model 2 in Figure l). As explained in
detail elsewhere.' the latest Australian
m e t h o d i m p l em e n t e d i n t h e S I D R A
package"' has entirely eliminated the
use of opposed turn adjustment factors.
and it usesopposed turn capacitiesin a
direct way. The method is equivalent to
using S : S/ + .t, + .t,.directly without
nced frrr ohtaining an averagesaturation
flow .r,,(see Figure 2). Furthermore. it
trcats the blocked time (9, - g,) as effective red time, thus extendingthe lost
time method of ARR No. 123 to shared
lanes. This method has advantagesover
the adjustment factor method in terms
of capacity and performanceprediction.
Other important differencesbetweenthe
opposed turn model of SIDRA and the
HCM model are discussedbelow.
Blocked Departures
As discussedpreviously.the lirst term of
the HCM left-turn factor formula
(Equation 2) relates to through traffic
departures before being blocked by left
turners, Sr, as in Equation 8. The use of
this capacity component in thc Swedish
capacity manual was reported a decade
ago.'' The Swedishcapacitymanual gave
two formulas for the casesof one or two
vehicles to queue before blocking the
lane ("blocking queue"). Hegarty and
Pretty applied this method to opposed
left turns in slip lanes(in Australia).'"
Their paper gave a general formula for
departures befrrrebeing blocked, which
uses the "blocking queuc" as a general
parameter.They also gavc a lbrmula for
the cascof a blockingqueuc of one,
which is the same as the HCM formula
except that the ideal saturati()n flow. s,
- 0.5 veh/s.is usedto calculatethe maximum number of dcparturesin the HCM
formula rather than the estimated
through traffic saturation flow, sr..
Although ARR No. 123did not model
dcpartures before lane blockage in
shared lanes. the SIDRA method employs a vcry generalizedshared lane
m o d e l t h a t p r e d i c t s c a p a c i t i e sb e f o r e
lane blockage using the general form of
the model givcn by Hcgarty and Pretty.rn
The "lane interaction" modcl has now
bccn used in SIDRA for a long time'and
a detailed discussionon thc topic can be
found elsewhere.'An important limitation of the HCM formula is that it appliesonly to the caseof a blocking queue
of one (or a "free queue" of zero using
the SIDRA definition). Thc parameter
affects the results significantly(see Figure 5 in cited reference7).
:
turn saturation flow in veh/h is s,,,,,,,,"
360(yB), A is the minimum headway in
an opposing traffic lane in seconds.and
the parameters tr and 0 are calculated
from
x:>3c
where the summation and multiplication
arc for lanesI - I to N, g, is a bunching
factor (proportion of unbunchedvchicles
in lth opposingtraflic lane),4, is the flow
rate in lth opposingtraffic lanc, and A is
as in Equation 21. Figure 3 showss,.values from thc HCM model (Equation l2)
and the SIDRA model (Equation 2l)
w i t h o : 4 . 0 , B - 3 6 ( X Y l 4 0 0: 2 . 5 7
s e c ,A : 2 s e c a n d 0 : 1 . 0( n o b u n c h ing). Equal lane flows are assumedfor
the two- and three-lane opposing flow
cascsin Figure 3. In the caseof unequal
lane flows, Equation 2l gives smaller .r,,
v a l u e s .A s t h e l a n e u t i l i z a t i o nr a t i ( ) i n creases,s,,decreases,and it approachcs
the one-lane .r..value when one of the
lane flows approaches the total flow
value. Thus. thc SIDRA model has the
advantageof sensitivityto the number of
opposingtraffic lanes as well as the lane
utilization in opposing traffic lanes.
It may be considered that when the
number of opposing lanes increase,fil-
1600
1400
Filter Tirrn SaturationFlow
1200
'I'he
filter turn saturationflow rate, s.,,in
the HCM method is given by Equation
12. This correspondsto the gap acceptance formula used in ARR No. 123.
Appendix F. The HCM formula and the
ARR No. 123 gap acceptance fcrrmula
do not take the number of opposing
lancs into account. In SIDRA. thc following gap acceptanceformula (seeThnner,'' and Gipps,'* and Tioutbeckrerr')is
u s e d t o e s t i m a t e. r , , t a k i n g i n d i v i d u a l
lane flows into account:
s":
Ioe
1000
S,
(veh/h)
BO0
i\._
600
400
\*rr::.,..--.
200
200
.a r/l
r - er*
(22)
0-fl(l-Lq,)
tering is more difficult. and thereforethe
gap acceptanceparametersa and p will
i n c r e a s c ,r e s u l t i n g i n l o w e r s , , v a l u e s .
