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OCR for page 77
CHAPTER 3
INTERPRETATION, APPRAISAL, APPLICATIONS
3.1 CAPACITY CHARACTERISTICS
This section summarizes the models developed for capacity prediction. These models can
ne used to predict capacity-related traffic characteristics for a range of conditions common to
interchanges and closely-spaced signalized intersections. The specific characteristics considered
include saturation flow rate, start-up lost time, end lost time, and lane utilization.
The capacity of lane group represents the maximum number of vehicles that can be served
by the group's traffic lanes during the time allocated to it within the signal cycle. A lane group
flowing at capacity is typically characterized by the continuous discharge of queued traffic for the
duration ofthe signal phase that controls it. To this extent, lane group capacity is dependent on the
discharge characteristics of the departing traffic queue. These characteristics include the time lost
at the start ofthe phase due to driver reaction time arid acceleration,the saturation flow rate, and the
time lost at the end of the phase due to a necessary change interval. The following equation is
commonly used to compute He capacity of a lane group:
gs t35)
3,600
with
where:
g = [G + Y + RC - (Is ~ le)] r) CP
c ' = capacity of the lane group, vpc;
g= effective green time where platoon motion (flow) can occur, see,
saturation flow rate for the lane group under prevailing conditions, vphg;
G= green signal interval, see;
Y= yellow interval, see;
RC = red clearance interval, see,
Is = start-up lost time, see,
[e = clearance lost time, see; and
CP = clear period during cycle/phase when subject flow is unblocked, sec.
(36)
Many of the variables defined in Equations 35 and 36 represent the basic set of capacity
charactenstics. Models for estimating these characteristics (i.e., saturation flow rate, start-up lost
time, and clearance lost time) for all traffic movements at interchange ramp terminals and closely-
spaced intersections are described in the following sections.
3 - ~
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3.. Saturation Flow Rate Mocle'
The saturation flow rate for a lane group can be predicted using the following equation:
where:
Nit X 50 Xf XfHV Xfg Xfp Xfbb XfRT XfLT fD fv
s = saturation flow rate for the lane group under prevailing conditions, vphg;
s0 = saturation flow rate per lane under ideal conditions, pcphgpl,
fW = adjustment factor for lane width,
All = adjustment factor for heavy vehicles;
jig = adjustment factor for approach grade;
fp = adjustment factor for parking;
fib = adjustment factor for bus blockage;
fRT= adjustment factor for right-turns in the lalle group;
fit= adjustment factor for left-t~s in the lane group;
fD = adjustment factor for distance to downstream queue at green onset; and
if = adjustment factor for volume level (i.e., traffic pressure).
(37)
The first seven adjustment factors listed in this equation represent those described in the HCM 63,
Chapter 99. The last two factors were developed for this research and are specifically applicable to
interchanges and closely-spaced signalized intersections.
A third adjustment factory was developed for this research that quantifies the effect of turn
radius on the saturation flow rate of a left or r~ght-turn movement. This factor is introduced bY
revising the adjustment factors for protected turn movements provided in Me HCM.
right and lefc-turn adjustment factors are:
fAT
fRT fF
JET
f[T fR
where:
1
1 + PRT: fR
1
- 1 )
LT( fR
These revised
: Protected, Shared Right-Turn Lane
: Protected, Exclusive Right-Turn Lane
: Protected, Shared Left-Turn Lane
: Protected, Exclusive Left-Turn lane
3 - 2
(38)
(39)
OCR for page 79
fR = adjustment factor for the radius of the travel path (based on the radius of the applicable left
or right-turn movement),
PRT = portion of right-turns in the lane group, and
PLT = portion of left-turns in the lane group.
Adjustment factors for permissive-only and protected-permissive phasing can also be developed
using Equations 38 and 39 as a basis.
The ideal saturation flow rate so represents the saturation flow rate of a lane that is not
affected by arty external environmentalfactors (e.g., grade), non-passenger-carvehicles (e.g., trucks),
and constrained geometucs (e.g., less than 3.6-meter lane Widths, curved travel path). In this regard,
the saturation flow rate would be equal to the ideal rate when all factor effects are optimum for
efficient traffic flow and the corresponding adjustment factors are equal to I.0. Based on this
deflation, it was determined that ideal conditions were represented by an infinite dist~ce-to-queue,
non-spillback conditions, a tangent alignment (i.e., an infinite radius), and a traffic pressure
representing that typically experienced during peak traffic periods. Under these conditions,
2,000 pcphgpl is recommended as the ideal saturation flow rate for all traffic movements at
interchanges.
One potential factor that was evaluated but not included in Equation 37 is that of phase
duration. Some evidence was found Mat drivers adopted larger saturation flow rates for chases of
short duration than for Dose of long duration. TO .' · .- ·
~· ~. ~in. . ~
However, the relationship was not felt to be
conclusive for both left-turn and through movements, thus, more research is believed to be needed
before an adjustment for phase duration can be recommended for general applications.
