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OCR for page 5
s
Chapter Two
PREVIOUS WORK
This chapter summarizes the work of Free researchers or
groups that constitute the major body of research
conducted onAWSC'nt~sectionsto date. lacquesHebert
published a study of Free Intersections in Chicago that
became the basis for the capacity guidelines of the 1985
HCM. Anthony Richardson developed a queuing mode}
usage headway data measured by Hebert. Researchers
at the University of Idaho developed emp~cally-based
models for capacity and delay that were published In
Transportation Research Circular (TRC) 373 and In the
1994 HCM update.
HEBERT AND THE 1985 HCM
Jacques Hebert (1963) proposed a capacity model for
AWSC intersections based on saturation headway values
for two cases, one In which the driver faced another vehicle
on the opposing or conflicting approaches and one In
which He driver faced no over vehicles. He measured
values of 4.0 seconds and 7.6 seconds for these two cases,
based on a study of three sites in Chicago conducted
during periods of continuous queuing. Saturation
headway values for these Ho cases are He basis for He
1985 HCM capacity procedures.
Hebert presented equations to forecast He capacity of an
approach based on the volume split between the two
intersecting sheets and He number of lanes on each
street. Equation ~ gives He capacity equation four an
intersection with one lane on each approach.
3600
c = -
10.15 - up
(1)
where vp is the proportion of He intersection volume on
the higher volume street. The 1985 HCM summanzed
Hebert's work into capacity guidelines that can be used
to assess He performance of an AWSC Intersection based
on demand split for 2-lane by 2-lane (i.e., one lane in each
direction), 2-lane by 4-lane, and 4-lane by 4-lane
intersections.
Tables ~ and 2 show the intersection cap acid by demand
split for a 2 by 2 Intersection and by intersection type for
a 50/50 demand split. Table ~ shows that He intersection
capac~h,r is maximum when the flow is evenly split among
all approaches; He approach cap recite under this split is
425 vph. Table 2 shows that simultaneous movement
from a two-lane approach can occur, increasing the
capacitor of the approach.
Table 1. Intersection Capacibr as a Function of Volume Split
............... :~. ~i ,.,.,.~. .,. ~,
SO/SO 1,900
SS/4S 1,800
60/40 1,700
6S/3S 1,600
70/30 1,SOO
Note: Demand Split is Me proportional split of Traffic between the
~n~g~
Table 2. Intersection Capacity as a Function of Intersection Type
. ~........... ................. , .. ........ ,.;
....................................................................................................................... .........................................................................................................................
2-lane by 2-lane 1,900
2-lane by 4-lane 2,800
I Plane by 4-lane 3,600
Note: Caries are based on SO/50 demand Split
RICHARDSON MODEL
Anthony Richardson (1987) proposed a method of
computing He capacity of an approach of an AWSC
intersection by iteratively computing the service time of
each approach based on the likelihood of vehicles being
present on the opposing and conflichug approaches. His
iterative method assumed two states, no vehicles on the
opposing or conflicting approaches and one or more
vehicles on the conflicting approaches. The
computational method converges quickly and is easily
implemented using computer software. While the basic
method is valid, the major 1imitadon of the Richardson
mode} is He small number of sates Hat are considered.
Richardson proposed an MIG/l queueing model to
estimate delay, using He Pollaczek-Khintchine formula.
OCR for page 6
6
This formula is given ~ Equation 2.
D xW(1 +C2)
g 2~1 - x)
(2)
where W is He average senice time (or time spent In the
first position In queue), x is the degree of saturation, and
Cw is the coefficient of variation of service times. The
total average delayis the sum of the time in queue, Dq, and
the time spent in He first position, W.
TRC 373 AND THE 1994 HCM
Between 1987 and 1989, the University of Idaho
conducted studies at AWSC intersections in the Pacific
Northwest and in Iowa to determine the factors that
influence capacitor and delay. Saturation headways were
measured and a capacity equation was developed from
these data.
This capacitor equation, and the supporting data, were
published as part of TRC 373 (19911. TRB's Committee
on Highway Capacity and Qualify of Senice proposed this
method to be used on an interim basis since it provided a
significant improvement over the method then Included In
the 1985 HCM. After several years of use by the traffic
cogineeiing community, Ellis method was published as part
of the 1994 - atetothe HCM as the approved procedure
to determine the capacitor of an AWSC intersection.
The 1994 HCM Update describes the basis for traffic
operations at an AWSC intersection:
The headway between vehicles departing from a STOP
line of an AWSC intersection is a function of the
conditions present on the other intersection approaches.
Minimum saturation headways are achieved if there is
not traffic on any of the other intersection approaches.
Maximum saturation headwinds result if tragic is present
on ad of the other approaches.
