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OCR for page 123
123
The procedure is described below in step by step form and
Is shown in Figure 70. It follows the general outline of We
1994 HEM Update, in Chapter Ten, Part m, Procedure for
Application.
.
.
Chapter Ten
RECOMMENDED COMPUTATIONAL PRO CEDUR1ES
This documents We computational procedures Mat are
recommended for computing capacitor and level of service
analysis at TWSC intersections.
INPUT.
Tic ~ tt
NO
~ -
CAPACITY AND IMPEDANCE I
| | V,, - CO N FLICKING TO LO M E |
1 ~
_
HARDENS OAF.
~ MAJOR LO
l - PEDEST. IMP.
. CRINOID RT
I ~ MINORS TO _
I . MINOR LT
2 - YES PART I I PART 11 1
MBN LT | MIN LT I
Two ~ ~
- | 2STAG'E CAP. |
_
INTERIM CAPACITY
'NO I
AVG QUEUE l
NO ~
~ | FLARED CAPACITY |
DELAY
+~
DELAY
. MOVEMENT
.. APPROACH
. INTERSECTION
- - AL = ~_
| QUEUES I
| AVERAGE
WARR^NTt;~
Figure 70. Recommended Computational Procedure
Step ~ - Input Data and Requirements
Identify and document the foBow~ng input data.
Refening to Figure 71: Me vehicular volumes by
movement for the hour of interest: Vat, V2, V3, V4,
Vs' V6, V', Vat, Vg, VIO, Vat,, V,2., and the
pedestnan volumes by movement for the hour of
interest divided by average group sizes: VL.' VR,
VO, Vs. (Note: U-turn tragic is counted as major
street left turn).
Percentage of heavy vehicles: PHV
PHVis the Combination Vehicles(%) + SU/RV(%)
Peak hour factor: PHF.
Number of through lanes on Me major street: N
per direction.
Major street left turn has shared lanes or blocks
rank ~ flows: saturation discharge flow for major
through and major right turns S2&3, S58~6
Number and use of lanes on the minor street
approaches.
Number of legs at the intersection: L'.
Grade of all approaches(°/O).
Other geometric features of interest:
channelization, two-way left-turn lane,
railed/striped median: storage k in median, flared
approach: storage k for right turn, upstream
signals for each direction i=2 amd/or 5 for the
platooned flow(s): cycle Ci, green time gi, initial
offset of, saturation flow si, platooned flow Vpi,
distance from intersection d
Step 2 - Volume Adjustment
The only adjustment for the volumes is to convert the Vi
; into 15-m~nute volumes, if a 15-m~nute analysis is desired
I in which case all the volumes should be divided by the
' PHF.
OCR for page 124
124
Crow Intersection -
T-Interseffion
~ 1
~ ~ to
1~=
Rank 1: 2, A, 5,
2: 1,4
~ i. 8, O
a) 3 8~.lll
4e 7.10
Ranl: l: 2, 3, s
2: 4,
~R,S
b) S: 7
Eighth 71. Movement Ranks
Step 3 - Determination of Critical Gap and Follow-up
Time
Determination of the critical gaps and follow-up times for
each minor steam movement is based on Table 54 and
Table 55, which account for Me effect of grades on the
minor approach, 2-stage gap acceptance if applicable, and
heavy vehicles.
Table 54. Recommended Critical Gap Values
Example:
If Grade(%) = 4, PHr, = 20%, N= 4, ~ = 3, then, for the
minor street left turn movement, the critical gap is:
(I - P~Jf7.5 + 0.2 x Grade - 0 79 + PHI' ( 7.5 +
2.0 + 0.2 Grade - 0.79
=Q-0.29(7.5+0.2X4-0.77 +0.267.5+2.0+
0.2x4 - 0.79
= B.0 sec.
