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OCR for page 123
APPENDIX E
A COMPUTATIONAL FRAMEWORK AND ILLUSTRATED EXAMPLES
FOR TRAFFIC-ACTUATED CONTROLLER MODELING
INTRODUCTION
The procedure for modeling traffic-actuated control developed under NIP Project 3~S contains
a number of analytically complex and iterative steps that do not lend themselves to manual computa-
tions. Therefore, an analysis program called ACT3-48 was developed in this study as a too! to
provide for demonstration and testing of the model. A computational Damework involving five
worksheets has been incorporated into the ACT3~8 program. The worksheets presented in this
report propose extensions to the original worksheets proposed by Courage and Ak~elik [~] for
modeling simple through and protected left turn phases.
The worksheets play a very important part in overcoming the "black box" image of complex models.
They provide a structure for presenting the results of intermediate computations in a common form
that is compatible with the proposed techniques. Thus, the format for the intermediate outputs pro-
duced by ACT348 was designed to be identical to the format of the worksheets. The computational
process is illustrated with two examples. The details of the analytical mode! and procedure used to
predict the trafflc-actuated signal timing plan [l, 2, 3, 4] and delay estimate [5] were described in the
indicated references. These details wall not be repeated here.
COMPUTATIONAL PROCESS
Each worksheet has its own purpose. The purpose of Worksheet ~ is to enter the data required speci-
fically for traffic-actuated control. Worksheet 2 is used to perform lane group data computation.
Worksheet 3 sets up the traffic-actuated timing computation. Worksheet 4 computes the green times
required to service the queues accumulated on the red phase. Worksheet 5 determines the green
extension times based on the unit extension time settings.
It is important to note that the analytical mode} developed in this study uses an iterative procedure
to predict the tra~c-actuated signal timing plan. Thus, while the worksheets themselves are quite
simple, the overall procedure contains iterative loops. The complete procedure involving the work-
sheets is illustrated in Figure EM In addition to the five worksheets, two iterative loops are indicated
as "Loop A" and "Loop B".
~AIL
-
Loop A. Required Time: This is an iteration between Worksheets 3 and 4. The purpose of
this iteration is to make the phase times converge to a stable cycle length. Worksheet 4 must
also refer to Worksheet 5 if phase time extensions are required to compute the required phase
times.
Appendix E: Page 1
OCR for page 124
Loop B. Phase Extension Time: This is an internal iteration within Worksheet 5. It is only
required when gap reduction features are employed. When the allowable gap is a function
of the phase time, the phase time cannot be computed without an iteration process.
4. Required
Times
(.,~,,
r ~ -I *-a.
5. Phase
Extension
Times
1. Data I ~1 2. Lane
Input ~ Groups
.~. ~
3. Cycle
Time
Adjustments
., A. ., ~
B ~
SYMBOLS
Main
Information
Flow
_
Worksheets
Iterative Loops
~J
'4,,,,,,,ei
Figure E-1. Iterative loops in the phase time and cycle length computation procedure
The computational worksheets are conceptually simple, but must be applied iteratively to arrive at
usefill results. The program is required because the iterative nature of the procedure makes it totally
impractical for manual implementation. The program is now fully functional and able to evaluate the
analytical models using a variety of data. It also provides a flexible computational tool for examining
other models that may be proposed.
WORKSHEET 1: lllAFFIC-ACTUATED CONTROL INPUT DATA
This first worksheet, presented in Figure E-2, gathers together all data required by the proposed
analytical model. As a convention that will be used in the presentation of all worksheets, the row
identification headings at the left side of the worksheets will be shown in lower case text if they are
input data and In UPPER CASE text if they belong to intermediate computations based on input data.
Appendix E: Page 2
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l
WORKSHEET 1: TRAFFIC-ACT UATED CONTROL INPUT DATA
APPROACH-SPECIFIC DATA Northbound Southbound Eastbound Westbound |
Left Turn: Treatment Codet 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
Position | Lead Lag N/A | Lead Lag N/A | Lead Lag N/A | Lead Lag N/A ||
Max Sneakers, S~, (vein)
Free Queue, Qf (vein) ;
Approach Speed, SP (mph)
Ring 1 and 2 T~ation Simultaneous Independent N/A Simultaneous Independent N/A
~_ F_
DESIGN PARAMETERS | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
WBL EBT NBL SBT EBL WBT SBL NBT
l
Ph~eType(LT,G,N,X) l l l l l l I 1
l
Phase Reversal? Y N Y N Y N Y N
Detector Location: Length, DL
Setback, DS
i . i .
Max Initial Interval, MxI
Added ~itial per AcWation, AI
Minimum Allowable Gap ~A
,
Gap Reduction Rate, GR
Pedestri ~
1 1 1 1
Maximum Green, MxG
IntergreenTime,l
Recall Mode (M~ Max, Ped, None) ! ! ! ! ! ! !
MIN VEH PHASE TIME, MnV:
| STARTING GAP, SG
| MIN INITIAL INTERVAL, MnI
| MAXIMUM PHASE TIME,MxT: MxG+I
| DETECTOR OCCUPANCY TIME, DT
1 (DL+18)/1~47SP I I I I
| TRIALPHASE TIME: Max(MnV,WDW+I)
Notes: 1. LT Treatment codes: (0) Prohibited, (1 ) PermiKed' (2) Protected, (3)Protected ~ Permitted, (4) Not Opposed.
Figure E-2. Worksheet I: Traff~c-actuatecl contro! input data
=
_
T I
1
T
Appendix E: Page 3
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Approach-Specific Data
The top portion of Worksheet 1 summarizes the approach-specific information. A separate column
is used for each of the four approaches. The following items are required:
Left Turn (:LT) Treatment Codes: The logic of the proposed mode} requires that the LT
treatment be identified explicitly. The codes used here are consistent with the HCM Chapter
9 planning method worksheets. These codes are defined in Section ~ of HCM Chapter 9.
0 = LT does not exist
~ = Permitted
2= Protected
3 = Protected plus permitted or permitted plus protected
4 = Not Opposed
The term "simple leR-turn protection"will refer to treatment number 2, in which the left turn
moves only on the protected phase. The terser "compound leflc-turn protection" will be used
to denote either protected plus permitted or permitted plus protected treatments. This is not
an attempt to replace any HCM terminology, but to augment the terminology with more
concise and easily understood references.