This microscopic perspective has a direct analogy at the
macroscopic level. The maximum flow rate on a given
approach can be achieved if there is not tragic on any of
the other approaches. The minimumflow rate on a given
approach results if tragic is evenly distributed among all
of the intersection approaches. Thus the key variable in
the determination of approach capacity is the relative
distribution of traffic volumes among the approaches.
This variable is called~volume distribution.
When tragic is evenly distributed! among the approaches,
the capacity of a single-lane approach is approximately
525 vph and the capacity of a four-leg intersection is
approximately 2, ]00 vph under ideal condEihons.
Research has found the capacity of a single-lane
approach, when there is no tragic on any of the other
approaches, is ],100 vph under ideal conditions.
Data published by Kyte and Marek (1989), by Kyte
(1990), subsequently in Transportation Research Circular
373, and now Included In the 1994 Update of He HCM,
suggest that four cases are needed to describe He
conditions faced by the subject approach driver at an
AWSC ~n~io~ These conditions are defined in Table
3.
Table 3. Saturation Headway Data for AWSC Idtersechons (1994
HCMUpdabe)
............................................... .......... .. = ~ ''"''""'''1
. ~...... ........................................ .
........................................................ . ~ ~. ~... ,.,., ,. . ~
All data 3.S S.5 6.S
Single lane 3.9 S.6 6.S
Multi lane 1.S 4.3 6.3 . .
Need Single Menses single lane approach mingle saw Multi lane notes
multi lane abroad sable sites. Case 1 occurs when the sect vehicle
does not fi~cee~a~oangorco~licting vehicles. Case 2 occurs Whence
subject vehicle faces only an opposing vehicle. Case 3 occurs u hen We
subject vehicle feces ably conflicting vehicles. Case 4 occurs whence
subject vehicle faces both opposing and conflicting vehicles.
9.0
9.0
9.3
The four headway cases listed In Table 3 do not directly
consider the effects of mining traffic. The case 2 headway,
which is a subject vehicle faced by an opposing vehicle and
no con Dichng vehicles, does not consider He elects of He
interaction of one or both of the vehicles laming and not
traveling straight through the intersection. The value of
5.5 seconds givenin Table 3 is assumed to cover the range
of combinations that actually make up case 2: for example,
pairs of through vehicles with no turning conflicts, one
through vehicle opposed by a led turning vehicle, one
through vehicle opposing by a rift homing vehicle, etc.
While the capacity equation given in the 1994 HCM
Update does provide an adjusunent for turning
movements, it is based only on the overall proportion of
mining movements and not on the microscopic or vehicle-
by- vehicle interactions that actually reflect the degree-of-
conflict resulting from bulging vehicle conflicts.
OCR for page 7
The capacity equation is given in Equation 3.
c = loony, + 700p + 200L, - 1ooLo
- 300LT' + 200RT' - ~nnr.T + cannot (3)
~vv~eLpc ' ~VV4~7C
The parameters In the equation are defined In Table 4.
Table 4. 1994 HCM Update AWSC Capacity Equation Parameter
Definition
.. ...................... ~
I Dehorn..
. .. ~ _ ~
Capacity ofthe subject approach
Vp, Proportion of intersection volume on subject approach
VpO Proportion of intersection volume on opposing
approach
~Number of lanes on subject approach
L Number of lanes on opposing approach
LTpo Proportion of volume on opposing approach fuming
left
RTpo Proportion of volume on opposing approach tuning
right
LT,,, Proportion of volume on conflicting approaches
turning left
RTp, Proportion of volume on convicting approaches
t~=
The delay formula now used In the 1994 HEM Update,
given In Equation 4, Is based on We volume/capacity ratio,
v/c. The mode! Is emp~ncally based but has Me important
proper of forecasting an exponentially- increasing value
Of delay as the volume/capacity ratio increases.
d = e3.S vJc
RECENT WORK
(4)
Two rum studies significantly add to the work previously
cited. The first was published in 1994 and the second
descnbes the results from Me pilot study from phase one
ofNCHRP 3-46.
1994 University of Idaho Study
Sanction headway date were collected by Kyte and others
(1994) for one approach of an AWSC intersection to
determine if there were subsets of these four basic cases
described in the 1994 HCM update that would better
reflect He vehicle-by-vehicle impedances described earlier.
Two separate series of tests were conducted. First, for
each of the four cases, the effect of He directional
movement ofthe subject approach vehicle was deteImined.
Second, subsets of cases 3 and 4 were identified and
tested.
Table 5 shows the saturation headways for the Trough
movement and right turn movement for each of the four
cases. Separation of the saturation headways by toning
movement results in considerably different saturation
headway and capacity estimates, with capacity differences
ranging from 27 percent to 50 percent between He Trough
movement capacity and He right horning movement
capacity. A difference In means test verified the
significance of the difference In these measurements at the
0.05 significance level.
Table 5. Effect of Tuming Movement on Approach Capacity of
AWSC Intersection
, , , , . . .