Distance-to-Queue Adjustment Factor.
~.. . ~. ~,
The distance-to-queue adjustment factor fD
accounts tor the adverse enect or downstream queues on the discharge rate of an upstream traffic
movement. In general, the saturation flow rate is low for movements that have a downstream queue
relatively near at the start ofthe phase; it is high for movements that are not faced with a downstream
queue at the start of the phase. Thus, the distance-to-queue adjustment factor is based on the
distance to the back of the downstream queue at the start of the subject phase.
The variable "distance to queue" is measured from the subject (or upstream) movement stop
fine to the "effective" back of queue. The effective back of queue represents the location of the back
of queue if all vehicles on the downstream street segment (moving or stopped) at the start of the
phase were joined into a stopped queue. If there are no moving vehicles at the start of the phase,
then the effective and actual distance to queue are the same. If there are no vehicles on the
downstream segment at the start of the phase, then the effective distance to queue would equal the
distar~ceto the through movement stop line at the downstream intersection. The distance-to-queue
is computed as:
n
D = L _ s lv (40)
Nd
3 - 3
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with
where:
Lv = (1 PHF) LDC + PHPLHV
(41)
D = effective distance to the back of downstream queue (or stop line if no queue) at the start of
the subject (or upstream) phase, m,
~ = distance between Me subject and downstream intersection stop lines (i.e., link length, m;
nS = number of vehicles on the downstream sheet segment (moving or queued) at the start of the
subject phase, vein;
N.' = number of through lanes on the downstream segment, Cartes;
[v = average large length occupied by a queued vehicle, m/vein,
[pc = lane length occupied by a queued passenger car (= 7.0 m/pc), mlpc;
L,HV = lane length occupied by a queued heavy vehicle (~ ~ 3 m/veh), m/veil, and
PHV = portion of heavy vehicles in the traffic stream.
The effect of distance-to-queue is also dependent on whether spilIback occurs during the
subjectphase. Spillbackis characterized by the backward propagation of a downstream queue into
the upstream intersection such that one or more of the upstream intersection movements are
electively blocked from discharging during some or all of their respective signal phase. If spillback
occurs dunug the phase, We saturation flow rate prior to the occurrence of the spillback is much
~ .~ ~ . ~ ~ ~ · ~ .. e - ~. ~ ~ ~ · . ~ ~ ~ - - ~
lower than it WOUlCl be ~i there were no spa. l hUS, the magnitude ot the adjustment to the
saturation flow rate is dependent on whether spilIback occurs during the subjectphase. A procedure
for determining if queue spillback occurs is provided Appendix C. The distance-to-queue
adjushnent factor is tabulated in Table 21. It can also be computed using the following equation:
f =
D
where:
fD = adjustment factor for distance to downstream queue at green onset; and
D = effective distance to the back of downstream queue (or stop line if no queue) at We start of
the subject (or upstream) phase, m.
no spillback
1 + 813
D
1 : with spillback
+ 21.8
D
(42)
3 - 4
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Table 21. Adjustment factor for distance-to-queue (fD)
.
Distance to Back of Spillback Condition
Queue at Start of
Subject Phase, mNo SpillbackWith Spillback
150.6490.408
300.7870.579
600.8810.734
1200.9370.846
1800.9570 892
2400.9670.917
3000.9740.932
3600.9780.943
Turn Radius Adjustment Factor. Traffic movements Mat discharge along a curved Ravel
path do so at rates lower than Rose of through movements. The effect of travel path radius is
tabulated in Table 22. It Carl also be computed using the following equation:
r
-
fR
1.71
R
where:
fR = adjusunent factor for the radius of the travel path; and
R = radius of curvature of the left-turn travel path (at center of path), m.
Table 22. Adjustment factor for turn radius IRE
Radius of the Travel Movement Type
Pd~
ale, m Left & Right-Turn Through
0.824 1.000
15 0.898 1.000
30 0.946 1.000
45 0.963 1.000
60 0.972 1.000
75 0.978 1.000
90 0.981 1.000
105 0.984 1.000
3 - 5
(43)
OCR for page 82
This factor was calibrated for lefts n traffic movements; however, a comparison of this
adjustment factor to that developed by others for right-sum movements indicates close agreement.
Therefore, this factor is recommended for use with both left and right-turn movements.
Traffic PressureAdjustmentFactor. Saturation flow rates are generally found to be higher
during peak traffic demand periods than dunng off-peak periods. This trend is explained by the
effect of "traffic pressure." In general, it is believed that traffic pressure reflects the presence of a
large number of aggressive drivers (e.g., commuters) during high-volume traffic conditions. They
demonstrate this aggressive behavior by accepting shorter headways dunng queue discharge than
would less-aggressivedrivers. As these aggressive drivers are typically traveling during the morrung
and evening peak traffic periods, they are found to represent a significant portion of the traffic
demand associated with these periods.
