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OCR for page 63
63
Chapter Eight
RECOMMENDED COMPUTATIONAL PROCEDllRES:
AWSC INTERSECTIONS
The research results presented In this report form the
foundation for the computational procedures for
determining saturation headways, computing capacities
and delay, and Betel rig level of senice for an AWSC
intersection. This section documents the fourteen steps
that make up the proposed computational procedures.
These procedures wall form the basis for the AWSC
mtersechon section of the new version of chapter ten of the
HCM. An example calculation is given to illustrate the
procedures. Figure 32 lists Me steps In He computational
procedures.
Step 1. Documentinitial Conditions
Step 2. Adjust volumes and determine lane
assignments
Step 3. Determine geometric group
Step 4. Determine base saturation headways
Step 5. Compute starting value for departure
headways
Step 6. Compute degree of saturation
Step 7. Compute actual value of departure headway
Step 8. If departure headway values converge,
continue to step 9; if not; return to step 6
Step 9. Make adjustment to departure headways
Step 10. Compute service times
Steps 1 1 and 12. Compute capacities
Step 13. Compute delays
Step 14. Compute level of service
Figure 32. Recommended Computational Procedures
INITIAL CONDITIONS AND ADJUSTMENTS
Step 1. Input Conditions
Five input parameters are required for this procedure.
These are listed below.
.
number and configuration of lanes on each
approach
vol~es by fuming movement for each approach
(v)
percent heavy vehicles on each approach (THE)
peak hour factor WHIT
length of study period or length of oversaturated
period, hours (T)
Step 2. Volume Adjustments and Lane Assignment
Step 2a. The volumes are converted to equivalent hourly
flow rates using the peak hour factor.
v= v
PHF
(36)
Step 2b. The homey flow rates are allocated to each lane of
each approach either as a result of direct observation or by
estimation.
Step 3. Geometric Group
Determine the geometric group for each approach. The
geometric group for the subject approach is based on the
number of lanes on the opposing and conflicting
approaches. The geometric groups are listed in Table 85.
Table 85. Geometry Group
. ~, 2 I: .............................. ;,. ...................
... .. ............. ... . ~.... it, .......... .......... .- .
~ ~.==~2'""'~22~"""""''~''''' 1':
T
1 41egarT 1 1
2 41eg - T 1 1
3al4a 4 leg orT 1 2
3b T . 1 2
4b 4 kg 1 2
S 41egacT 2 1 or2
6 4 kg orT 3 _
2
1
2
2
1 or2
3
Step 4. Base Saturation Headways
The sa~ationheadwa~r for each lane for degree of conflict
case ~ is determined from Table 86. The adjustments for
turning movements and heavy vehicles are made using
Table 87 and Equation 37.
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64
h,,,~, = h, ~ hate Per ~ ho - par ~ ho - pin (3
where hubris the adjusunent to the case i base headway, hi
is the base saturation headway for case i, h~T-dj is the
headway adjusdnent for led turns (either 0.2 or 0.5,
Table 86. Saturation Headway Values by Case and Geometry Group
depending on geometry Casey, hRT.atj is tile headway
adjustment for ritht~ns (either-0.6 or-0.7), hHV ,dj is the
headway adjustment for heavy vehicles (~7), PAT iS the
proportion of led-tarning vehicles on Me approach, PRT is
the proportion of right-t~ning vehicles on the approach,
and PHV is We proportion of heavy vehicles on the
approach.
.~ . ~t If ~ ~ 1
1 0 3.9 3.9 4.0 4.3 4.0 4.S4.S 4.S 1
2 1 >2=3 147 14.7 1 4.8 1 1 11 62
3 1 >~-3 15.8 1 58 1 59 1 6.2 1 5.9 1 44 1 6446
7.0 17.° 1 7.1 174 17.1 1~.6 17g 1 S
1 21~ 1 96 1 9.6 1 9~7 1 100 1 97 1 1~2 1 IT : ]
Table 87. Saturation Headway Adjushnent Factors by Geometry Group
,.~ . ~ 1'"~' ' 'I ' :~ 1 . . . 1 ''''''I ' '''''"" '1"' ' 6~ 1''' ''my -
.............................................. ....................... ....................... ................ , .,,,,,,,,.,,., .............................. . , l,,.,, ; ;
, LT 1 0.2 1 0.2 1 0.2 1 0.2 1 0.2 1 0.2 1 0.5
RT -0.6 ~.6 ~.6 ~.6 ~.6 ~.7
HV 1.7 1.7 1.7 1.7 1.7 1.7 1.7
O.S
.7
1.7
. ,
HEADWAY AND SERVICE TIME
Step 5. Starting Value for Departure Headway
The initial or starting value for the departure headway for
each lane is established. The default value is 4 seconds.