The follow-up rime is:
( pH'J x3.5 +P,~,x(3.5 + 1)
0.2X4.5 = 3.7 see
(1 - 0.29 x3.5 +
cad - COP
Ad]=tment Factors
Heavy Vehicle*
Grades%
Three-Leg
2-Stage Gap Acceptance**
4.1
1.0
6.2
1.0
0.1
6.S
1.0
0.2
,
-1.0
4.1
1.0
0.2
-~0.7
-1.0
2.0
6.9***
2.0
0.1
-
6.S
2.0
0.2
-1.0
7.S***
2.0
0.2
-0.7
-1.0
Notes: *Combined critical gap is computed based on the proportion of passenger cars and heavy vehicles; ** In 2-stage gap acceptance situations, only one major
street direction is crossed at a time; *** Assumes tum occurs into '`nearest" exit lane.
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125
Table 55. Recommended Follow-Up Time Values
Ad]~*nent Factors
Heavy Vehicle.
Note: *O.9-second adjustment for sintle-lane sins, and l.O-second
adjustment for multi-Lane sow Combined follows time is computed
based on the proportion of passenger cars and heavy vehicles. ** In 2-
stage gap acceptance station, use same k as for V7. Vim
Step 4 - Adjus~anent of Capacity for Effect of Upstream
Signals (cm,8 and cm,,~; cm,7 and c,,,l0)
Refer to Figure 61. This step should be used when an
upstream signal is less than or equal to I/4 mile Tom Me
TWSC intersection.
Step 4.~. Obtain the platoon dispersion "spread ratio" for
each upstream signal (direction 2 Tom left and direction 5
Tom nght). Use the dine-distance concept In Appendix I
of the 1994 HEM as a basis for the method. Add a
platoon dispersion sub-model, similar to the recursive
aIgon~m used by TRANYST-7F signal analysis software
(Van Aerde et al 1995~:
Q' = FQ'-T + (1-F)Q,'~ Ohs)
where
A' are the vehicles Moving at the subject location
In time slice t
Qua are the vehicles departing from the upstream
signal In time slice t
Fis ~ /~} +~pta)
T=pta
to is the distance to upstream signal / average
speed of platoon
a is the dispersion factor alpha (constant for a
given roadway)
,8 is the dispersion factor beta (constant for a
given roadway)
The algorithm is used to disperse a platoon departing at
sanction flow rate from the upstream signal. The "spread
ratio" at the TWSC location is defined as ache ratio between
the time the dispersed platoon occupies at the TWSC
location and the time that the platoon required to discharge
Dom the upstream signal. Checks that the spread ratio
does notnes~tinjoining of platoons from adjacent cycles,
or in flows less Man the non platooned Bows. If either of
these situations occurs then there is no effect of signals
from that direction.
Step 4.2. Calculate the platooned and nomplatooned flow
rates at the subject TWSC intersection. The platoon flow
is obtained by dividing the platooned flow rate at the
upstream signalby~e spread ratio. The unplatooned flow
rate is obtained by multiplying the unplatooned volume by
the spread ratio. Check that unplatooned flow is less than
the platooned flow. If not, Mere is no effect of signals
Dom that direction.
Step 4.3. Use the cycle lengths, Initial oif;ets, queue
discharge times, and the spread ratios to calculate a series
of "begin platoon" and "end platoon" events from each
major street for the whole analysis period.
Step 4.4. Sort these events chronologically and examine
their sequence to calculate the proportion of the hour
during which each of the following fow arrival flow
"regimes" exists:
no platoons
platoons both directions
platoons from left only
platoons from right only
The flows within each ofthese regimes are obtained in step
4.2.
Step 4.5. For each controlled movement at the TWSC
intersection, the capacity is calculated as the weighted
average (using He proportions in step 4.4) of the
capacities within each flow regime (as win He current
1994 HEM method) i.e. steps 4 through 17 are repeated.
Step 5 - Computation of Capacity for Rank 2 Major
Left Turn Movements (c,,,l anti c,,,)
Step 5.1. Compute total conflicting volume Vc 1 and Vc4
based on Table 56.