Position Codes: These are required to distinguish between leading and lagging led turn
protection. The terms "leading" and "lagging" apply equally to the cases of simple and
compound le~c-turn protection. These codes do not apply if the leg turn is not protected.
The worksheet offers a simple choice of "Lead," "Lag" or "N/A". The definition is very
simple: leading left turns precede the movement of the opposing through traffic and lagging
left turns follow it.
Sneakers: This describes the number of left turns per cycle that are dismissed at the end
of a permitted phase. An implicit default of two sneakers per cycle is built into the
supplemental permitted left-turn worksheets for purposes of determining the mirumum
saturation flow rate. Since any vehicle that rests in the detection zone wait extend its respec-
tive phase, a more detailed treatment of sneakers will be required for traffic-actuated control.
Free Queue: The current pretimed mode! assumes that the first perrn~tted leg turn at the
stop line will block a shared lane. This is not always the case, as the through vehicles in the
shared lane are often able to "squeeze" around one or more led turns. This is a definite defi-
ciency of the pretimed model, but it is especially critical with traffic-actuated control, because
vehicles In the free queue do not occupy the detector and therefore do not extend the green
phase. A permitted left turn stopped on the detector must be treated entirely differently in the
modeling process than one that is stopped beyond the detector.
Appendix E: Page 4
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Approach Speed, SP: The speed of vehicles on a signalized intersection approach is not
important to the current HCM Chapter 9 methodology. It is, however, required in the
analysis of tra~c-actuated operation. It determines the passage time between the detector
and the stop line as well as the portion of inter-vehicle headways during which a presence
detector is occupied. When modeling the operation of vehicles at traffic signals, it is common
to assume a single value for speed throughout the cycle.
Termination of Rings ~ and 2: The nature of dual-ring control requires that the second
phases of rings ~ and 2 terminate simultaneously because they yield control to approaches
with convicting traffic. However, control may pass Tom the first phase to the second phase
of either ring without causing any conflict. Independent termination of the first phases
improves efficiency in the allocation of time among competing movements and is generally
exploited for this reason. The type of operation created by independent termination is
sometimes referred to as "phase overlap."
It is, however, not essential that the phases terminate independently. Older single-ring con-
troller operation may be approximated by requiring that the first phases of each ring (i.e.,
phases ~ and 5 or 3 and 7) terminate simultaneously. In some situations involving coordi-
nated arsenal routes, it is common to force both rings out of their first phase simultaneously.
The model developed considered simultaneous or independent termination as legitimate alter-
natives.
It is possible that one or more of the first phases will not be used, because its associated left
turn is not protected. In this case, the question of simultaneous or independent termination
will not apply. This is another multiple-choice entry on the worksheet. The alternatives are
"Simultaneous," "Independent" and "N/A".
Phasing and Detector Design Parameters
The bottom portion of the worksheet includes all the data items specific to each of the eight phases
represented on Figure E-~. A separate column is provided on the worksheet for each phase. The first
group includes the design parameters relating to phasing and detector placement. The following data
items are included:
--I- r
Phase Type: This is the first of several phase-specific inputs that are required. A phase that
is not active will not be recognized in any of the subsequent computations. Inactive phases
are indicated by an "X" in the appropriate column of the worksheet. A leflc-turn phase will
be considered active only if it accommodates a protected left turn. A through phase will be
considered active whenever it accommodates through, left or right traffic. Active phases will
be designated by:
Appendix E: Page 5
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"it" If the phase accommodates a protected ieDc turn on a green arrow.
t'Tt'
ttGt'
t'N't
If the phase accommodates through and right-turning traffic only. In this
case, all leD turns are accommodated entireIv on another chase (i.e..
leflc-turn protection).
, ~simple
If any left turns are accommodated on this phase, opposed by oncoming
traffic. This will occur on phases with permitted led turns and those with
compound leflc-turn protection.
If the phase accommodates, in addition to other movements, led turns that are
not opposed at any time in the phase sequence. This will happen at "T"
intersections, on one-way streets and in cases in which the phasing completely
separates all movements on opposing approaches.
Note that right turns are not referenced specifically in these designations. Right turns are
assumed to proceed concurrently with the through traffic.
Phase Reversal: Normally the first phase in each ring on each side of the battier (odd
numbered phase) handles protected left turns and the second phase (even numbered) handles
the remaining traffic. This creates a condition of leading left-turn protection. When lagging
lefc-tu~n protection is desired, the movements In the first and second phases are interchanged.
Most controllers provide an internal function to specify phase reversal. For purposes ofthis
discussion, two phases may only be swapped if both phases are active.
Detector Length, DL: Defined as the effective distance, measured parallel to the direction
of travel, through which a vehicle will occupy the detector. A user-specified design parameter
influenced by local practice. The detector length influences the choice of other parameters,
such as the allowable gap in traffic that will terminate the phase.
Detector Setback, DS: This is the space between the downstream edge of the detector and
the stopline.
Controller Settings
The controller itself has several operating parameters that must be specified for each phase.
Collectively, these will be referred to as the "controller settings," because they must be physically set
In the controller with switches, alpha-numer~c keypads or some other electrical means. The following
settings will exert a significant influence on the operation of the intersection and must therefore be
recognized by the analysis methodology:
Appendix E: Page 6
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Maximum Initial Interval, M0: Used only when the initial interval is extended under
volume-density control. Must be long enough to ensure that a queue of vehicles released at
the beginning of green will be in motion at the detector before it terminates.
Added Initial Per Actuation, Al: Used only when the initial interval is extended under
volume density control. This value wall depend on the number of approach lanes. It should
be long enough to ensure that each vehicle crossing the approach detector on the red will add
an appropriate increment of time to the initial interval.
Minimum Allowable Gap, MnA: This is a user-specified controller parameter, the effect
of which wid be discussed later as the proposed models are exercised. It is typically set in the
range of 2-3 seconds. It establishes the threshold for the length of the gap in traffic that wait
cause the phase to terminate. The value of MnA is usually influenced to some extent by local
practice.
It is important to distinguish between the time gap and the time headway between vehicles.