The effect of traffic pressure was found to vary by traffic movement. Specifically, the left-
turn movements tended to be more affected by pressure as their saturation flow rates varied more
widely then those of the through movements for similar conditions. It is possible that this difference
between movements stems from the longer delays typically associated with left-turn movements.
Based on the preceding definition, it is logical that the effect of traffic pressure is strongly
correlated with the demand flow rate in the subject lane group. Thus, the effect of traffic pressure,
as represented by traffic volume, is tabulated in Table 23 for each movement type. It can also be
computed using Me following equation:
fv =
.07 - 0.00672 v`'
1.07 - 0.00486 vat
: left-turn
through or right-turn
where:
fV = adjustment factor for volume level (i.e., traffic pressure); and
v'' = demand flow rate per lane (i.e., traffic pressure), vpcpl.
(44)
As noted previously, ideal conditions were defined to include a traffic pressure effect
representative of peak traffic penods. In this regard, traffic pressures under ideal conditions were
defined as 10 and 15 vpcpT for the leh-turn end through movements,respectively. These flow rates
are conservativein their representationofhigher volume conditions es they exceed 80 to 90 percent
of all traffic demands that were observed at the field study sites. One consequence of this approach
to defining ideal conditions is that it is possible for the traffic pressure adjustment factor to have
values above I.0 when the flow rate is extremely high.
3 - 6
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Table 23. Adjustment factor for volume level (ices, traffic pressure) ~v)
. Traffic Volume, Movement Type
vpcpl Left-Turn Through & Right-Turn
3.0 0.953 0.947
.
6.0 0.971 0.961
9.0 0.991 0.974
12.0 1.011 0.988
15.0 1.032 1.003
18.0 1.054 1.018
21.0 1.077 1.033
24.0 1.100 1.049
3.~.2 Start-up Lost Time
The start-up lost time associated with a discharging traffic queue varies wad its saturation
flow rate. More specifically, start-up lost time increases way saturation flow rate because it takes
more time for We discharging queue to attain the higher speed associated with Me higher saturation
flow rate. The recommended start-up lost times corresponding to a range of saturation flow rates
are provided in Table 24. These values Carl also be computed using the following equation:
1 = -4.54 + 0.00368 s. > 0.0
s
where:
is = start-up lost time, see, arid
s' = saturation flow rate per lane trader prevailing conditions (= shy), vphgpl.
(45)
The recommended start-up lost times are applicable to left, through, arid r~ght-turn movements.
Table 24. Start-up lost time (!J
Saturation Flow Rate, vphgpl | Start-up Lost Time, see
__
1,400 0.61
1,500 0.98
1,600 1.35
1,700 1.71
1,800 2.08
1,900 2.45
2,000 2.82
2,100 3.~S
3 - 7
OCR for page 84
unavailable for traffic service. This time is intended to provide a small hme separation between the
~. . · . . · · . . · . - ~
3.~.3 Clearance Lost Time
The time lost at the end of the phase represents the portion of the chance interval that is
franc movements associated wan successive signal phases and, Hereby, promote a safe change in
right-of-way allocation. Clearance lost time at the end of the phase can be computed as:
le = Y ~ RC - gY (46)
where:
le = clearance lost hme at end of phase, see;
Y= yellowinterval,sec;
RC = red clearance interval, see; and
gy= effective green extension into the yellow interval, sec.
For speeds in the range of 64 to 76 km/in and volume-to-capacity ratios of 0.~8 or less, the
average green extension is 2.5 seconds. This average value is recommended for use in most capacity
analysis. More appropriate values can be computed from Equation C-51 in Annendix C when the
~. . ~. ~, . _ ~~, ~. ~.
~ r
speeds are outs~cte the garage or o~ to -lo hm/h or whence tor the analysts period exceeds 0.~.
3.~.4 Lane Utilization
Dnvers do not distribute themselves evenly among the traffic lanes available to a lane group.
As a consequence, the lane of highest demand has a higher volume-to-capacity ratio and the
possibility of more delay than the other lanes In the group. The HCM (3) recognizes this phenomena
and offers the use of a lane utilization factor Uto adjust the lane group volume such that it represents
the flow rate in the lane of highest demand. The adjusted lane group volume can be computed as:
v' = vg'U
where:
v ' = demand flow rate for the lane group, vpc;
v =
g
unadjusted demand flow rate for the lane grouts voc: and
U= lane utilization factor for the lane group.
~, . . .
(47)
There are two reasons for an uneven distubutionoftraffic volume among the available lanes.