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126
Table 56. Evaluabon of Conflichng Rank Volume V,,
Major Street LeR Tunt
Minor Sbeet Ri~t Ibm
For 2-stage Gap Acceptance
Minor Sbeet lbrough Movement
Minor Street LeB Turn
V2/N ~ + O.S V31) + VR ?)
V,/N 2) + O.S V61) + VI, 'J
l
part I (near side ~om leD)
2Vl+V2+0.S V31)+V5"
2V4 +V, + O.S V61) + VO "
2V1 + V2 + O.S V31) + VS 7)
2V4 + V5 + 0.5 V61, + VO "
+ part II (far side Bom right)
+ 2V4+ V, + V6" + VO ~
+ 2V1 + V2 + V33) + V31 77
+2V4+VJN+0.5V6~+Vu~+Vll8+V~'J
+ 2V1+ V2/N + O.SV3 ~ + V6 + V, + VR
1
Notes: 1) If there is a ntht-turn lane on the major street, V3 or V6 should not be considered; 2) If ~ere is more ~n one lane on the rank road, V2 and V5 are
considered as ha£lc volumes on the ri~t lane (apprommately 1/N ofthe total volume. N is the number of ~rough lanes); 3) If right-twningt~fF~c from the major
road is separated by a biangular island and has to comply with a YIELD or STOP Sign, V6 and V3 need not be considered; 4) Itntht-t~ningtraffic bom the minor
road is separated by a triangular island and has to comply wi~ a YIELD or STOP sign, V9 and V~2 need not be considered; S) If movements 11 and 12 are
controlled by a STOP sign, V'' and Vl2 should be halved in~is equatio~ Similarly, if movements 8 and 9 are controlled by a STOP sign, V, and V9 should be
halved; 6) Omit V9 and V,2 for multilane s~tes, or to halve their values if the minor approach area is flared; 7) Pedestrian groups V, with higher prion~ that conflict
with the subject movement may also be ~`ded (Figure 10.2).; 8) Omit thefarthest right turn V3for subyset movement 10 or V6for subject movement 7 if the
major street is multi-lane.
Step 5.2. Compute movement capacities (c'`,~ C~,4) using
Harders equation ~quation 166), or graphs may be
provided.
vc. J tc
3600
c = V e
1-e 3600
(166)
Step 5.3. Compute probability of queue-free state pO i using
Equation 167.
PO'= 1 - ' (167)
m,,
where
.
For major street shared lane, use Equation 168. ~
* 1 1 - po,
1- (S +S
f
where
.
=5,ifi=4;
k=3,ifi= 1;
=6,ifi=4,
Sj is the saturation flow rate for major s~eet
through traffic streams
Sk is the saturation flow rate for major street right
turn traffic
Step 6. Computabon of Impedance by Pedestrians for
Minor Street Approach Movements
Step 6.~. Calculate walk t~me for group to cross one trave!
lane:
tw = ~rnis ~ (N-l),ff (169)
(168)
i=l,4;
j=2,ifi= I;
w is the travel lane width; default w = 12 ~
n ~s the number of lanes crossed at a time; default
n =l
s is the waL~ng speed; defaults: s = 4.5 fps
average, s = 3 f~s children or elderly
N is the number of rows in peclestrian group;
defallltN= ~ if V< 100 ped/h~ measure otherwise
tf is the follow up time for consecutive rows of
pedestnans; use tf = 2
he above assumptions s~mpliiN,r the equation to: tu, = 2.7
OCR for page 127
127
seconds average, or 4.0 seconds for children or elderly).
The equivalent "volume/capaci~" ratio of pedestnan
groups Vh required to calculate impedance would be:
Vh~t,,/3600 (1703
Then, Me impedance factors for h = C, R. 0, S are (refer to
Figure 71~:
pa,,` = 1 - (vlc3h Aim
.