The time headway indicates the elapsed time between the successive arrival of two
consecutive vehicles at a detector. The time gap indicates the elapsed time between the
departure of the first vehicle from the detector and the arrival of the second. The time gap
is what is led of the headway after the detector occupancy time has been subtracted. A
tra~c-actuated controller using presence detectors views the passage of traffic in terms of
gaps and not headways.
Gap Reduction Rate, GR: This determines the rate at which the allowable gap is reduced
in volume-density controllers as the green display continues. There are subtle differences in
the definition of the gap reduction rate among controllers. For purposes of this project, a
linear reduction rate (seconds reduction of gap per second of elapsed green time) will be
assumed.
Pedestrian Walk plus Don't Walk, WDW: This is m~n~rnum time given to each phase when
pedestrian demand is registered or the pedestrian recall is active. It inclucles both the
pedestrian walk and flashing don't walk intervals. These are actually entered into the
controller as two separate parameters, but wall be combined for purposes of this analysis. If
the pedestrian timing function is not implemented in a particular phase, the WDW value
should be entered as zero.
Maximum Green, MxG: This is a user-specified parameter, the effect of which will be
discussed later. Local practice open plays an important part in the determination of maximum
green times.
Appendix E: Page
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Intergreen Interval, I: Another user-specified controller parameter determined in accor-
dance with local practice. The intergreen interval consists of a yellow change interval fol-
iowed by an all-red clearance interval. These two intervals are entered separately into the
controller, but will be combined here to simplify the analysis.
Recall Mode: This detenn~nes how a phase will be treated in the absence of demand on the
previous red phase. The options are:
None: The phase will not be displayed.
Max: The phase will be displayed to its specified maximum length.
Min: The phase will always be displayed to its specified minimum length, but may
be extended up to its specified maximum length by vehicle actuations.
Ped: The phase will be given the filet Walk plus Flashing Don't Walk and may be
extended farther, up to its specified maximum by vehicle actuations.
This function will have a significant effect on the operation of the controller. For example,
the maximum recall option wall have the effect of creating a pretuned phase.
Preliminary Computations
Several items computed Tom the above data will remain fixed, and are not subject to modification
as a result of iterative computations. These values are included at the bottom ofthe worksheet for
use in subsequent computations. They appear on the worksheet in upper case letters because they
are computed values. In some cases, they are actually controller settings, but their values may be
computed in terms of data that have already been established.
Minimum Phase Time for Vehicles, MnV: This is actually a traffic engineering input, but
it is included here as a computed value because it is subject to modification by other control
parameters. It is an important input to any process for computing an implementable timing
plan. It does not appear in the HCM Chapter 9 data at this time because HCM Chapter 9
does not offer the ability to compute timing plans. On the other hand, it is not possible to deal
realistically with traffic-actuated control without recognizing the existence of a minimum
phase time. For compatibility with other signal timing programs, the phase times include all
intervals, including green, yellow and all-red.
For purposes of the worksheet, the minimum phase time must be replaced by the maximum
phase time MUG + ~ if the "Recall to Maximum" mode is In effect, and therefore, it is treated
on the worksheet as a computed value.
Appendix E: Page 8
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Starting Gap, SG: If the gap is reduced during the green phase under volume-density
control, a starting gap must be specified. It is common to choose a value for the starting gap
equal to the passage time Tom the detector to the stop line. The SG may be computed as:
SG= DS / 1.47SP
If this value is equal to or less than the minimum allowable gap, MnA, then gap reduction
would not normally be employed. In this case, SG = ~A.
Min Titian Literal, MnI: This determines the minimum green time to be displayed. Given
a specified value of the minimum phase time for vehicles, MnV, the minimum initial interval
may be calculated as:
HI = MT1V - ~ - SG
Maximum Phase Time: The maximum time that may be assigned to the phase. This may
be computed as (MUG + T). Throughout the iterative process, the computed green times
must be checked to ensure that they do not exceed this value.
Detector Occupancy Time, DT: This is the time during which a vehicle passing over the
detector at the approach speed will occupy the detector. It may be computed as (DL+~) /
I.47SP. This assumes an average vehicle length of IS feet. In computing the estimated
length of a phase extension, DT must be added to the controller's current allowable gap
threshold to determine the vehicle headway value that win cause a phase to terminate.
Trial Phase Time: This will provide the starting point for the iterative procedure that will
determine the estimated phase times. The procedure, as described later, constructs an initial
timing plan based on the minimum acceptable phase times. Using the data already entered on
this worksheet, the minimum acceptable phase times would be either the minimum phase time
for vehicles, MnV, or the minimum phase time for pedestnans, (WDW + I), whichever is
greater.
WORKSHEET 2: LANE GROUP ASSIGNMENTS
Figure E-3 shows the Lane Group Assignment Worksheet. The purposes ofthis worksheet are:
I) To associate each of the lane groups with a signal phase;
2) To identify the movements that occur in each lane group; and
3) To convert the volumes and saturation flow rates entered on previous HCM Chapter 9
worksheets into units of vehicles per second. The timing computations on subsequent
worksheets wait require these units.
Appendix E: Page 9
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; --
WBL EBT NBL SBT EBL WBT SBL NBT
Thase Movement~ (T TR) .
Opposing Through Phase
LT EQUIVALENT S. E~
LG 1: No of!~nes
LG Movements (LTR) ~7 ~T
Volume(vph) l I T I I 1 1 1
ARRIVAL RATE, ql (vps) ~T I I I I T
Platoon Ratio Rp
GREEN ARR RATE, q.1 (vps)
Sat Flow Rate (vphg) l l l l l l l l
SERVICE RATE, sl (vps) l l l l l l l |
LG2: No.ofLanes l l l l l l l |
Movements (LTR) l l l l l |
Volume (vph)
ARRIVAL RATE, q2 (vps)
Platoon Ratio R
GREEN ARR RATE, q,2 (vps)
Sat Flow Rate (vphg)
SERVICE RATE, s2 (vpsg) l l l l l l
LG3: No. of Lanes l l l l l l I
Movements (LTR) l l l l l l l
Volume(vph) l l l l l I 1.