One reason is the inherent randomness in the number of vehicles in each lane. While drivers may
prefer the lesser-used lanes because of He potential for reduced travel time, they are not always
successfi~! in getting to them for a wide variety of reasons (e.g., Friable to ascertain which lane is
truly lowest in volume, lane change prevented by vehicle in adjacent large, driver is not motivated
to charge lanes, etc.~. Thus, it is almost a certainly that one lane of a multi-lane large group will have
more vehicles in it than the other lanes, during arty given cycle.
3 - ~
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The second reason for an uneven distribution ofbaffic volume among the available lanes is
driver desire to "preposition" for a turn maneuver at a downstream intersection. This activity
commonly occurs on the arterial cross street at interchange ramp terminals and at any associated
closely-spaced intersections. This propositioning causes drivers to concentrate in one lane at the
upstream ramp terminal or intersectionin anticipation of a turn onto the freeway at the downstream
ramp terminal.
Random Behavior Model. The lane utilization factor for an intersection lane group that
does not experience propositioning (e.g., at an isolated intersection) is dependent on the degree of
randomness in the group's collective lane-choice decisions. In addition, it is also based on the
group's traffic volume on a "per cycle" basis. In general, lane utilization is more uneven for groups
with low demands or a high degree of randomness or both. The recommended lane utilization
factors for random lane-choice decisions are provided in Table 25. These values can also be
computed using the following equation:
U =
r
1 ~ 0.423 ( 2 . 1 ~ 0~433 N'
where:
Ur = lane utilization factor for random lane-choice decisions;
v' = demand flow rate for the lane group, vpc, alla
N= number of lanes in the lane group.
JV- 1
2 v'
(48)
The recommendediane utilization factors are applicable to left, ~rough, and nght-turn lane groups.
Table 25. Lane utilization factors for lane groups with random lane choice (Ur)
Lane Group Flow Number of Lanes in the Lane Group
Rate, vpc ~1 2 ~3
5.0 1.00 __1.32 1.67
10.0 1.00 1.22 1.45
15.0 1.00 1.17 1.36
20.0 1.00 1.15 - 1.31
25.0 1.00 1.13 1.28
30.0 1.00 ~1.12 1.25
35.0 1.00 1.11 1.23
40.0 1.00 1.10 ~1.22
-
4
2.08
1.74
.59
1.51
1.45
1.41
1.38
1.35
3 - 9
OCR for page 86
PrepositioningModel. The lane utilization factor for interchanges and associated closely-
spaced intersections can be stronglyinfluencedby drivers prepositioningfor downstream turns. The
magnitude ofthe effect is largely a site-specific characteristic,depending on Me number of vehicles
turning left or right at the downstream intersection (or ramp terminal). If this information is
available (such as from a turn movement count where downstream destination is also recorded), the
lane utilization factor can be computed as:
Max (v' , v' ~ JO
U = 1.05 dl dr `49y
P v'
where:
Up = lane utilization factor for propositioning;
I'm= number of vehicles in the subject lane group that watt be thing left at the downstream
intersection, vpc;
V 'fir = number of vehicles in the subject lane group Mat watt be turning right at the downstream
intersection, vpc; and
Marfv dab V dart = larger of v 'a'' and v 'or
Lane Utilization Factor. The possibility of preposition~ng must be evaluated to determine
whether to use Equation 48 or 49 to estimate the lane utilization factor U. This possibility can be
determined from the following test:
MaX(Y'd`' V err) > ~prepositioning
Maxfv 'dl, v tarry
< _
V' N
: no preposltlonz'2g
Based on the outcome of this test, the lane utilization factor is computed as:
U=
Up: propositioning
Ur: no propositioning
(50)
(51)
The distance to the downstream intersection could effect the propensity of drivers to
preposition into their desired lane. In recognition ofthis effect, the test equation is recommend only
for intersections located in interchange areas or near other closely-spaced intersections where the
inter-signal distances are less than 300 meters.
3 - 10
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3.2 INTERCHANGE CAPACITY ESTIMATION METHODOLOGY
3.2.1 Signal Timing
A two-level signalized interchange is essentially composed of two closely spaced
intersections (except for a SPUN) connected by an internal arterial link. As shown in Figure 34, each
intersection will have an arsenal input phase (a), and most will have a ramp input phase (b) together
with an arsenal left turn phase (c). Elapsing cycle time is upward in the example phase sequences
depicted in Figure 34. All diamond interchanges end two-quadrantparclos wall have all three phases
per intersection in some configuration. Some four-quadrant parclos (Parclo BB) do not need the
ramp phase (b) and others (Parclo AA) not the arterial left turn phase (c). Thus, for most interchange
cases, three separate protected phases serve each ramp terminal. In 1973, Munjal (12) graphically
examined the three critical conflicting phases at each intersection of a diamond interchange. This
phase notation was adopted by the widely used diamond interchange computer program, PASSER
Ill, developed by Texas Transportation Institute in ~ 977 (139.
Almost all signal timing plans used at two-level interchangestoday can be described by using
the a:b:c phase sequence in four combinations together truth a related signal offset between the two
Various phase overlap
intersections.