Table 57 shows approximate impedance factors that may
be appropriate for planning applications. The assumptions
would need to be vended wad empirical data.
Table 57. Sensitivity Test for Impedance Factor Due to Pedestrians
(s = 4 Ups, w = 12 ft)
0.96
0.86
n77
Two of the four pedestrian crosswalks h = it, R. O. S watt
be crossed by each minor approach vehicle.
The movement capacity C''4 for aD minor street movements
i depends on calculation of a capacity adjustment factor
which accounts for Me impeding effects of higher-ranked
pedestrian movements. This pedestrian capacity
adjustment factor is denoted fir for all movements h and,
for ad minor street movements i, cart be expressed as:
fop typo, h (172)
where Poh is the probability that conflicting pedestnan
movement h wiR operate in a queue-free state and i is the
street movements only.
An adjustment factor p' for Me statistical dependence
between queues of different pedestnan steams is not
accounted for since pedestrian flows are expected to be
light.
Step 7. Computation of Capacity for Rank 2 Minor where
Street Right Turn Movements tc,~,, and c~,,,2)
Step 7.~. Compute total conflicting volume vc9 and Vc~2
based on Table 58.
Step 7.2. Compute potential capacities using Harders
equation (Equation 166~.
Step 7.3. Compute movement capacities,, c. ).
Can i = Cp i X f' (173'
where
i=9,12,
if i = 9 then h = S,R
ifi=12thenh=O,L
A'= capacity adjustment factor
= product of conflicting pedestrian pO'
=PsXPRfori= 9
=POxpLfori= 12
Step 8. Computation of Capacity for Rank 3
Movements (c-,8 and cull)
Step S.1. Compute total conflicting volume Vc8 andVcl1
Step 8.2. Compute potential capacities(cp8, c pl) using
Harders equation.
Step 8.3. Compute movement capacities,, c. .
Cm ~ = Cp i X I' (174)
where
.
.
.
.
i= 8, 11;
A= capacity adjustment factor
=f,p X poll x Pok (Ifj, k are shared lanes use p*),
j=4;
kin 1;
Step 8.4 Compute probability of queue-free state pO i Tom
Equation 167.
Step 9. Computation of Capacity for Rank 4
Movements(c,,,7 and c-,1O)
Step 9.L Compute total conflicting volume Vce7 and Vat lo .
Step 9.2.Compute potential capacities(cp,, cp1O) using
Harders equation.
Step 9.3 Compute movement capacities(cm,, Cal, 1O).
Cm i = Cp i X f' (175)
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Representative terms from entire chapter:
shared lane
128
where
and if
.
i= 7, 10;
Hi= capacity adjustment factor
= ~ x pi' x pOj;
P/i = 0.6spl/i P. i + 0.6 ~(17~
P i = Po k X fk (17~
· i=7, h=~;L j= 12, k= 11;
=10, h=O3R j=9, k=8;
Step 10. Adjustment of Capacity for Effect of Two-
Stage Priority (c, .,8 and c,~,,l1; C,,,, 7 atld c,, ,IJ
Step 10.~. Determine storage size k for each movement in
the median from design or field observations (if k = 0 skip
to step ~ I).
Step ·0.2. For each of the four movements (7,8,10,!I),
perfonn the follow ng additional capacity calculations. The
example is presented for movement 8:
.
.
Define conflicting volumes using Table 56.
vl + v2- volume of priority street left turning
traffic at part I + volume of major street through
traffic coming from the left at part I in Figure 50.
vs= volume of the sum of all major street flows
comingirom the right at part ~ In Figure 50.
From Step 4 through 8:
c~v,+v2+vs)= capacity at a cross intersection for
minor through traffic with a major street traffic
volume of v~+v2+vs
Repeat steps 4 Trough 8 with relevant conflicting
movements to get:
cave + vie= capacity at part
cove)= capacity at part II
Calculate adjustment factor a, and intermediate
variable y
a = 1 - 0.32e~l3~ for k> 0 (178)
C(V1 + v2) - c(vl + is + Vs) (179)
~V; - V1 - ~V1 + V2 + as)
.