GREEN ARR RATE, q,3 (vps)
ARRIVALRATE, q3 (vps) l l l l l | ~
Platoon Ratio Rp l l l l l l l
Sat Flow Rate (vphg) l l l l l l 1:
SERVICE RATE, s3 (vpsg) T I T T T I
VEHICLE RIVAL RATE, VAR
PedVolume(pph) l I ~ ~=
PED ARRIVAL RATE. PAR: (pps)
Figure E-3. Worksheet 2: Lane group data
Appendix E: Page 10
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The lane group breakdown should come directly from the HCM Chapter 9 Volume Adjustment
Worksheet. Typically, the lefc-turn phases will have only one lane group and the through-traffic
phases may have up to three lane groups.
The first line ofthis worksheet indicates ad the movements ~,T,R) accommodated by the phase. The
next line deals with progression quality. Basically, the arrival type (AT) from the HCM Chapter 9
Input Data Worksheet is repeated here. Arrival type 3 is commonly used at ~ly-actuated isolated
intersections, where progression is not a factor and the green arrival rate is assumed to be equal to
the red arrival rate. In coordinated operation, the AT input value will determine the green and red
arrival rates ofthe through movements ofthe arterial.
The next line is the phase number of the opposing through phase which opposes the permitted left
turns of the subject phase. For example, NEMA phase 6 is the opposing through phase of NEMA
phase 2 because the movements for NEMA phase 6 will oppose the permitted leD turns for NEMA
phase 2. The last line for this top portion is left turn equivalence, Eat, which is the through-car
equivalent for each permitted le~c-turning vehicle during the unsaturated opposing flow. The values
of Eel can be obtained from Figure 9-7 of HCM Chapter 9.
Six subsequent lines are associated with each lane group:
Number of Lanes: From the HCM Chapter 9 Input Data Worksheet
Volume (vph): From the HCM Chapter 9 Volume adjustment worksheet. The adjust
ment for PHE should be applied if a peak IS-m~nute analysis is
desired. The lane utilization adjustment should not be applied since
this adjustment adds fictitious vehicles.
Arrival Rate: Convert hourly volumes to vehicles per second.
Platoon Ratio:
tne platoon ratio, Rp, is obtained from HCM Table 9-3. This value
is based on the arrival type. Rp will be used to determine amval
rates on the red and green phases. In HCM Table 9-3, the default
values for amval types I, 2, 3, 4, 5 and 6 are of 0.333, 0.667, 1.000,
1.333, 1.667 and 2.000, respectively.
Green Arrival Rate: The arrival rate during the green phase (veh/sec) which is equal to
the product of arrival rate and platoon ratio.
Sat Flow Rate: From the HCM Chapter 9 Saturation Flow Adjustment Worksheet
(vphg).
Service Rate: Convert the hourly rate to vehicles per seconds of green.
Appendix E: Page 11
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Worksheet 4: Required Phase Times Based on 1
PHASE
DATA
Int Red Time
Lost Time tl
Lost Time tsl
LG 1 Mov'ts
Grn Arr
Red Arr
ELI
PL
Svc Rate
Eqiv Svc
Net Svc
QatBOS Qs
Green G
fq
Land Utl
Svc Time
Wait Time
Tot Time
ResQ Qp
ResQ Qp'
2 Mov'ts
Grn Arr
Red Arr
ELI
PL
Svc Rate
Eqiv Svc
Net Svc
QatBOS Qs
Green G
fq
Land Utl
Svc Time
Wait Time
Tot Time
ResQ Qp
ResQ Qp'
Max Ph Time
BASE PH TIME
Ph
No.
4
6
Q
--------____l________________________________ v/c Ratio
RING 1 RING 2
1(WBL) 2(EBT) 3(NBL) 4(S8T) 5(EBL) 6(WBT) 7(SBL) 8(NBT)
58.56 38.87 58.56 38.87
3.00 3.00 3.00 3.00
2.00 2.00 2.00 2.00
LT L LTR
0.04 0.08 0.08
0.04 0.08 0.08
2.65 2.90 2.60
0.68 1.00 0.33
0.48 0.48 0.44
0.22 0.17 0.29
0.18 0.10 0.20
0.10 3.61 4.44
34.87 54.56 34.87
1.05 1.00 1.05
1.00 1.00 1.00
2.59 39.48 24.94
11.98 5.37 4.69
14.57 44.86 29.63
0.00 0.00 0.00
0.00 0.00 0.00
TR
0.07
0.07
2.65
0.00
0.43
0.43
0.36
4.33
34.87
1.05
1.00
14.51
0.00
14.51
0.00
0.00
.
64.00
14.57
.
0.08
0.08
2.90
1.00
0.48
0.17
0.10
3.61
54.56
1.00
1.00
39.48
5.37
44.86
0.00
0.00
TR
0.11
0.11
2.90
0.00
0.48
0.48
0.37
4.65
54.56
1.00
1.00
14.54
0.00
14.54
0.00
0.00
64.00
44.86
Arr Delta
Rate Value
0.04
0.04
2.60
1.00
0.48
0.19
0.15
2.12
54.56
1.00
1.00
16.02
8.96
24.99
0.00
0.00
TR
0.17
0.17
2.60
0.00
0.96
0.96
0.80
6.98
54.56
1.00
1.05
11.18
0.00
11.18
0.00
0.00
64.00
24.99
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
64-00
29.63
.
Worksheet 5: Green Extension Times:
Max Min Comp Adj New
Hdwy Hdwy Ext Ext Hdwy
4.09 9.82 9.82 4.09
4.09 13.48 13.48 4.09
4.09 9.55 9.55 4.09
4.09 11.81 11.81 4.09
.
0.16 0.50
0.33 0.50
0.13 1.50
0.28 0.50
Base Ph Time
Ph Ext Time
REQ PH TIME
MIN PH TIME
COMP PH TIME
0.96
0.92
0.89
0.90
4.09
4.09
4.09
4.09
Computed Phase Times Including Extension Intervals
,
Phase ~12345
MovementsUBLEBTNBLSBTEBL
,
44.86
13.48
58.33
15.00
58.33
14.57
9.82
24.39
15.00
24.39
29.63
9.55
39.18
15.00
39.18
78
SOLNBT
24.99
11.81
36.80
15.00
36.80
Figure E-12. Worksheets 4 of iteration 14 for the permitted left turn example
Appendix E: Page 36
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blorksheet 3a Traffic-Actuated Timing Computations
Iteration
15
A B Total A B Total
Ring 1 PH Swap?