Table 24 illustrates these phase sequence como~na~ons.
combinations are also possible, depending on the Interchange type anct signal onset.
Table 24. Basic Signal Phase Sequences at Interchanges
Phase l Left-Side Right-Side | Signal
Combination Intersection Intersection Sequence
1 | abc
2 abc acb Lead-Lag
3 acb abc Lag-Lead
4 acb acb Lag-Lag
~.
red ~,,
Figure 35 presents typical signal timing plans for some common interchange types for
illustrative purposes. The four-phase strategyis depleted for diamondinterchanges. As can tee seen,
n~rti~1 ~l~verl~f~ (arc in contrast to traditional diamond interchanges, provide some
application variation but do not change the basic concepts. Two-quad pros have three phases per
intersection;whereas, four-quad parclos have only two phases per side, deleting the ramp Phase b
(Parclo BB) or arterial left turn Phase c (Parclo AA). The two-quad parclos may have Phase c in
the inbound direction to the interchange (Parclo AA) or in Me outbound direction (Parclo BB).
Moreover, the ramp phases (Phase b) may be ire advance of the cross street (Parclo AA), as in a
conventional diamond, or beyond (Parclo BB). Parclos provide one distinguishing phasing
difference to diamonds in that right-turn (sometimes free) signal overlaps are common. Single-point
urban interchanges (SPUN) basically employ a conventional intersection phasing sequence, using
3 - I]
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INTERCHANGE Procedural Design
Analysis performed using
existing software packages
Inferface
· HCS
PASSER tl, ID
TRANSY7-7F
Offer srare
1
A~atysis
Operational analysis as
perforrnedby ff,e
specific program
Output
Capacity
Delay
LOS
Input
Turning movemerd volumes for
one interchange forth
Type of analysis requested
Int~nge types to analyze
Geometric and Simon
Condemns
1
C_
Analysis
1
Database conversion
algoritfuT
Analysis to be performed
using proposed new single
software package
, _
_
Analysis
Volume A~J~nt Module
Satua0 - Flew Rate Module
Effective Green Module
Capacity Analysis Module
Level of Service Module
Output
Future or existing fuming volumes for chosen
interchanges
LOS and performance measles for chosen
intone
Ranldng based on o~a~al performance
measures and LOS
Figure 39. Fltow diagram of optional procedural dlesign for INTERCHANGE.
3 - 32
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3.5 SIGNAL TIMING IMPROVEMENTS FOR CLOSELY SPACED INTERSECTIONS
Developing optimal, or even good, signal timing plans for signalized interchanges that
connect to a high-volume signalized crossing arterial is a complex task and current technology is
limited. Unintentionally poor signal timings may produce oversaturation end avoidable congestion.
Even if oversaturationis unavoidable due to excessive traffic volumes, improved operations can be
provided along the arterial and interchange ramps by avoiding signal plans that we be inefficient
for the given situation. All aspects of the operations should be examined. Short links, say less than
~ 50 m, are especially troublesome. Links that have a predominate input flow are subject to demand
starvation, and much of the downstream green may be wasted if a poor signal plan is implemented.
On the other hand, links having nearly balanced input flows, as can often happen around
interchanges with high local access demands, are insensitive to some operational control measures.
No unproductive conslra~nts should be placed on the overall system to try to treat such overloaded
links for all other links would probably only get worse and no appreciable benefits would likely
accrue. The following models are provided as guidelines toward improving traffic signal control
during these problematic situations.
Signal timing, traffic pattern, and queue storage length are principal factors of flow control
during such high-volume conditions. Effects of these factors on flow were illustrated in Chapter
Two. Within signal timing, signal offset is a robust and critical control vanable. In this section,
signal offset, din, is defined as the elapsed time from the start of green of the major phase at the
upstream intersection carrying the highest volume of input traffic onto the link id to the start of
green ofthe arterial through phase at the downstream intersection. The upstream major phase will
usually be the arsenal input phase, but not always in cases of high-volume turning traffic. The offset
described below may become "negative" meaning an early start of the downstream green, but the
offset used in the signal plan must be the equivalent"moduTo C" offset. Two offset controls will be
described: (] ~ queue clearance offset and (2) storage offset. The larger ofthe two offsets should not
be exceeded In most cases currently envisioned if peak flow efficiency is to be maintained.
3.5.! Queue Clearance Offset
In special arterial traffic signal coordination cases where all the arsenal traffic is 100%
through traffic (arsenal dominance), the ideal signal offset between the upstream signal and the
downstream signal would be equal to the travel time over the link for the running speed of the ~c.