Step 6. Degree of Saturation
Compute Me degree of saturation for each approach. The
degree ofsaturation (x) Is the product of the flow rate
and Me departure headway Ad.
x = roll /3600
. ~,!'dt
Step 7. Actual Value of the Departure Headway
The actual departure headway for each lane, based on
hectic flow on the opposing and conflicting approaches, is
computed based on the probability of each lane having a
vehicle waiting at the stop line. This probability is a
combined probability based on each possible case of
vehicles either being present or not present in each lane.
Equation 39 gives the expected value of this distribution.
h`= ~P[C]h~
(38)
(39)
where ha is He expand value of the headway distribution,
P[C] is die probability of degree of conflict case i, and be
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65
is the saturation headway for case i.
The probability, PUCE, for each degree-of-conflict case is
computed based on Me degree of saturation on each
approach. For We opposing approach, the conflichug
approach from the left, and the convicting approach from
the right, the ratios are given by xO, X<:L, and x,,
lively. For single lane approaches, Me probabilities
are computed using Me foDow~ng equations.
P[C1] = (1 - xo) (1 - Xci) (1 - FOR) (40)
PtC2] = (Xo) (] - x=) (1 - x=) they
P[C3] = (1 - xo) (ice) (1 - PER)
+ (1 - xo) (1 - ACE) (XCR) (42)
P[C~ = (Jo) (1 - x~ (x=)
+ (xo) (XCZ) (} - X=) + (1 - xo) (X=) (X=) (43)
PtCS] = (Xo) (ACE) (Xa~) (44)
For muld-lane approaches, the departure headway is given
by Equation 45.
12
ho = EP[Cd ho (4~
~1
Step S. Convergence
If the expected value of Me departure headway has
changed less than some value (say 0.01 seconds) on each
approach, the analyst can proceed to step 9. If Me
expected values are stiff changing, the analyst should
return to step 6 to compute a new value of the degree of
saturation.
Step 9. Adjustment to Departure Headway
An adjustment to the converged value of departure
headway is made to account for the interdependence
between the degree of conflict cases. This adjustment is
computed using Equation 46.
P,,,t,fil] = P[.~1 + a~ - ~ - 1] t4o
where Padj~i,k] is Me probability of degree of conflict case
i given case k and ~ is a constant.
Step 10. Service Time
The service time is computed using Equation 47 and the
depar~eheadway~computed from step 9 and Me move-
up time, m. A move-up time of 2.0 seconds is used for
sites from Groups ~ through 4 and 2.3 seconds for sites
from Groups 5 and 6.
s = hi - m (471
CAPACITY
Two values of capacity are computed, each based on a
different concept of capacity.
Step Il. Capacity Based on Concept ~
The capacitor of each approach is computed assuming that
Me Bows on the opposing and conflicting approaches are
held constant. The Even flow rate on the subject lane is
increased and the departure headways are computed for
each approach using steps 5 Trough 9 of this
computational procedure until the degree of saturation for
any lane reaches one. The current value of the subject
approach How rate is the maximum possible throughput or
capacity of this lane.
Step 12. Capacity Based on Concept 2
The capacitor of each approach is computed assuming that
the g~ven~ow rates oneach~ntersection approach are held
In constant proportion to each over. All flow rates are
increased incrementally and the departure headways are
computed for each approach using steps 5 through 9 of
this computational procedure until the degree of saturation
for any lane reaches one. The current value of flow on
each lane is He maximum possible throughput or capacity
of that lane.
DELAY AND LEVEL OF SERVICE
Step 13. Delay
Average stopped delay per vehicle is computed for each
lane and each approach using Equation 48.
[ ~ 450T]] (48)
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66
where d is the average stopped delay per vehicle, s is the
service time, x is the lane or approach degree of saturation,
and T is the length of the measurement interval or
congested period. The intersection delay is the weighted
average of the delay on each of the approaches.
Step 14. Level of Sernce
The level of service for each approach and for the
intersection is determined using Table SS and Me
computed values of stopped delay.
Table 88. Level of Service Ranges
, ;
.... , . ,: ,.,,,.~.,,,,,~,.a. ~,.~.,~, ': ' ~
A O-S
B S - 10
C 10 -20
D 20 -30
E 30 -4S
F >4S
,
SAMPLE CALCULATION
A sample calculation is presented here to illustrate We
proposed computational procedure. The example
intersection has one lane on each approach wad flow rates
and We percentage of heavy vehicles shown In Table 89.