Movts
PH Time
Ring 2 PH Swap?
Movts
PH Time
RING 1-2 DIFF
CYCLE COMPONENTS
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
No-------- Ho
EBT-------- SBT
24.3924.39 58.33
No-------- No
UBT-------- NBT
39.1839.18 36.80 36.80
-14.79-14.79 21.54 21.54
_ 39.180.00 58.33 0.00
Uorksheet 3b: Timing PLan sensitivity Capacity Parameter Estimation
,
Old Cyc 97.5 1 234 56 78
New Cyc 97.5 UBL EBT NBL SBT EBL ~JBT SBL NBT
58.33 39.18 36.80
0.00 0.00 21.S4
58.33 39.18 58.33
55.33 36.18 55.33
39.18 58.33 39.18
42.18 61.33 42.18
38.87 58.56 38.87
39.18 0.00 39.18
Unadj PH Time
Adjustment
New Ph Time
Eff Green 9
Int Red Time
Eff Red r
Red Time
Startup Time
24.39
24.39
14.79
39.18
36.18
58.33
61.33
58.56
0.00
,
58.33
Cycle convergence has been achieved at 97.5
Figure E-13. Worksheet 3a of the last iteration for the permitted left turn example
Appendix E: Page 37
OCR for page 160
EXAMPLE 1
Cycle: 97.5 1,JBL EBT
39.18
14.57
Phase T i me
Sat Green
+ + + + + + + + + +
~56
SBTE3L~JBT SBL
58.33 39.18
44.86 29.63
+
7 8
NBT
58.33
24.99
LG 1 Mov' tsLTLLTRL
Volune147.37275.00300.00150.00
f lt0.480.310.640.32
Finat Sat828.26560 651003.10580.62
Eff g36.1855 3336.1855.33
Final g/C0.370 570.370.57
Capacity307.30318 14372.17329.48
v/c Rat'o0.480.860.810.46
QAP du22.8720.8227.8417.12
xo0.830.830.830.83
fdl1.161.181.161.16
kd0.290.920.600.47
Delay d126.5424.4732.2319.90
Delay d20.002.710.000.00
Tot Delay26.5427.1832.2319.90
+ + + + + + + + + +
LT Vol0.00 275.00 0.00 150.00
LT Cap0.00 318.14 0.00 329.48
LT v/c0 . 00 0 .86 0 .00 0 .46
LT QAPdu 0.00 20.82 0.00 17.12
LT xo0.00 0.00 0.00 0.00
LT kd0.00 0.00 0.00 0.00
LT d10.00 24.47 0.00 19.90
LT d20.00 2.71 0.00 0.00
LT Delay0.00 27.18 0.00 19.90
+ + + + + + + + + +
LG 2 Mov'ts TR TR TR
Volune 252.63 400.00 0.00 600.00
f lt 1.00 1.00 0.00 1.00
Final Sat 1556.00 1732.00 0.00 3465.00
Eff g 36.18 55.33 0.00 55.33
Final g/C 0.37 0.57 0.00 0.57
Capaci ty 577.30 982.83 0.00 1966.23
v/c Rat, o 0.44 0.41 0.00 0.31
QAP du 23.03 1 1 86 0.00 1 1 .03
xo 0.83 0 83 0.00 0.83
fd1 1.13 1.11 0.00 1.08
kd 0.43 0.94 0.00 1.15
Delay d1 25.97 13.16 0.00 11.95
Delav d2 0.00 0.00 0.00 0.00
Tot belay 25.97 13.16 0.00 11.95
_ _ _
v/c Ratio 0.48 0.86 0.81 0.46
+ + + + + + + + + +
Figure E-14. Summary worksheet for the pe~mitted left turn example
Appendix E: Page 38
OCR for page 161
~ N
Nor t h-Bout h Or SB
19
Forth-south Or FIB
Figure E-IS. Intersection layout for the example of compound! left turn protection
4ppendixE: Page 39
OCR for page 162
NCHRP PROdECT 3-48: CAPACITY ANALYSIS OF TRAFFIC ACTUATED SIGNALS
Worksheet 1: Traffic-Actuated Controt Input Data
Filename: EXAMPLE2 (Conpound LT Prot) Museum Rd at North-south Dr
+ +
APPROACH NORTHBOUND SOUTHBOUND
DATA
EASTBOUND ~JESTBOUND
LT Treatment3333
LT PositionLeadLanLeadLead
Sneakers2.002.002.002.00
Free Queue0.000.000.000.00
Speed30303030
Termination ---- Independent - ~- Simultaneous
PHASE RING 1 RING 2
DATA 1(WBL) 2(EBT) 3(NBL) 4(SBT) 5(EBL) 6(WBT) 7(SBL) 8(NBT)
Phase Type
PH Reverse?
Det Length
SetBack
L G L G L GLG
No No No No No NoYesYes
30 30 30 30 30 303030
O O O O O OOO
~+ + + + + + + + +
Max Initial 8 18 8 18 8 18 8 18
Add Initial 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Min Gap 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50
Reduce Gp By 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
ilalk + FDW 0 20 0 20 0 20 0 20
Max Green 15 45 15 45 15 45 15 45
Change + Clr 5.00 5.00 5.00 5.00 5.00 5.00 5.00 5.00
Recall Mode N P N P N P N P
. . . . . . . . . .
VEH MINIMUM 15 25 15 25 15 25 15 25
STARTING GAP 2.50 2.50 2.50 2.50 2.50 2.50 2.50 2.50
MIN INITIAL 7.50 17.50 7.50 17.50 7.50 17.50 7.50 17.50
MAX PH TIME 20 50 20 50 20 50 20 50
DT OCC TIME 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09
TRIAL TIME 15.00 25.00 15.00 25.00 15.00 25.00 15.00 25.00
+ + + + + + + + + +
tJorksheet 2: Lane Group Data
+ +
PHASE RING 1 RING 2
DATA 1(~BL) 2(EBT) 3(NBL) 4(SBT) 5(EBL) 6(\JBT) 7(SBL) 8(NBT)
PH Movements L LTR
Arr Type 3 3
Oop PH 0 6
Lt Equiv 0.00 2.55
+ + + +
LG1 # Lanes 1 1
Mov'ts L L
Vol~ne 200 300
Arr Rate 0.06 0.08
Rp 1.00 1.00
Grn Arr 0.06 0.08
Sat Flow 1710 1710
Svc Rate 0.48 0.48
+ ~.
