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51
Chapter Six
SERVICE TIME
The purpose of this chapter is to determine the quality of
the forecasts of Me proposed headway model.
Determining the quality of a forecast is difficult, and
requires the establishment of criteria by which the
forecasts can be evaluated. The criteria used here include:
.
the amount of error present In the forecasts, that
is, some measurement of the difference between
the measured value and the forecasted value,
Be likely causes of the error, and how much of the
error is attributable to measurement, the mode!
structure, and to randomness,
comparison of the forecasts win those produced
by previous procedures, and
comparison of the forecasts to some other metric.
The chapter opens with a brief discussion of the field
measurements of service time and related parameters. The
mode} is tested with theoretical values to determine if it
correctly forecasts headways over a wide range of
conditions. Next, He model forecasts are compared to the
field measurements of service time. Here, consideration is
given to three measurement errors: the mean absolute
forecast error (MAFE), the mean absolute percent error
(MAPE3, and the standard error (SE3 of the forecast. Four
data sets are included in these compansons: the Group ~
sites,the sites from Groups 2, 3, and 4, He Group 5 sites,
and He pilot study sites from Phase ~ of this study.
Finally, a summary of the evaluation of the mode} forecasts
is presented.
FIELD MEASUREMENTS
The senice time, or the time that a vehicle occupies He
first position in queue, was measured for every vehicle at
each of the approaches that were videotaped during this
study. During periods of continuous queueing (that is, at
least one vehicle was already present when the next vehicle
arrived), He move-up time and saturation headway were
a so measles The move-up time is the bme between the
departure of one vehicle Tom the stop line and the time for
the next vehicle in line to move up to the first position.
The saturation headway is the bme between the departure
of one vehicle Tom the stop line to the departure of the
next vehicle.
These three parameters are computed from the following
three events that were recorded for each vehicle:
.
.
.
the bme that a vehicle enters the queue,
the lime that a vehicle arrives at He first position
(at the stop line), and
the bme that a vehicle departs from He stop line.
One part of the forecast error that must be considered is
that resulting from measurement error. As part of He
Phase ~ pilot study conducted as part of this project, an
estimate of this measurement error was made. It was
found that the bme recorded for the same event on a
videotape by the same observer had a mean absolute
difference of 0.3 seconds, With a standard deviation of 0.26
when multiple nuns were made using the same videotape.
This measurement error must be considered when
assessing the quality of the forecasts described in
subsequent sections of He chapter.
THEORETICAL MODEL TESTING
Theoretical input values, over a wide range of traffic
conditions, were used to determine if the computational
procedure yielded logical results. For example, if there is
no traffic on any of the approaches except for the subject
approach, the mode} should forecast headways of 3.9
seconds. Three tests were conducted using a flow rate of
300 vph on the subject approach The results are shown In
Figures 17 through 19.
.
When the opposing volumes were varied from 0
to 1000 vph, the forecasted headways ranged
from 3.9 seconds to 4.7 seconds. This is the
expected range for case ~ to case 2 conditions.
When the conflicting from the left volumes were
varied from 0 to 1000 vph, He forecasted
heads rs ranged Tom 3.9 seconds to 5.9 seconds.
This is the expected range for case ~ to case 3
conditions.
When the flows on He opposing and conflicting
approaches were varied from 0 to 1000 vph, the
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52
forecasted headways ranged Tom 3.9 seconds to
9.6 seconds. This is He expected range Tom case
~ to case 5 conditions.
The results show Hat the theoretical mode! formulation is
consistent and correct.
Boo ,
Opposing Volume
Figure 17. Effect of Oppesing Volume on Departure Headway
1 000
0 500 1000 ,
Opposing Volume
Figure 18. Effect of Conflicting Volume on Departure Headway
Case 5 Headway Analysis
IN
US
I
0 500 1000
Opposing Volume
Fig'~ 19. Effect of Opposing and Conflicting Volumes on
Departure Headway
MODEL TESTING WITH FIELD DATA
Forecasts of ache service time (the forecast value of the
departure headway minus the move-up dme) were
compared to the measured values of He service time using
5-minute average data points for three site groups: Group
I, Groups 2 through 4, and Group 5.