However. there may not be a direct relation bctween the number of opposing
traffic lanes and the gap acceptancc parameters. Visibility, opposing traffic
speed, grades, the actual crossing distance (which could be more than the
sum of opposinglane widths), and so on
are expectedto affect the gap acceptance parameters. In SIDRA. the uscr
can specify o and B parameters for each
opposedturn and can model specificsituations more closely.
For the HCM option in SIDRA. the
default parametersin Equation 2l have
been calibrated against Equation l2 tbr
the one-lane case (c - 4.0, 36(XYg :
l 4 ( X )A
, : 2 , 6 - 1 . 0 ) .A s s e e ni n F i g u r c
3, thc resultsfrom the two equationsare
close for this case, but SIDRA may predict significantlyhigher .s,,values in the
caseof multilane opposingflows, particularly for heavy opposing flows.
The HCM method implies that various adjustment factors (product /, in
Equation 6) multiplies the opposed turn
saturation flow. .r1,,,(see Equations 7 and
l7). Therefore, if a direct and explicit
modelingapproachwere used, Equation
12 would be used ass,, : (lafi) - u,,)/,
and Equation 15 would be used as S,. :
(21\
where o is the acceptcd critical gap in
s e c o n d s ,p i s t h e m i n i m u m d e p a r t u r e
headwayin seconds(maximum opposed
400
600
800
1000 1200 1400 1600 1800
Total opposingflow (veh/h)
Figure3. Opposedturn saturationflow rate (s") during the unsaluratedpart of the
opposingmovementgreenperiod as a function of the total opposingflow rate (the
HCM and SIDRA models).
.JUNE,1989. 25
IIE JOURNAT
'l'his
(l + p,) f,.
m e a n st h a t t h e H C M
method adjusts the opposed turn filter
rate (hasicallya gap acceptanccprocess)
and the number of departuresat the end
of the green period by all the factorsthat
go into /, (including lane width, grade,
area type, adjacent parking, heavy vehicles, etc.). While the correctnessof
t h es e a d j u s t m e n t s i s d c b a t a b l e . t h c
SIDRA method can emulate the HCM
opposed turn fbrmula by using default
valuesof the follow-up hcadwayas 36(X)/
p : l4(X)/, and the nunrbcr of departures after the grcen period as .S,.: ( I
+ p,)f,.
DeparturesAfter the End of the
Green Period
In relation to interval 3 in Figurc l, the
use of thc S. valuc needs to be clarified.
In the "Approximatc Model l" of Figure
I. and in the HCM moclcl shown in Figure 2, 9,, includes the encl gain since g,.
is dcfined as (g g,) whcre g is thc effective green timc (g : displayedgreen
time plus end gain lessstart loss).Thcrefore, S. (or n, in Figure l) is used as
"dcpartures after thc end of elfective
g r ec n p e r i o d . " I f t h i s p a r a m e t e r i s
countcdas thc number of dcpartures
during the yellow and all-red intervals,
that is. after the end of the displayed
grcen period, this methocl will double
count a smallamount of departures
(equal to s,,b for cxclusiveturns. where
D is the end gain). In SIDRA, this is
taken int<taccount by using this paramcter as the number of departures (per
lanc) after the end of the displayedgreen
pcriod.
The Use of Estimated Saturation
Flows
In contrast with the FICM method. thc
S I D R A m e t h o d u s e st h e c s t i m a t c d( a d justcd in the HCM technology) saturat i o n f l o w ( s , ) r a t h c r t h a n t h e i d e a ls a t u ration flow (.r, : lll(X) vch/h) for
. Unopposed traffic in shared lanes
when mixing the opposed and unopposed (e.g.. left and through) traffic.
. The opposing traffic to determine the
g,. and g, pcriods. and
. Calculating the maximum possibledepartures as a parameter frrr thc formula to predict number of departures
before bcing blocked.
Schorr and Jovanis found that the opposing traflic saturation flow is the most
. JUNE{989
26 . ITEJOURNAL
scnsitiveand important parameterin the
opposed turn model, akrng with the opposing flow volume.'' The following example demonstratesthis point clearly.
C o n s i d e r a s i n g l e e x c l u s i v el e f t - t u r n
lane where left turns are opposed by a
single-lanc traffic stream consisting of
through and right turning vehicles.The
opposcd left turn volume is flOveh/h and
the opposing traffic volume is 600 veh/h
(40o/o right turns). The following saturation flow adjustment factors apply to
both streams:
. Thc intersectionis in a central business
district area (1, : 0.90),
. Lane widths are l0 ft (/- : 0.93), and
. Heavy vehiclesconstitute 87a of total
traffic (f,, : 0.96).
For the opposingstream a right-turn adjustrnent factor of f,,, : 0.94 applies.