LG2 ~ Lanes
Mov'ts
Vol~ne
Arr Rate
Rp
Grn Arr
Sat Flow
Svc Rate
VEH ARR RATE
Ped Volume
PED ARR RATE
+.
o
;
3
o
0.00
L LTR L LTR L LTR
3 3 3 3 3 3
0 8 0 2 0 4
0.00 2.18 0.00 8.20 0.00 5.75
+ + + + + +
1 1 1 1 1 1
L L L L L L
50 100 300 200 100 50
0.01 0.03 0.08 0.06 0.03 0.01
1.00 1.00 1.00 1.00 1.00 1.00
0.01 0.03 0.08 0.06 0.03 0.01
1710 1710 1710 1710 1710 1710
0.48 0.48 0.48 0.48 0.48 0.48
, + + + + +
10 1 0 1 0 1
TR TR TR TR
0 6000 500 0 300 0 250
0.00 0.170.00 0.14 0.00 0.08 0.00 0.07
0.00 1.000.00 1.00 0.00 1.00 0.00 1.00
0.00 0.170.00 0.14 0.00 0.08 0.00 0.07
0 17470 1737 0 1747 0 1737
0.00 0.490.00 0.48 0.00 0.49 0.00 0.48
+ + + + + + + +
0.06 0.25 0.01 0.17 0.08 0.14 0.03 0.08
0 50 0 50 0 50 0 50
0.00 0.01 0.00 0.01 0.00 0.01 0.00 0.01
L LTR
3 3
0 2
0.00 8.20
0.17 0.08
50 0
0.01 0.00
+ + .
Figure E-16. Worksheets ~ and 2 for the example of compound left turn protection
Appendix E: Page 40
OCR for page 163
The signal timing computations for the last two iterations of the compound led turn protection
example are illustrated on Figures E-17, ENS and E-19. Figure E-20 shows the summary worksheet
for capacity and delay. Note that in the computation of green extension time in Worksheet 5, the
arrival rate is an equivalent through flow rate for the whole lane group. However, the extension time
computation for the through phases does not include the equivalent through flow rate of the permitted
left turns with compound left turn protection because the permitted left turns clo not actuate the
detector to extend the permitted phase. The final cycle length for this example is 130.2 seconds.
Both eastbound phases, through and protected left turn, are at their maximum times. Movements
with overflow delays include the eastbound through and left turn movement, the southbound through
and the westbound left turn movement.
Appendix E: Page 41
OCR for page 164
Worksheet 3a: Traffic-Actuated Timing Computations
A
Ring 1 PH Swap?NoNo
MovtsUBLEBT
PH Time20.0050.00
Ring 2 PH Swap?NoNo
MovtsEBLUBT
PH Time20.0029.09
RING 1-2 DIFF0.0020.91
CYCLE COMPONENTS20.0050.00
.
B TotalA B Total
No No -------
NBL SBT -------
70.0012.71 47.40 60.11
------Yes Yes -------
-------NBT SBL -------
49.0930.26 13.44 43.69
20.91-t7.55 33.96 16.42
0.000.00 0.00 60.11
Uorksheet 3b: Timing Plan sensitiv~ty Capac~ty Parameter Est~mation
Old Cyc 129.212 345 6 7
New Cyc 130.1UBLEBT NBL SBTEBL UBT SBL
Unadj PH Time20.0050.00 12.71 47.4020.00 29.09 13.44 30.26
Adjustment0.000.00 0.00 0.000.00 20.91 16.42 0.00
New Ph Time20.0050.00 12.71 47.4020.00 50.00 29.85 30.26
Eff Green 916.0046.00 8.71 43.4016.00 46.00 29.85 26.26
Int Red Time110.1180.11 117.40 82.71110.11 80.11 100.26 99.85
Eff Red r114.1184.11 121.40 86.71114.11 84.11 100.26 103.85
Red Time60.1180.11 99.85 82.7160.11 80.11 82.71 99.85
Startup Time0.0020.00 70.00 82.710.00 20.00 100.26 70.00
Recall ModeNP N PN P N P
Veh Arr Rate0.060.25 0.01 0.170.08 0.14 0.03 0.08
Av Vehs on Red6.1220.03 1.63 13.799.18 11.13 2.78 8.32
Prob (No Vehs)0.030.00 0.25 0.000.01 0.00 0.10 0.00
Veh Min Time15.0025.00 15.00 25.0015.00 25.00 15.00 25.00
Adj Veh Min14.4925.00 11.23 25.0014.92 24.97 13.51 24.98
Ped Arr Rate0.000.01 0.00 0.010.00 0.01 0.00 0.01
Av Peds on Red0.000.00 0.00 0.000.00 0.00 0.00 0.00
Prob (No Peds)1.000.00 1.00 0.001.00 0.00 1.00 0.00
Ped Min Time5.0025 .00 5 .00 25 .005 .00 25 .00 5 .00 25 .00
Adj Ped Min0.0025 .00 0.00 25 .000 .00 25 .00 0.00 25 .00
+ _ + + + + + + + + +
LG 1 Mov'ts L L L L L L L L
Grn Arr 0.06 0.08 0.01 0.03 0.08 0.06 0.03 0.01
Red Arr 0.06 0.08 0.01 0.03 0.08 0.06 0.03 0.01
EL2 0.00 0.00 0.00 0.00 0.00 0.00 0 .00 0.00
Free G gf 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
QSTOoD gq 0 .00 20.82 0.00 0 .04 0.00 46. 06 0.00 17.55
QatEb~ Qr 4.10 0.00 1.44 2.41 5.34 0.00 0.00 0.00
QatEOF Qf 4.10 0.00 1.44 2.41 5.34 0.00 0.00 0.00
QatEOQ Qq 3.56 1.74 1.44 2.41 5.34 2.56 2.78 0.24
QatBOS Qs 4.10 1.74 1.44 2.41 5.34 2.56 0.00 0.24
+ + + + + + + + + +
LG 2 Mov'ts TR TR TR TR
Grn Arr 0.00 0.17 0.00 0.14 0-.00 0.08 0.00 0.07