............ .............................. ................................. .........................................
............ ,
......................... ......... .. : . . ~e~
. ~................ .............. ................ ; ~ .
............ ................................ ......................... ................................ ................................ ............ . ~e
................................... ...... = , , . . ~,
1 3.0 2.1 1200 1714 +43%
2 4.2 2.8 8S7 1286 +50%
3 6.3 4.9 S71 73S +29%
4 7.9 6.2 4S6 S81 +27%
Note: lUis the~routh movement. RTis~e light~m movement.
Another way of improving the AWSC intersection capacity
procedure is to detenIiine if the four cases can be divided
into subsets that better reGect the conditions faced by the
subject vehicle. For example, case 3 states that the subject
vehicle Is faced by vehicles on the convicting approach and
not on He opposing approach. But this case can include
one or two conflicting vehicles, one from the left or one
from the right, or both.
Several subsets were considered for cases 3 and 4 to
determine if additional cases are justified. Table 6 lists
these subsets. Table 7 shows He saturation headways that
were measured for each of the six subsets.
OCR for page 8
8
Table 6. Subsets for Saturation Headway Cases
, ~ ., If : 5 - !
3a One conflicting vehicle Bom Me right
3b One conflicting vehicle Bom We led
3c One conflicting vehicle from both the leR and Me
right
4a One conflicting vehicle Bom the leR and one
opposing vehicle
4b One conflicting vehicle Bom the right and one
opposing vehicle
4c One conflicting vehicle Dom bow Me led and right,
and one opposing vehicle
, i,. _ .
Table 7. Saturation Headways for Subsets for AWSC Intersections
.. .. .. . . . . .- ; . . . . . ... . . . . , ; . . .
... , .........................
....... ... ~ ,~, ,a:' =:e . . ~...... ....
3a S.1 1.60 31
3b S.~6 1.38 20
3c 6.8 1.67 36
4a 6.9 1.62 32
4b 6.8 1.S7 62
4c 8.4 2.39 82
Note: SD is the standard deviation. Obs is the number of
observations.
First, Me study found Mat there was no statistically
significant difference between cases 3a (5. l seconds) and
3b (5.6 seconds). That is, from the standpoint of the
subject approach driver, it makes no difference if a
conf icing vehicle approaches Mom the left or the right, as
tong as there is only one cor~flichng vehicle.
But there is a significant difference between cases 3a or 3b
and case 3c (5. ~ to 5.6 seconds, and 6.8 seconds). Thus if
one conflicting vehicle is present on both the leR and Me
right approaches, Me saturation headway for Me subject
vehicle is different, in this case longer, Man if the subject
vehicle is faced by only one convicting vehicle.
Also, there are some differences In the three case 4
subsets. Similar to the results for case 3a and 3b, Mere
is not a significant difference between the case 4a (6.9
seconds) and 4b (6.8 seconds) subsets. But Mere are
differences between cases 4a and 4b and case 4c (~.4
seconds) subsets. Thus, while Me direction of approach
on the conflicting approach does not make a difference,
He number of conflichug and/or opposing vehicles is
significant.
NCHRP 3 46 Pilot Study
For the pilot study, Phase ~ of NC~P 3-46 (Kyte, et.al.,
1993), saturation headways were measured for a total of
4,863 vehicles for these four cases. These results are
shown in Table S. While the specific headway
measurements are somewhat different, the relative
magnitudes for the two studies (TRC 373 data and
NCHRP 3~6 pilot study data) are similar.
As discussed above, one of the shortcomings of Me TRC
373 classification system was the I~m~ted number of cases
considered, particularly the lack of consideration given to
(~) the number of opposing or convicting vehicles faced by
the subject approach vehicle, (2) the directional movement
of the subject approach vehicle, and (3) the effect of
vehicle type.
To more accurately assess He effects of opposing and
conflicting vehicles, eight cases were proposed. The
saturation headways measured during the pilot study were
classified into these eight cases and are listed in Table 9.
Several conclusions can be drawn from these results:
.
.
.
The approach direction of a conflicting vehicle
(either from He left or Dom the nght) does not
affect the saturation headway of the subject
approach vehicle. The saturation headway values
for cases 3 and 4 are nearly equal; the values for
cases 6 and 7 are also nearly equal.
The number of vehicles on the conflicting
approach (either one or two) does make a
significant difference in the saturation headway of
the subject approach vehicle. Note that the values
for cases 3 and 4 are lower than for case 5.
While the specific approach does make a
difference if the subject vehicle faces only one
opposing or conflicting vehicle (the headway for
case 2 is less clan the headway for either cases 3
or 4), it does not make a difference if the subject
vehicle faces two opposing or conflicting vehicles
(cases 5, 6, and 7 are nearly He same).
