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OCR for page 57
57
Chapter Seven
DELAY MODELS
The purpose of this chapter is to detenn~ne the quality of
the forecasts of the proposed delay 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,
the 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 with those produced
by previous procedures, and
comparison of the forecasts to some other metric.
FIELD MEASUREMENTS
Three events were recorded for each vehicle on the subject
stop-con~oDed approach: the time that the vehicle entered
the end of the queue, the time Hat it arrived at the stop line
in lbe first queue position (these times are equal if there is
no queue present when the vehicle arrives at the
intersection), and the time Mat it departed from the stop
line. The time difference between these first two events is
the bme In queue. The time difference between the second
and~ird events is the service time. The sum of these two
times is the total delay.
The total delay for each vehicle was aggregated into five
minute intervals, with the delay for a given vehicle
attributed to He time central in which it departed from the
stop line. The average delay for a given time Interval is the
sum of the total delay divided by the number of vehicles
departing Dom the stop line doling that interval.
MODEL TESTING
Three combination capacity and delay models were tested.
Mode! ~ used the service time forecasts (Capacity Mode}
2, extended) end relay Model I. Mode} 2 used service
bme forecasts (Capacity Mode! 2, extended) and He TRC
373/1994 HCM Update delay mode} (Delay Mode! 2~.
Mode! 3 used the capacity and delay procedures of He
1994 HEM Update models. Forecasts were prepared for
each ofthe~ee groups: Group I, Groups 2~, and Group
5. Mode! 3 forecasts were prepared only for the Group
sites.
Figures 24 through29 show plots of He forecasted delay
vs the measured delay values. The plots show that the
points are sea - Ed along a line connecting equal values of
forecasted delay and field data.
100
,
: :
go-,
a
2
Model 1 Forecasts
Group 1 Sites
1
10 100
Field Data
Figure 24. Delay Forecast,Model 1, Group 1 Sites
100 ~
~ 10
Model 2 Forecasts
Group 1 Sites
1
10 100
Field Dam
Figure 25. Delay Forecast, Model 2, Group 1 Sites
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58
100
~ 10
If
1
1
Model 1 Forecast
Groups 2,3, 4 Sees
Field Dam
100
I9~ 26. Delay Forecast, Model 1, Groups 24 Sites
100
-
.o
~ 10
2
1
Model 2 Forecast
Groups 2,3, 4 Sites
1 10
Field Data
..
Figure 27. Delay Forecast, Model 2, Groups 2~ Sites
100
10
nil
IL
1
100
8
~ 10
a'
.8
a
IL
Model 2 Forecast
Group 5 Sites
1
Field Data
Figure 29. Delay Forecast, Model 2, Group 5 Sites
100
Table 73 presents a summary of the CHAFE, the MAPE,
and the SE for the three groups. The MAFE is under ten
seconds for all of the mode} forecasts. The MAPE varies
Tom 36.9 percent to 73.S percent for all but one case, but
since the mean measured delay is 10. } sec/veh, this level
of variation is tolerable. The SE vanes from S.2 to 30.7.
Table 73. Delay Forecast Errors
Model 1 Forecast
Group 5 Sees
Field Data
100
Figure 28. Delay Forecast,Model 1, Group 5 Sites
Group 1
Model 1
Model 2
Model 3
Group 2
Model 1
Model 2
Model 3
Group 3
Model 1
Model 2
Model 3
VALIDATION
3.9
4.8
4.0
6.7
7.3
6.6
8.2
36.9%
S2.6%
69.6%
S1.0%
69.S%
73.8%
264.3%
The field data collected as part of the Phase I pilot study
were used to validate the two proposed delay models. The
date collected et the three AWSC intersections with single
lanes on each approach make up this validation data set
with 125 5-minute data points.
Delay Forecasts
The delay forecas s were plowed against the measured field
delay for Me 5-minute data for Tree single lane sites.
These plots are shown in Figures 30 and 31. Table 74 lists
the delay forecast errors.
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Representative terms from entire chapter:
delay models
s9
100
10
1
Model 1 Forecast
Validation Sew (Singe Lane Sites)
Table 7S. Level of Service Ranges for Stop Controlled
tcrsechons
Fluid Dam
100
Figure 30. Delay Forecast, Model 1, Validation Sims
100 -,
al
60
Table 78. M6dd 2. LOS Forecast Group 1
Table 82. Model 2. LOS Forecast, Group 5
Table 79. Model 1. LOS Forecasts, Groups 2~
............
A
B
C
D
Table 83. LOS Forecast, Validation Sites
Table 84. LOS Foists, Validabon Sites
Table 80. Model 2. LOS Forecasts, Groups 24
o
8
6
1
O
. O
Table 81. Model 1. LOS Forecast, Group 5
............
.. I.... .
134
168
22
1
l
.................
O
1
c . =3
l ..............
~-
O
O
2
O
O
O _
BINDINGS AND RECOMMENDATIONS
The analysis presented In this working paper support
several important findings pith respect to a decision on the
appropriate capacity and delay models for AWSC
intersections. These findings support a conclusion to
recommend Capacity Mode} 2 (as extended) as the basis
for capacity analysis of end relay Model ~ for computing
delay for AWSC intersections.
Findings
Five findings can be made based on He results presented
in this section.
Variation of Forecasts. When the degree of saturation
exceeds 0.8, the second term of Me delay equation
61
dominates' and the standard deviation is of similar
magnitude to the mean This means that the wide scatter
Hat is evident ~ He delay plots for higher values of delay
is expect This vanabon is also expected since the
its ofthe sanction headway measurements for Melee
of conflict cases 3 Trough 5 show a higher standard
deviation than the headway values for cases ~ and 2.
Potential models for delay. Both the proposed delay
mode} and the 1994 HEM Update mode! provide good
forecasting results.
Model testing. All models produce reasonably good
forecasts with similar degrees of forecast errors.
Mode! validation. The forecast quakier is approximately
the same as for the models tested using the study data.
[eve! of Service Forecasts. All models produce LOS
forecasts either equal to or within one LOS grade of the
measured LOS value, more than 90 percent of the time.
Models 1 and 2 produce somewhat better forecasts than
the 1994 HEM update.
The forecasts generally lie on or above the diagonal
connecting equal values of LOS. This is conservative in
one sense: poorer LOS values are predicted than are
filly observed, particularly for LOS E and F. However,
this may In some cases lead to signal warrants being
prematurely met
Recommendations
The analysis presented in this report shows that bow Delay
Models 1 and 2 produce good quality forecasts. While the
mode} testing results weighed slightly in favor of Delay
Mode} 2, the validation study showed that Delay Mode} ~
may beige more appropriate tool. Butane choice between
the two modelsis difficult. Since Delay Modellis based
on traffic Dow theory considerations, while Delay Mode!
2 is not, it Is recommended Hat Delay Mode} 1 be included
in the proposed computational procedure to forecast delay
and level of senice.
62