As non-arsenal traffic (assumed to be non-coordinated) becomes a larger portion of the link flow,
queuing dunng red increases and the downstream offset should be reduced to "clear the cross-street
queue" before arrival of the major platoon. One offset selection model of this process is:
r ~
where:
~3 ~- - r (93)
u s
0,j = relative offset between major phases on link i-j, see,
L = length of link id, meters,
3 -33
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u = running speed of arterial link flow, mps;
r = effective red of downstream signal, see;
or = downstream arrival volume on red, vph, and
s = saturation flow of downstream phase, vphg.
As the upstream turning volumes become a larger percentage of the total downstream volume, then
or increases, the downstream queue grows, and the relative offset Bit should be reduced from the
ideal progression offset to reduce spillback.
Using the Highway Capacity Manual's (3) concept of detennining the proportion of arsenal
traffic alTiving on the downstream green, P. then the queue clearance offset would be
l
=
(1 - P) vC
in u s
where:
Bid
L
u
p
v
C =
relative offset between major phases on link i-j, see;
length of link id, meters;
running speed of arsenal traffic flow, mps;
proportion of arsenal traffic arriving on downstream green;
total downstream arterial arrival volume on phase, vph; and
cycle length, sec.
(94)
Onsets less than that given above would be expected produce some demand starvation. Any
reduction in offset from Me ideal should not exceed the green time necessary to saturate the phase.
During undersaturated conditions, offsets greater than this value will produce some queue spillback
on the major (arterial) phase which may result in queue spillback into the intersection and
oversaturation on the upstream link if the downstream link is too short (See Equation D-] I.
3.5.2 Maximum Storage Offset
Another limit placed on signal offset adjustment that should be considered during high-
volume conditions is related to the length ofthe link. To minimize the chances of demand starvation,
the link offset should not be less than
L 3600 NL
e..=
" u s! u 3.5
~
~
where:
u
N
s
1
0,j = relative offset between major phases on link id, see,
L = length of link id, meters;
~ .~, ,
naming speed of arterial traffic flow, mps,
number of lanes on link id;
saturation flow of downstream phase, vphg; and
queue storage length per vehicle, about 7 m/vein.
3 - 34
(95)
OCR for page 111
The final selection of offset should consider many factors, including the volume level, traffic
pattern and degree of saturation of the downstream signal. However, to enhance the throughput
efficiency dunng high-volume conditions, the link offset shows not be less than the larger of
Equations 94 arid 95 given above.
3.6 ARTERIAL WEAVING SPEED ANALYSIS METHODOLOGY
The procedure for computing the speeds of vehicles in the arsenal weaving section is outlined
in the flow chart shown in Figure 37. This flow chart illustrates the sequence of computations
required to compute the average running speed of artena] through and weaving vehicles in the
weaving section. The arterial weaving section of interest is the one created by the combination of
a signalized interchange off-ramp and an adjacent, closely-spaced signalized intersection.
| Input Data Geometr~cs
Traffic
| M a ne Over S peed to r Arteria I Th roug h Ve h icles, Um a I
| Weave Maneuver Distance, Drew |
1
,
Probability of Being Blocked, Pu
r Maneuver Speed for Weaving Vehicles, Um,w
Figure 37. Flow chart to determine speeds in an arterial weaving section.
The weaving maneuver considered is the off-ramp nght-turn movement that weaves across
the arterial to make a leflc-turn at the downstream signalized intersection. The terminology "arterial
weaving" is adopted in this methodologyto clearly indicate that the weaving occurs on streets whose
traffic flow is periodicallyinterruptedby traffic signals, as compared to the more extensively studded
weaving that occurs on uninterrupted flow facilities.
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3.6.1 Maneuver Speed for Arterial Through Vehicles
Input data needed to compute the maneuver speed for arterial through vehicles includes the
average arterial speed and flow rate entering the weaving section. This average speed represents the
desired speed of the traffic stream when there is no weaving activity present. The arterial maneuver
speed can be computed with the following equation:
Um = 1.986 U0 7~7 e (-0 634 Vo/3600) (96)
where:
U,,2, a = average maneuver speed for arterial through vehicles, m/s;
Ua = average arterial speed entering the weaving section, m/s; and
Va = average arterial flow rate entering the weaving section, vph.
The average maneuver speed is defined as the average running speed of arterial vehicles
through the weaving section. It represents the ratio of travel distance to travel time within this
section. The arterial and weaving maneuver speeds are computed in a similar manner; however, they
do not tend to converge for low volume conditions. This trend is due to the fact that the weaving
maneuver generally has to accelerate from a stopped (or slowed) condition whereas the arterial
maneuver generally enters Me weaving section at speed.
3.6.2 Maneuver Speed for Weaving Vehicles
The average maneuver speed for weaving vehicles is dependent on a variety of traffic
conditions and events. Traffic conditions include the average arterial speed entering the weaving
section, volume of weaving vehicles, and available weaving maneuver distance. The primary traffic
event is the probability ofthe weaving vehicle not teeing blocked from entering the weaving section
or delayed during its maneuver.