OCR for page 9
Table 8. Saturation Headway Data
,., ,.,. , , , _ ,, , , ,. ,,, . . ,
. ,. ~.. ,.,, ...... .......
1. No other vehicle on any
2. One or more vehicles on the
opposing abroad only
3. One or more vehicles once
conflicting approaches only
4. One or more vehicles on
both Me opposing and
conflicting approaches
. ~, .................. . .
.......... ~.2 ~................. .
3.2 3.9
4.9 S.6
6.3 6.S
8.0 9.0
The saturation headways for each of the three directional
movements of Me subject approach vehicle were computed
and are Even In Table 10. The following conclusions can
be drawn from the information presented in this table.
The tuning movement direction has a significant
effect on We saturation headway of the subject
approach vehicle. In seven of the eight cases
listed, the saturation headway for the left turning
vehicle is higher Man for the through movement,
which in tum is higher than for the right turn
movement.
Table 9. Saturation Headway Data for AWSC Intersections, Pilot Study
9
.
.
K the through movement Is taken as the base case,
adjustment factors can be computed for Me effect
of fuming vehicles on the saturation headway.
For left turn vehicles, this adjustment factor is
0.90. This means that the capacity reduction due
to left turning vehicles is 10 percent. For right
En vehicles, the adjustment factor is 1.36, or 36
percent higher than for through vehicles.
The assessment of saturation headways without
respect to subject vehicle turning movement did
not show a (difference between cases 3 and 4, and
cases 6 and 7. Such a difference, however, might
be e2~1 when the directional movement of the
subject vehicle is considered. The data presented
in the table do not support this expectation.
The saturation headway measurements for passenger cars
and heavy trucks show a significant difference. Table ~ ~
shows the computed saturation headways for these two
vehicle types. In every case, Me saturation headway for
passenger cars is lower than that for heavy trucks. This
difference averages I.5 seconds, or 22 percent. These
headways can be translated into capacity flow rates, 563
veh/br for passenger cars and 462 veh/hr for trucks. This
results in a passenger car equivalent of I.2 for trucks at
AWSC intersections.
. F ~ ~ ~ ~ ~
....... 1 ~ . ~ ~ , ~.. ~ .
1 I No odes vehicle | No other vehicles 1 3.0 1 3.0 l
2 One vehicle No other vehicles 4.7 4.8
3 No other vehicle One vehicle from the left approach 5.7 5.9
4 No over vehicle One vehicle from We light approach 5.7 5.6
S No other vehicle One vehicle from both the left and right approaches 7.3 7.1
6 One vehicle One vehicle from the left approach 7.3 7.2
7 One vehicle One vehicle from the right approach 7.4 7.3
8 One vehicle One vehicle from both the left and right approaches 9.1 9.2
Notes: The values are based on the mean ofthe mean values measured for each ofthe 13 subject approaches of this pilot study. 4L5L4 is Leg single lane
approach sites.
OCR for page 10
10
Table 10. Saturation Headways by Subject Approach Movement Direction
......................................................
. ~.~
1 52 ~' ''~1
,, .,. _ "'" ''"'"''"''' ~""i' ':""''"""'"''''"'" ' -; it_ ~
. ~.' ~''""'"''"'1'''"" ~''''1'"' ' 'I'""''' ~q
1 4.0 85 1.7 3.7 200
2 6.2 71 1.8 5.0 288
3 S.9 60 1.6 5.6 149
4 6.2 20 1.4 6.0 69
S 7.1 39 1.S 7.3 107
6 8.0 134 2.0 7.0 308
7 8.9 37 2.1 7.5 151
8 10.7 70 4.6 9.2 203
S16 6.4 1475 l
, . -.-.~.-.-.-.-.-.-.-. ~BJ.~C~V.:~VEJA-'OIL L-~* .43-.- ~
.-.....
:::::::::::::::::::~.:::::::::::: :-:
4.0
6.2
S.9
6.2
7.1
8.0
8.9
10.7
.
1.3
1.S
1.S
1.3
1.6
1.8
1.8
2.7
2.8
3.8
S.2
4.S
6.4
6.3
S.4
8.0
71
60
42
19
18
37
11
22
1.3
1.3
1.8
1.1
1.1
1.8
1.1
2.1
Mean
7.1
4.7
280
Notes: Hazy is the saturation headway, Obs is the number of observations; StDev is the standard deviation.
Table 11. Saturation Headways for Passenger Cars and Trucks
1
2
3
4
S
6
7
8
3.2
4.8
S.7
S.7
7.4
7.2
7.6
9.2
798
758
355
341
521
624
668
694
4.6
S.9
7.6
8.7
8.3
7.9
7.9
11.6
15
19
3
12
IS
17
18
Total
64
4759
7 g
, , , , . , 104 l
Note: Obs is He number of observations.
Representative terms from entire chapter:
saturation headways