Red Arr 0.00 0.17 0.00 0.14 0.00 0.08 0.00 0.07
EL2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Free G gf 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
QSTOpP gq 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
QatEOk Qr 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21
QatEOF Qf 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21
DatEOQ Qq 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21
QatBOS Qs 0.00 14.02 0.00 12.04 0.00 7.01 0.00 7.21
8
NBT
Cycte convergence has not been achieved. Difference = .8
Figure E-17. Worksheet 3 of iteration 5 for the example of compound left turn protection
Appe~zdix E: Page 42
OCR for page 165
Worksheet 4:
~red Phase Times Based on 1
Target
Ratio
PHASE
DATA1(1JBL)
Int Red Time110.1t
Lost Time tl4.00
Lost Time tsl3.00
LG 1 Mov'ts
Grn Arr
Red Arr
ELI
PL
Svc Rate
Eqiv Svc
Net Svc
QatBOS Qs
Green G
fq
Land Utl
Svc Time
Wait Time
Tot Time
ResQ Qp
ResQ Qp'
RING 2
6(WBT) 7(SBL) 8(NBT)
80.11 100.26 99.85
4.00 4.00 4.00
3.00 3.00 3.00
0.01 0.03 0.08 0.06 0.03
0.01 0.03 0.08 0.06 0.03
0.00 2.18 0.00 8.20 0.00
0.00 1.00 0.00 1.00 0.00
0.48 0.48 0.48 0.48 0.48
0.48 0.23 0.48 0.06 0.48
0.46 0.20 0.39 0.01 0.45
1.44 2.41 5.34 2.56 0.00
8.97 42.40 15.00 45.00 15.00
1.04 0.99 0.98 0.98 0.98
1.00 1.00 1.00 1.00 1.00
6.27 14.82 16.37 465.63 0.00
0.00 0.04 0.00 46.06 0.00
6.27 14.86 16.37 511.69 0.00
0.00 0.00 0.00 2.54 0.00
0.00 0.00 0.00 0.54 0.00
TR TR TR TR
0.17 0.00 0.14 0.00 0.08 0.00 0.07
0.17 0.00 0.14 0.00 0.08 0.00 0.07
2.55 0.00 2.18 0.00 8.20 0.00 5.75
0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.49 0.00 0.48 0.00 0.49 0.00 0.48
0.49 0.00 0.48 0.00 0.49 0.00 0.48
0.32 0.00 0.34 0.00 0.40 0.00 0.41
14.02 0.00 12.04 0.00 7.01 0.00 7.21
45.00 0.00 42.40 0.00 45.00 0.00 25.26
0.98 0.00 0.99 0.00 0.98 0.00 1.05
1.00 0.00 1.00 0.00 1.00 0.00 1.00
46.12 0.00 37.74 0.00 20.09 0.00 21.31
0.00 0.00 0.00 0.00 0.00 0.00 0.00
46.12 0.00 37.74 0.00 20.09 0.00 21.31
0.00 0.00 0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00 0.00 0.00
50.00 20.00 50.00 20.00 50.00 20.00 50.00
46.12 6.27 37.74 16.37 20.09 0.00 21.31
ilorksheet 5: Green Extens i on T i mes
.
Arr DettaPhi Max Min Comp Adj New
Rate ValueValue Hdwy Hdwy- Ext Ext Hdwy
0.06 1.500.95 3.59 3.59 8.69 7.42 3.59
0.17 0.500.96 3.59 3.59 9.99 3.88 3.59
0.01 1.500.99 3.59 3.59 6.50 6.50 3.59
0.14 0.500.97 3.59 3.59 9.70 9.70 3.59
0.08 1.500.93 3.59 3.59 9.19 3.63 3.59
0.08 0.500.98 3.59 3.59 9.19 9.19 3.59
0.03 1.500.98 3.59 3.59 7.91 7.91 3.59
0.07 0.500.98 3.59 3.59 9.08 9.08 3.59
Computed Phase Times Including Extension Intervals
RING 1
2(EBT) 3(NBL) 4(SBT) 5(EBL)
80.11 117.40 82.71 110.11
4.00 4.00 4.00 4.00
3.00 3.00 3.00 3.00
L L L L
0.06 0.08
0.06 0.08
0.00 2.55
0.00 1.00
0.48 0.48
0.48 0.20
0.42 0.11
4.10 1.74
15.00 45.00
0.98 0.98
1.00 1.00
12.58 18.08
0.00 20.82
12.58 38.91
0.00 0.00
0.00 0.00
LG 2 Mov'ts
Grn Arr
Red Arr
ELI
PL
Svc Rate
Eqiv Svc
Net Svc
QatBOS Qs
Green G
fq
Land Utl
Svc Time
blait Time
Tot Time
ResQ Qp
ResQ Qp'
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
Max Ph Time 20.00
BASE PH TIME 12.58
l
0.01
0.01
5.75
1.00
0.48
0.09
0.07
0.24
25 .26
1.05
1.00
6.50
17.55
24.04
0.24
0.00
Phase #
Movements
Base Ph Time
Ph Ext Time
REQ PH TIME
MIN PH TIME
COMP PH TIME
NBL
12.58 46.12 6.27 37.74
7.42 3.88 6.50 9.70
20.00 50.00 12.76 47.44
14.49 25.00 11.23 25.00
20.00 50.00 12.76 47.44
678
EBLUBTSBLNBT
16.3720.090.0021.31
3 639.197.919.08
20 0029.287.9130.38
14.9225.0013.5125.00
20.0029.2813.5130.38
Figure E-~. Worksheet 4 of iteration 5 for the example of compoun~i left turn protection
Appendix E: Page 43
OCR for page 166
Llorksheet 3a: T raf f i c -Actuated T imi ng Computat i ons
I terat i on
A B Totat A
Tota ~
R i ng 1 PH Swap?No No - - - - - - - -NoNo
Movts tJBL EBT -------- NBL SBT
PH Time 20.00 50.00 70.00 12.76 47.44
R i ng 2 PH Swap? No No - - - - - - - - Yes Yes
Movts EBL ~JBT -------- NBT SBL
PH Time 20.00 29.28 49.28 30.38 13.51
RING 1-2 DIFF 0.00 20.72 20.72 -17.62 33.93
CYCLE COMPONENTS 20.00 50.00 0.00 0.00 0.00