The average arterial speed was discussed in the preceding section. The average weaving flow
rate Vw represents the number of vehicles that completed off-ram~right-to-downstream-left-turn
maneuver during the analysis period, it is a subset of the number of vehicles that enter the arterial
via the off-ramp. The remaining variables require computation, equations for this purpose are
described in the following paragraphs.
The available weaving maneuver distance L4 w represents the average length of arterial
available for a weaving vehicle to complete its weave maneuver. This distance can be estimated as:
V r L
a v
L = ~ x (97)
1 -
51 Nt
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where:
[q w = average length of queue joined by weaving vehicles, m.
s' = saturation flow rate per lane under prevailing conditions (~ I,800), vphpI,
N. = number of arterial through lanes in the subject direction, lanes,
r = effective red time for the downstream intersection through movement; see, and
average lane length occupied by a queued vehicle (See Equation C-45.), m/vein.
The "probability of a weaving vehicle being unblocked" Pu represents the portion of time
that the end of the off-ramp (i.e., the beginning of the weaving section) is not blocked by the passing
ofthe arterial traffic stream or the spilIback of a downstream queue. This probability is dependent
on the length of the weaving section. A "Ion"" weaving section is defined as a section that has
sufficient length to allow a weaving driver to weave across the arterial one lane at a time. If this
minimum length is not available, then the section is referred to as "short." The weave maneuver in
a short section requires the simultaneous crossing of all arterial lanes (in Me subject direction) using
more of a "crossing" than a "lane-changing" action. The equation for estimating Pu is:
P u ~ ~N ~ ~Ir ~ ~ ~ ~2 0
where:
Pu = probability of a weaving vehicle being unblocked,
I~ = indicator variable (~.0 if Dm w ~ 90 by, - A, 0.0 otherwise);
Dm w = average maneuver distance for weaving vehicles (= tw - [q w)' m, and
[a = distar~ce between the off-ramp entry point and the stop line ofthe downstream intersection
(i.e., the length of the weaving section), m.
It should be noted that Pu is equal to 0.0 when the average queue length equals the length of the
weaving section (i.e., when Dm w is effectively zero).
Using the probability of a weaving vehicle being unblocked and the weaving volume, the
average weaving maneuver speed can be computed as:
Um w = 3 741 U0408 e ~l] 045~} -PU) VW/3600)
where:
U., w = average maneuver speed for weaving vehicles, mJs; and
Vw = average weaving flow rate, vph.
(99)
Like the arterial maneuver speed, the weaving maneuver speed is defined as the average running
speed of weaving vehicles through the weaving section.
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3.6.3 Example Application
The following example is used to demonstrate the application of the arterial weaving speed
analysis methodology. The arsenal weaving section has the following attributes:
Geometric Data:
Number of arsenal through lanes in the subject direction, N. = 2 lanes
Length of the weaving section, to = 200 meters
Traffic Data:
Average arsenal speed entering Me weaving section, Ua = 12.5 m/s (45 km/in)
Average arsenal flow rate entering the weaving section, Va = 1,000 vph
Average weaving flow rate, Vw = 170 vph
Saturation flow rate per large, s' = 1,800 vphgpl
Elective red time for the downstream intersection, r = 50 seconds
Average lane length occupied by a queued vehicle, [v = 7.0 m/vein
Analysis:
1 . Using the average arterial speed and flow rate, the average maneuver speed for arterial through
vehicles Um a can be computed as ~ 0.2 m/s.
2. Using the arterial flow rate, elective red time, saturation flow rate, and number of lanes, the
average length of queue joined by weaving vehicles [q w can be computed as 135 meters.
3. The average length of queue, combined with the weaving section length, yields a maneuver
distance Dm w of 65 meters.
4. Based on the maneuver distance of 65 meters, it can be concluded that the weaving section is too
short for a driver to weave by changing lanes one at a time. The driver is more likely to cross
all lanes at the same time (i e., IL = 0 0)
5. For short weaving sections, the probability of a weaving vehicle being unblocked Pu is computed
as O.52.
6. The weaving flow rate and probability of blockage can be used to compute the average weaving
maneuver speed Um w as 8.2 m/s.
If the weaving section length were 3 00 meters long then it would be characterized as a "Ion""
section. In this case, weaving through the section would likely occur one lane at a time and the
weaving speed would increase to 9.~ m/s. However,,the predicted arterialthrough movement speed
Um a is unchanged (i.e., it equals ~ 0.2 m/s).
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3.7 RAMP WEAVING CAPACITY ANALYSIS METHODOLOGY
The procedure to determine the interchange ramp weaving capacity across the connecting
arsenal street for a specific progression factor arid arsenal through volume is shown in Figure 40.
The flow chart illustrates the methodology to determine the ramp weaving capacity for crossing He
arterial arid mar~euvenug into a downstream left turn bay given progressed flow along the arsenal.
The procedures are as follows.