Figures 20 Trough 22 show plots of the forecasted service
time vs the measured values of the service time for the
three site groups. ~ ad cases, there is significant scatter
around the line connecting equal values of mode} forecast
and field measurement. The data pouts that are most
divergent in the lower right portion of the plots are
probabb,r camp by blockages (usually by pedestnans) that
result In higher Han expected service times.
Service Time Forecast
Group 1 Sites
10
O _ ~ ~c ;~;~e~ ;-;_;--_
5-=~ ~ ~ ~-..
~ O ==~ ~:~ =-== =
0 5 10
Field Measurement
Figure 20. Senrice Time Forecast, Group 1 Sites
Service Time Forecast
Groups 2,3,4 Sites
10 1 1 1 1 1 1 1 1 1
1 1 I T 1 T T 1 1
~ = = =
._ .- -. A< ,,
~ s .~a F;.- ~ ,
If ~, :~. - ~';~' , . .
-` .q .__ --
O r 11 1 1 1 1 1 1 1 ~
0 5 10
Field
Figure 21. Service Time Forecast, Groups 2~ Sites
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53
Service Time Forecasts (Group 5)
30+ dda pools per hl~l
10
~ 5
o
o
5
Field Service Time
10
Figure 22. Service Time Forecast, Group 5 Sites
Table 68 presents a summary of the mean absolute
forecast error (MAFE), the mean absolute percent error
(MAPE), and tibe standard forecast error (SE) for the three
groups. The MAFE is the mean of the absolute values of
the forecast errors for each of the 5-m~nute data points.
The MAPE is the mean of the absolute values of these
forecast percent error'. The SE is given in Equation 35.
SE =
Table 68. Model Forecast Errors
~ (Sf - sm2)
i
(35)
1 . . . - ; .................................................... . . . . . . . . . . . . ..... ............
............................ ............................. ................................. ........... ........ .. .....
I .:.:.:.:.:.:.:~n :.:.:.:.:.:.:.:. .:.:.:.:.:.:.::~:.:~:~.:~.::.:~: :::.:.:.:.:.~....:.. :: · :: ::: it: :: ::
. 1 0.8 3.3% 1.1
2~ 0.8 19.2% 1.3
S 1.3 29.3% 1.9
Note:~4FE = mean absolute forecast error,AL4PE = mean absolute
percent error, ~ = standard forecast error
The MAFE ranges from 0.S seconds to I.3 seconds. If the
measurement error is approximately 0.3 seconds, Me
remaining 0.5 to I.0 seconds must be attributed to either
mode! error or Me result of random error. By comparison
for Me Group ~ sites, Me values that are forecasted from
the mode} range from I.9 seconds (degree of conflict case
~ with 3.9 seconds for the departure headway minus 2.0
seconds for Me move-up timed to 7.6 seconds (degree of
conflict case 5 of 9.6 seconds minus 2.0 seconds for the
move-up timed. The mean measured field value for the
Group ~ sites was 4.} seconds. Thus the MAFE ranges
from ~ ~ percent to 42 percent of Me extreme values, and
is 20 percent of the mean measured value. These are not
intended to be comparisons m~ an absolute standard but
simply to provide a perspective of the quality of the
forecasts for this model.
Table 68 also shows that the forecast error increases with
Me complexity inherent In multi-lane operations present at
Group 5 sites.
Some of the error is also attributable to the measurement
uncertainty In the move-up time. When Me proportion of
time that a continuous queue is present is low, the number
Of measurements of the move-up time is also low. This
increases the uncertainty in Me estimation of this value.
Tables 69 Trough 71 show Me MAFE, the MAPE, and Me
SE for Me individual sites within these groups.
Table 69. Model Forecast Errors
Group 1 Sites
...................................
..............................................................
.....................................................................
...................................................................
....................................
........ %. - d. ~ ........... - d. - ~ .;
:-:-:-:-:: :-:--1~=':-:-:-:-:-::: ·:~:~:~:~:~:~ly~.~:: :~:~:~:~:
............ ........................................
AU Data
CEA303
CEA304
NEA201
NEA204
NEA20S
NEA206
NEA208
NWA401
NWA403
NwA40
swAnnh
0.77
0.60
0.64
0.81
0.82
0.77
1.07
0.87
0.7S
0.79
0.61
ncs
3.3%
-S.1%
-4.6%
9.1%
14.1%
11.4%
19.1%
12.S%
-11.0%
-13.3%
2.8%
_1 5°/n
1.07
0.79
0.72
1.10
1.02
1.01
1.49
1.29
1.09
1.08
0.84
~._ _ . 0.91
Note: MANE = mean absolute forecast enor,MAPE = mean absolute percent
error, ~ = standard forecast error.