Thcrefore. the combined correction factor for the opposing stream is /. :
.fuf* f ,,, f u, - 0.75-53,and the saturation flow is s,,,,: l8(n x 0.7-553: 1360
veh/h. For the opposed left turns,.f. :
f . J * f , , , : 0 . t t 0 3 - 5 a. n d t h e s a t u r a t i o n
flow is s : 1800 x 0.U035f,,, : 1446f,,,.
Assume that the cycle time and green
time are 120sec and -57sec, respectively
(S4lc- (1.475).The rcsults for the HCM
model and the SIDRA model are summarizcd in Thble l. The fundamentaldifferencebetwcen the two models for this
cxample is that the HCM model usesthe
idcal saturationflow {1800veh/h).
whercas the SIDRA model uses the es-
timatcd saturation flow (slightly lcss
than 1360 veh/h) for the opposing
stream. As a result, the predictedg,.values are very different (25.5 sec versus7.1
sec). The HCM method predictsJ,, :
0.269 and s : 1446 x 0.269 : 3U9veh/
h. As shown in Thble I this is equivalent
kr a capacity of 6.153 veh/cycle or 1ll5
veh/h. The c<lrrespondingSIDRA values
are much less because g,, is much
smaller. It is seen that the HCM model
will grossly underpredict the degree of
saturation and delay (level-of-service C
versus F) in this case.
Conclusion
In conclusion,neither the old"-'r nor the
newt t Australian methods assume "filtration for the entire green period."" The
HCM method,' as in the early Australian methods, implies the use of a saturation flow averaged over the entire
green period and converted to an adjustment factor. The latest Australian
method (SIDRA) has eliminated the use
of opposed turn adjustmentfactors.r''lt
employs a direct and explicit approach
to model individual lane capacities,and
then simply adds lane capacitiesto obtain the btal capacity for a lane group.
By contrast, the use of adjustment factors means that the capacitiesare first
converted to adjustment factors (with
lossof accuracyresultingfrom inevitable
generalizations)and then converted to
capacitiesagain.
Toble'1.An Exomple lo Compore the HCM ond STDRA
Opposed furn Modets
HCM
SIDRA
Opposing soturotionflow, soo
Unsoturoledporl of opposing green
period, g,
Opposed lurn solurolionflow, s,,
during g"
Deporturesotler lhe green period, n,
Copocity per cycle, $ = (s"9"/3600)+
1800veh/h
'1358veh/h
25.5sec
7.{ sec
643 veh/h
'1.6veh
661 veh/h
1.6veh
nl
6.'153veh
57 sec
389 veh/h
185veh/h
0.433
2.909veh
I sec
{309 veh/h
87 veh/h
o.9'17
15.8
1.'
16.9
42.8
48.8
91.6
F
Effectivegreen time, g
Averoge soturotion llow, s = 5/g
Copocity per hour, O = s9lc = 3600 S/c
Degree of solurofion
Averoge slopped deloy
uniformlerm, d,
overflow ferm, d"
lotol,4=d"*d"
Level of service
c
Ihc modeling of capacitiesby the adlustment factor method was necessary
for thc simple manual methods of the
past.This is no longer necessarywith the
widespread use of computerized methods by the traf{ic enginceringprofession.
l'he direct modeling method. which
treats the blockcd intervalsas lost time.
allows for various differenccsin individual lanes to be identified. This improves
performance prediction signilicantly. For
example.shared laneswith opposcd
turns can have longer cffectivered times
than adjacent lanes This has clear adv a n t a g c si n t h c p r e d i c t i o n o f q u e u e
lengthsfor turn bay storagccapacitycalculations. The morc complex cases of
'protected
plus permittcd" phasing,opposed turns with two lcvels of priority
( e . g . t u r n s f r o m s l i p l a n c s ,o r t h e V i c toria and New Zealand priority rules).
t h e c a s e sw h e n t h e o p p o s i n g a n c l o p posed traffic have right of w:ry at different times. de facto exclusivclanes, right
turn on red (U.S.). and so on can be
modeled directly.This obviatcsthe need
to develop a multiplicitv o[ increasingly
complicated and incrcasinglylcss accurate adjustment factor formulas to cope
w i t h m a n y c o m p l e x s i t u a t i r t n s .T h e
readeris referred to the articlc by
Akqelik fbr a more dctailed discussion
on sharcd lane capacitv models in gencral and thc SIDRA sharedlane capacitv
model in particular.
Acknowledgment
.fhc
author thanks Peter Lowe. the exccutivc director of the Australian Road
RescarchBoard, for permissionto publishthis article.
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ITEJOURNAL. JUNE,1989 27