Input Data: Geometrics
Traffic
~ c
Ramp Capacity for Random Flow along Arterial, Q R (Eq. 100)
~ c
Adjustment for Sneakers Q'~ = QR + SR (Eq. 101)
~I
Adjusted Ramp Capacity for given PF = Q PF (Eq. 102)
Figure 40. Flow chart to determine ramp weaving capacity.
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3.7.1 Ramp Capacity During Random Flow
Data necessary to compute ramp capacity for random flow are total arterial volume, number
of lanes on the arsenal in the direction of merging operations, and the coefficients a, ,0. The data
required to determine the ramp capacity for progressed flow include the number of lanes on the
arterial, the required PF and v/c ratio e The number of lanes of the arterial are used to select the a arid
,B coefficients Tom Table 26 which are employed in the exponential regression equation for
estimating ramp capacity during random flow conditions given below.
V -ad,
QR -Din
1-e '
where:
OR = ramp crossing capacity, vph;
V, = arterial through volume, vph;
~= coefficient of Me model = TC / 3600, and
,6 = coefficient of the model = Hs / 3600.
Table 26. Coefficients of the exponential regression mode!
Thru Lanes | 1 large 1 2 Caries | 3 larches
.
Coefficients a ~a ~
Exponential 0.00195 0.000657 0.00118 0.000574 0.00088 0.000565
R2 Value 0.9977 0.9995 0.9989
Conversion of I Tc l I Tc I ] Is | Tc | H
Values (sec.) 7.02 2.36 4.26 2.06 3.17 2.03
Table 26 shows the coefficients a and ,8 of the exponential model computed for one, two and
three thru lanes of arterials. The coefficients in the proposed exponential equation are accurate
estimations of the TRAF-NETSIM imulated operations in terms of standard errors and their
vanances.
3.7.2 Adjustment for Sneakers
Additional ramp capacity may be obtained by ramp vehicles weaving across the arterial flow
during the phase change intervals of the upstream signal. Simulation studies suggest that as many
as three "sneakers"per phase change may cross during capacity conditions . Thus, the ramp crossing
capacity adjusted for sneakers would be
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/ 3600 S n
QR = QR ~
where:
Q R
QR
so
no =
C
-
ramp weaving capacity adjusted for sneakers, vph;
ramp weaving capacity for random flow, vph; and
sneakers per phase change, vehicles,
number of phases per cycle; and
cycle length.
3.7.3 Adjustment for Progression
(101)
Ramp weaving capacity is affected by the quality of progression on the arterial street. The
quality of progression is identified in the Highway Capacity Manual by progression factors. In order
to obtain the ramp weaving capacity for different progression factors, weaving adjustment factors
for progression, fpF are determined and multiplied by the ramp capacity which has been adjusted for
sneakers. The adjustment procedure is
QPF QR fPF
where:
QPF
Q R
fPF
ramp weaving capacity adjusted for progression, vph;
ramp weaving capacity for random flow, vph; and
ramp weaving adjustment factor for progression.
The adjushnent factors for progression range from 0. ~ to ~ .0 and are determined from
fpF = 1 + 0~015 * e [0.0044*~-3.05*PF]
where:
fPF = ramp weaving capacity adjustment factor,
PF = HCM progression factor, and
V, = arterial volume per hour per lane (vphpl).
(102)
(103)
Note that HCM PF values exceeding 1.0 should be replaced by their complimentary value to 1.0.
That is, a PF of I.3 should be replaced by a value of 0.7 in the above equation. The progression
factors are determined from Table 9. ~ 3 in the ~ 994 Highway Capacity Manual (39.
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3.7.4 Example Application
Geometric Data:
Number of lanes on arterial
Number of lanes on ramp
Link length between ramp and downstream intersection
Traffic Data:
Arterial Through Volume
Cycle Length
Lost time per Phase
Analysis:
Ramp Capacity
(for three lane arterial)
~ (for three large arterial)
Sneaker Volume
= 3 lanes
= 1 lane
= 1 83 meters (600 feet)
= 1500 vph
= 100 seconds
= 4 seconds
0.000565
[From Table 26]
[From Table 26]
[3 vein/phase * 2 phase change intervals * 36 cycles
- 216vph
Assume the ramp capacity for a PF of 0.2 and v/c of 0.6 is to be determined.
Ramp capacity for random flow
Substituting values in the above equation yields
QR
QR = 701 vph
Accounting for ramp vehicles weaving during the phase change interval
Q R
= QR + Sneaker Volume
= 701 + 216
= 917vph
For progressed flow along the arsenal having a PF of 0.2 and a v/c of 0 6, IF can be determined
from Tahie 20 as ~ 074 Therefore
Ramp Capacity for a PF of 0.2 and v/c of 0.6: QPF = Q R * fPF = 91 7 * 1. 074 = 984 vph
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Representative terms from entire chapter:
saturation flow