Worksheet 3b: Timing PLan sensitivity Capac,
OLd Cyc 130.2 1 23
New Cyc 130.2 UBL EBT NBL
Unadj PH Time
Adjustment
New Ph Time
Eff Green 9
Int Red Time
Eff Red r
Red Time
Startup Time
20.00 50.00
0.00 0.00
20.00 50.00
16.00 46.00
1 10.20 80.20
1 14.20 84.20
60.11 80.11
0.00 20.00
43.90
16.31
60.20
ity Parameter Estimation
5 6
EBL UBT
4567
SBTEBLUBTSBL
12.7647.4420.0029.2813.51
0.000.000.0020.7216.31
12.7647.4420.0050.0029.82
8.7643.4416.0046.0029.82
117.4482.76110.2080.20100.38
121.4486.76114.2084.20100.38
99.8582.7160. 1 180. 1 182.71
70.0082.760.0020.00100.38
Cycte convergence has been achieved at 130.2
NBT
30.38
0.00
30.38
26.38
99.82
1 03 .82
99.85
70.00
Figure E-19. Worksheet 3a of the last iteration for the example of compoun~i
left turn protection
Appendix E: Page 44
OCR for page 167
+ ~ - - - - - - - + - - - - - - - + - - - - - - - + - - - - - -
EXAMPLE2 1 2 3 4
Cycle: 130.2 UBL EBT NBL SBT
EBLLIBT
Phase Time 20.00 50.00 12.76 47.4420.0050.00
Sat Green 12.58 46.12 6.27 37.74 16.37 20.09
SBL
29.82
0.00
LG 1 Mov' ts
Volune
fit
Final Sat 1710.00
Eff g16.00
Finat g/C0.12
Capaci ty210.13
v/c Rat ~ o0.59
QAP du37.95
xO0.64
fd11.15
kd0.76
Delay d143.68
Delay d24.72
Tot Delay48.40
LLL
123.20115.2043.23
0.950.230.95
411.921710.00
50.008.76
0.380.07
158.18115.11
0.730.38
7.5449.31
0.640.64
1.191.17
1.050.07
8.9857.60
8.990.00
17.9757.60
77. 10184 .8076.8022.906. 77
0.460.950.080.950.23
825 201710.00144.001710.00410.34
13 6216.0050.0029.8217.62
0.100.120.380.230.14
86.31210.1355.30391.6555.52
0.890.881.390.060.12
42.6931.1724.830.008.81
0.640.640.640.640.64
1.211.161.291.101.21
0 181.050.760.180.07
51 :n36.0731.910.0010.64
0.008.994.720.000.00
51.7345.0636.630.0010.64
LT Vot
LT Cap
LT v/c
LT QAP du
Ll xO
LT kd
LT d1
LT d2
LT Delay
0.00300.00
0.00368.31
0.000.81
0.0022.09
0.000.64
0.001.05
0.0025.67
0.008.99
0.0034.66
0.00100.00
0.00477.96
0.000.21
0.0032.91
0.000.64
0.000.18
0.0039.88
0.000.00
0.OO39.88
+ + + + + + .
LG 2 Mov'ts
Volume
fit
Final Sat
Eff 9
Final g/C
Capac i ty
v/c Rat ~ o
QAP du
xO
fd1
kd
DeLay d1
DetaY d2
Tot telay
TR
0.00600.00
0.001.00
0.001747.00
0.0046.00
0.000.35
0.00617.20
0.000.97
0.0041.47
0.000.79
0.001.12
0.001.27
0.0046.50
0.0019.04
0.0065.54
~R
0.00500.00
0.001.00
O. 001737.00
0 0043.44
0.000.33
0.00579.51
0.000.86
0.0040.59
0.000.79
0.001.12
0.00t.OO
0.0045.54
0.003.07
0.0048.60
+ ++ ~+ _~
v/c Ratio 0.590.970.38 0.89
+ ~+++ +
0.00200.00
0.00265.43
0.000.75
0.0032.91
0.000.64
0.000.76
0.0039.16
0.004.72
0.0043.88
~+
TR TR
0 00300.000.00250.00
0 001 .000.001 . 00
0.001747.000.001737.00
0.0046.000.0026.38
0.000.350.000.20
0.00617.200.00351.97
0.000.490.000.71
0.0032.870.0048.35
0.000.790.000.79
0.001.110.001.14
0.000.590.000.32
0.0036.590.0054.89
0.000.000.000.00
0.0036.590.0054.89
+++
0.881.390.06
++++
0.0050.00
0.00170.64
0.000.29
0.0043.83
0.000.64
0.000.07
0.0051.25
0.000.00
0.0051.25
Figure E-20. Summary worksheet for the example of compound left turn protection
Appendix E: Page 45
OCR for page 168
APPENDIX E REFERENCES
Courage, K. G. and R. Ak~elik, "A Computational Framework for Modeling Traffic-
Actuated Controller Operations," Working Paper NCHRP 3-48-1, Transportation Research
Center, University of Florida, Gainesville, May 1994.
Courage, K. G. and P-S. Lin, "A Computational Framework for Modeling Traffic- actuated
Controller Operations," Working Paper NCHRP 3-48 - , Transportation Research Center,
University of Florida, Gainesville, August 1994.
Courage, K. G., D. B. Fambro, R. Ak~elik, P-S. Lin, M. Anwer, "Capacity Analysis
of Traffic-Actuated Intersections," NCHRP 3-48 Draft Interim Report, TRB, National
Research Council, Washington D.C., January, 1995.
Ak~elik R. arid E. Chung, "Calibration of the Bunched Exponential Distribution of
Arrival Headways," Road and Transport Research, Vol. 3, No. I, 1994, pp. 42-S9.
Ak~elik, R. "Extension of the HEM Progression Factor Method for Platooned Arrivals,"
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Appendix E: Page 46
Representative terms from entire chapter:
cycle length