Calculate ct = total capacity of the intersection for
subject movement
C = a xt~xt'' i-l)x[
129
1.0
0.9
0.8
0.7
0.6
a, 0.5
0.4
0.3
~ .~>
0.1
0.0
Figure 72. Tw~Stage Gap Acceptance, k~1
~ k- 1 ~
i
,~
~ . . .
0.0 0.1 0.2
~ .... .... .... .... ... .... ~
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
[C|V5)-V1]1C~ (-)
. . .
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
0.0 0.1 0.2 0.3
[C(V5)-v1llco (_)
- 0.9
0.8
-0.7
-0.6
_
_0.5
- 0.4
Figure 73. Tw~S1age Gap Acceptance, ~2
Step 11. Computation of Shared Lane Capacity
If minor sheet approach has shared lane, or a flared
approach to accommodate two vehicles alongside at the
stop line, fiche shared lane capacity should be calculated
using equation IS2.
Al + VT + VR
Hi.,
Vat + Yr + OR (182)
cm, L cm. T cm' R
where
cn,R is the mtenm capacity of right turn movement in
shared lane, veh/hr.
Step 12. Computation of Delay
Comoutadon of vehicle delaY for each lane. Note:
CSH is Me capacity of shared lane, veh/hr;
Vat is the volume of left turn movement In shared
VT is we volume of through movement in shared ~ = 3600 + 90~}T ': Vr
lane, veh/br;
VRis We volume of r~ghtt~n movement In shared
lane, vehlhr,
cat is the interim capacity of led turn movement
in shared lane, veh/hr;
CAT is the interim capacity of Trough movement
In shared lane, veh/hr,
If were is a flared lane on a minor shared
approach, then d should also be calculated for
each movement as if they had exclusive lanes;
If upstream signal effect was included (step 4),
then equation IS3 may overestimate random
delay. An adjustment may be provided from
filture research.
I 3600 US
]2 4, C-es - (~83)
J 4507
where
· d is the average vehicle delay, sec/veh;
C~,X is the capacity for movement x, or for shared
lane, Thor;
Vx is the traffic volume for movement x, or for
131
shared lane, veh/hr;
· T is the analysis time penod, hr. (T = 0.25).
Step 13. Determination of Delay to Rank ~ Vehicles
{;P2, D3, Ds, D6)
If the major street left turns 1, 4 share a lane with rank ~
movements 2 and 3, 5 and 6 respectively, then these rank
~ movements may experience delay due to blockage by the
major left turns. The proportion of rank 1 vehicles being
blocked is 1-p*oi as defined belong. Note that on a
multilane road, only the major street volumes In the lane
which may be blocked should be used in the calculation as
V `' and V i2. On multilane roads if it is assumed that
blocked rank 1 vehicles do not bypass the blockage by
moving across into over Trough lanes (a reasonable
assumption under conditions of high major street flows)
then Vi, = VAN.
The average delay to.rank 1 (through j or right turn k
at,,=
vehicles on this approach is Even by:
~ (i - pa;) x d'"°P~kp X ~ Vl,[
Vit ~ yin N21 (~84)
(I po')Xd~kfl N=1
As defined In step 4 (and In 1994 HEM Equation 10-3~:
p*0 = 1- Pa i
1- (S'+S ~
where
(185)
i=1,4;
j = 2, if i = 1, or
=5,ifi=4;
kit 3, if i= 1, or
=6, ifi=4;
Sj is the saturation flow rate for major street
through traffic streams
So is the saturation flow rate for major street right
turn traffic
Step 14. Determination of Level of Service
Step 14.1. Check volume/capacibr ratio for each minor
street movement. If V/c2 1, then LOS ="F". Determine
levelofservice according to Table 58 for each minor street
movement or approach lane, and the major street leR turn.