Table 89. Traffic Volumes for Sample Calculation
.,.~
Nor&bound
LT SO S
TH ". . 200 S
RT ' - 7S S
. .
Southbound
LT SO S
TH 100 S
RT 50 S
Eastbound
LT SO S
TH 300 S
RT SO S
Westbound
LT IS S
TH 400 S
RT 2S S
.
Step 1. Input Conditions
Five~ut parameters are required for this procedure. The
values of these parameters are documented. There is one
lane on each approach. The flow rates and percentage of
heavy vehicles are shown in Table 89. The peak hour
factor is one. T is assumed to be 0.25 hours.
Step 2. Volume Adjustments and Lane Assignment
The hourly flow rates are converted to equivalent hourly
flow rates using the peak hour factor. Since the peak hour
factor is one, He equivalent hourly flow rates are the same
as the given input flow rates. There is one lane on each
approach so all of the flows will be on the same lane on
each approach.
Step 3. Geometric Group
This intersection is Group ~ since there is one lane on each
approach. No geometric adjus~nent in the saturation
headway is required.
Step 4. Base Saturation Headways
The base saturation headways are computed starting with
the values given In Table 86. Left turn and right turn
adjustments are applied using the factors Even in Table
87. The results for each approach are given in Table 90.
Table 90. Base Saturation Headways
................................... .................... ...................... .................... ....................
D.~c Am . ~ ................................ ....... ........... , ...........
. ~ ...................................... .................................... .................................. ..
1 3.8 3.9 3.9 4.0
2 4.7 4.7 4.7 4.8
3 S.8 S.S S.S S.9
4 7.0 7.0 7.0 7.1
S 9.6 9.6 9.6 9.7
. ~. i.
Step 5. Starting Value of Departure Headway
The initial or starting value of departure headway for each
lane is established. The default value is 4 seconds.
Steps 6 and 7. Degree of Saturation and Actual Value
of the Departure Headway
The final values for the degree of saturation and departure
headway for each approach are given in Table 91.
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67
Table 91. Degree of Saturation and Deparh~re Headway
'2 '. ~. _ .
Dcgrec of Sanction 0.69 0.4S 0.81 0.90
Departed Headway 7.6 8.1 7.3 7.2 .
l
Step 8. Convergence
The calculations converged after four iterations.
Step 9. Adjustment to Departure Headway
The departure headways are adjusted to account for senal
correlation. A value of a of 0.01 was used. The final
values of degree of saturation and departure headway are
given in Table 92.
Table 92. Degree of Saturation and Deparhlre Headway
~-,,.~5,,,,,,51
Degree of Sanction 0.64 0.42 0.76 0.84
Departure Headway 7.1 7.6 6.8 6.8
_
Step 10. Service Time
For Group ~ sites, the move-up time is 2.0 seconds. This
value is used to compute the senice time, given the
departure headway for each approach. The values are
shown in Table 93.
Table 93. Semce Time
Service Time 1 S.1 S.6 4.8 4.8
, .
Capacity Calculations
Two values of capacity are computed, each based on a
different concept of capacitor. The results from both
capacity calculations are given in Table 94.
Table 94. Capacity Calculations
Concept 1
AM
lotion
Concept 2
App~
Moon
463
lS13
342
1481
414
lS89
217
1481
S03
1478
434
1481
S18
1442
488
8
Step 11. Capacity Based on Concept 1
The capacity of each approach is computed assuming that
the flows on the opposing and conflicting approaches are
held constant. The given flow rate on the subject lane is
increased and the departure headways are computed for
each approach using steps 5 through 9 of this
communions procedure until the degree of saturation for
any lane reaches one.
Step 12. Concept Based on Concept 2
The capacity of each approach is computed assuming that
He given flow rates on each intersection approach are held
in constant proportion to each other. AD flow rates are
increased incrementally and He departure headways are
computed for each approach using steps 5 through 9 of
this complexional procure until the degree of saturation
for any lane reaches one. The current value of flow on
each lane is the maximum possible throughput or capacity
of that lane.
Step 13. Delay
Average stopped delay per vehicle is computed for each
lane and each approach using equation 48.
Step 14. I,eve} of Service
The level of service for each approach and for the
intersection is determined using Table 88 and the
computed values of stopped delay. The results are shown
in Table 95.
Table 95. Delay and Level of Service Calculations
.
, 0 : .
............................................... .
, ... ..
. ~
, . , ..... ;
|Delay
ILevel of Service
17.0
C
11.1
C
23.8
D
33.3
E
OCR for page 68
68
, . ~ .
Representative terms from entire chapter:
flow rates