Table 70. Model Forecast Errors
Groups 2, 3, and 4 Sites
AU Data
0.77
NWA402 0.81
NWA406 0.60
NWA407 0.99
SEA101 0.94
SEA1OS 0.3S
SWA002 1.39
SWA004 1.77
SWA008 1.34
SWAOO9 0.60
19.2%
12.6%
10.6%
27.1%
20.3%
10.1%
SS.7%
39.S%
2S.1%
21.7%
1.29
0.99
1.81
1.05
1.12
0.46
1.74
1.77
1.43
0.70
Note: My= mean absolute fores error,lL4PE= mean absolute
percent error, SE= standard forecast error.
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Table 71. Model Forecast Errors
Group 5 sires
, · · ~ ~ 5$
All Data 1.33 29.3% 1.87
CEA307/308 0.75 26.4% 1.03
NEA202/203 0.92 26.7% 1.51
SEA104/107 2.01 33.0% 2.47
1 l
Note: M:4FE = mean absolute forecast e'ror,lL4PE = mean absolute
percent error, ~ = standard error ofthe forecast
VALIDATION
Mode} validation is the testing of a calibrated mode] using
empirical data Mat were not used to initially calibrate the
model. The data collected as part of Phase ~ of this project
were used to validate the proposed senice time based
capacity model. Drying this pilot study, data were
collected at five AWS`; sites, four single lane sites and one
site with both single and multi-lanes on its approaches.
Figures 23 shows He plot office forecasted senice time vs
the measured service time for single lane sites. As before,
the data are scattered along Me line connecting equal
values of He mode! forecasts and field measurements.
The MAFE, MAPE, and He SE are shown In Table 72.
The mean forecast error is I.4 seconds, slightly higher than
He forecast error for the three other data sets presented In
the previous section.
Service Time Forecast
Validation Sites (Single lane Sites)
10
l . 5
o
o
5
Held Measurement
10
Figure 23. Service Time Forecast, Validation Sites
Table 72. Model Forecast Errors, Validation Sites
All Data
1.4
Is 3O/~
~ s
Note: ~ = mean absolute forecast e'ror, M 4PE = mean absolute
percent e'ror, By= standard error ofthe forecast
FINDINGS AND RECOMMENDATIONS
The analysis presented here supports a number of
significant findings with respect to a decision on an
appropriate capacity mode} for AWSC intersections.
These findings support a conclusion to recommend the
service time mode] as the basis for capacity analysis of
AWSC intersections.
Findings
Four findings based on the analysis of the proposed service
time mode! are presented here.
Capaci~Mode! 2. Richardson proposed a service time
based mode! using the values of saturation headway
measured by Hebert. While it is a substantial
improvement over any previous method for computing
capacity, Here are four problems with this model. First,
the limitation of only two cases is severe. Drivers face
much more complex conditions based on the Interaction of
two or more vehicles simultaneously trying to enter the
intersection. Second, vehicle type affects the saturation
headway. Third, the driver~on-the-right rule of Len does
not correctly describe intersection operations. Fourth, a
Ianfication is needed on what He mode} actually
forecasts.
Proposed service time model. An extension of Capacity
Mode! 2 is presented The mode! is based on five cases,
each reflecting a different level or degree of conflict faced
by the subject approach driver. The probability of
occurrence of each case is based on He traffic intensity on
He opposing and conflicting approaches. The
interdependence or interaction between the traffic streams
shows the need for iterative calculations to obtain stable
estimates of service time.
Mode] testing Forecasts of service time were made for
each of the three site groups. The MAFE range from 0.S
to I.3 seconds, while the MAPE ranged from 3.3 percent
to 29.3 percent.
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Validation. The service time mode} was validated using
the data collected at five sites during the Phase ~ pilot
study. The mode! performed well producing a MAFE of
I.4 seconds and a MAPE of 25.3%.
Recommendations
The service time mode], an ex ensign of Capacity Mode} 2,
is recommended as the basis for the new capacity
estimation procedure to be included In the next edition of
the HCM. This recommendation is based on testing and
analysis of this mode} using data collected during this
study.
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Representative terms from entire chapter:
mean absolute