(Note that the LOS thresholds have been adjusted to be
equivalent to those for signalized intersections, so that
direct comparisons for a given movement are more valid).
Step 14.2. Detente weighted average total delays and
LOS aggregated for each approach.
Step 14.3. Determine the weighty average total delays and
LOS aggregated for ad delayed vehicles, including 1be
delayed rank ~ vehicles, in the entire intersection
Step 14.4 Determine the weighted average total delays and
LOS for aggregated for all movements, including un-
delayed rank ~ vehicles, In We entire ~ntersechom
Table 58. Determination of LOS Based on Average Delay
ll E |
s6.S
>6.6 and s l9.S
>19.6 and s32.S
>32.6 and sS2
>S2.1 and s78
>80
Step 15. Determination of Average Queue Lengths
(delay in vehicle-hours)
For each of the four levels of aggregation in Step 14
calculate the average queue, the product of Me number of
subject vehicles and the average delay divided by 3600.
Step 16. Adjustment of Capacity for Flared Minor
Approach (c, .,8 and c', ,~; C,,,, 7 and c,,, I)
Refer to Figure 74:
Step 16.~. Let the shared lane case be the worst case.
Calculate the total approach capacity cam, then delay in
vehicle hours (step 14~. This is equivalent to the average
queue on the approach for the shared lane case.
Step 16.2. Let the separate lane case be the best case.
Calculate the total approach capacity c,~ = c708+c,,
then delay in vehicle hours (i.e. skip the sham lane
calculation in step Il. Den recompute steps 12 Trough
15~. This is equivalent to the average queue on the
approach for the separate lane case.
Step 16.3. Derive amaximumieng~ in vehicles A,,, of the
flared area above which traffic flows approximately like it
would tee on two separate lanes. This could be assumed to
be equivalent to the average queue in 16.2 plus one vehicle
rounded up to an integer number of vehicles (alternatively,
a more conservative approach would be to calculate and
132
use the 95th percentile queues Tom the HEM 1994, Figure
10.S instead office average queues in steps 16.1 and 16.2~.
Step 16.4. Using the queue storage Kit,,,., at the site, make
a linear interpolation between Me shared lane formula
capacity (w~thk=O) andante sum ofseparate lane capacities
(w~thk determined in step 3~. This can be shown to yield
Me following capacity equation:
Casual = (Ccepar~C~ Cot K~ / ~ + Cat
= c',p,,~,, k,m,,, / k,,= + Cody 1- ken,,,/ kit (~86)
Step 16.5. Recompute steps 12 through 15 using the
capacity Bom step 16.4)
Step 17. Comprehensive Assessment of V/C, Delay,
Queue Measures of Effectiveness
For Me worst delayed lane, obtain:
.
average delay per vehicle from step 14.1
average queue Dom step 15
volume/capacity
Lookup the above three parameters on Figure 75 to obtain
a comprehensive assessment of the performance of the
critical movement or lane group. This step may also be
repeated for any lane group.
.,
~ FACTUAL ~
43: J
ad:
CSEPARATE-
CFLARED
CSHARED
ILL
1~1 ~ 11 1A 11
1 , ,
KACTUAL
QUEUEk
Figure 74. Capacity Approximation at Intersections with [fared
Minor Street Approach
_:
OX
al,
K~x
133
REGION 2
1 000
100
~n
-
CO
a)
C]
a)
O) 10
CO
0
1
0/
7
REGION ~
- '
=
Figure 75. Queue/Delay Relationship
Queue/Delay Relationship
REGION 3
I! ~ ~
v/c - 0.2
v/c - 0.4
~.
. . . ..
. . ..
. . . . . ..
. . . . . ...
Average Queue
10
. __ _
lYY4 AM _ ~ :, ''
-A- 100
v/c - 0.6
v/c- 0.8
V/C- 0.9
via- 1.0
v/c- 1.2
via- 1.4
134
lo.,
