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OCR for page 75
75
Chapter Seven
DELAY
This chapter documents Me delay model testing results
against the field data. Model 2.5 was given the first
priority among other models based on the model selection
criteria discussed In chapter three. Testing of available
simulation models is also documented in this chapter.
BASIC DELAY MODEL TESTING
The recommended time-dependent delay model (Model
2.5) is given here again:
D ~ 3600~900T TV _ 1 ~ 4t V _ 1) ~ (3~CX~C)] (114)
where D is the average vehicle delay, sec/veh, c is the
cap acid for the movement, vehA~r, Vis the traffic volume
for the movement, veb/hr, and T is the analysis time
period, hr.
It is important to note Cat the quality of the delay estimate
is limited by the accuracy of the capacity model. This is
clear in Equation 114 by the number of terms containing
the parameters c and v/c.
The recommended delay model was tested against the
field-collected data. Figures 41 and 42 show the delay
estimation results for all of the sites with standard
geometry and traffic flow charactenstics. Each data powt
represents an average result for a 15-minute central.
Figure 41 shows the result when generally recommended
critical gap and follow-up time were used (Table 28 and
29), and Figure 42 shows the result when site-specific
critical gap and follow-up time were used. The analysis
bme period (T) of 0.25 hour (15 minutes) was used. The
regression and statistical results are shown in Table 40.
It is clear that using the site-specific critical gap and
follow-up time give better results than using the
recommended ones based on general conditions. It should
be noted that there are some data points for which the
model significantly overestimates the delay. These data
points were observed in the high delay range, which means
Cat Me intersections are most likely close to capacity. As
mentioned before, the delay model becomes more sensitive
when Me volume/capacity ratio approaches over
saturation. In this case, slightly underestimating the
capacity will result in significantly overestimating delay.
Table 42 shows the delay model results In terms of the
level of service (LOS). The number of sites with the same
LOS predichon and with one level difference are shown in
the table. The delay model predicts the same LOS as the
field observations in about 50 percent of Me cases and is
within one level difference in about 90 percent of the cases.
In the F level of service range, there is a slight bias towards
the model producing a worse LOS Can in the field This
may be due to the field sites having higher capacities than
modeled due to effects such as upstream signals, two-stage
gap acceptance, and flared minor approaches. These
ejects are considered in chapter eight.
1 000
s
~ 100
In
8
10
1
1
aOO Al /
O ,,, O O 0:
O I I ~ Oat
0 0 _0'
. . . . ..... . . . . ....
~T T i T ~r r ~ r
T T ~ JET
10 100 1000
Field Delay, sec/veh
Figure 41. Delay Model Result for Standard Sites; Generally
Recommended Critical Gaps and Follow-Up Times
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1000
100
10
/
O O \:
0 0 .p - to
o ~5
Limo 0
O
. . . .
r ., ....l
1
10 100 1000
Field Delay, sec/veh
Figure 42. Delay Model Results for Standard Sites; Site Specific
Critical Gaps and Follow-Up Times
Table 40. Summary of l relay Model Results Using Capacity Model
1.1 and Different Critical Gap and Follow-Up Time Values
~-- --- - . . : b
............... ......................... ''''' ' ' .......
. ,.,. .
Constant 4.72 -5.S3
Std Err Y 11.82 23.62
R: 0.67 0.6S
No. Obs. 218 218
Deg of Freedom 216 216
X CoeŁ 0.96 1.81
Std Err. Coef. 0.0S 0.09
MAE 7.6 13.1
MAPE 4S.8% S7.2%
Because an intersection may not be congested for the entire
analysis period, a smaller value for T. the time of
oversaturation, may be appropriate. To test this effect, a
value of T = 5 minutes was also tested in the delay
equation. The results are shown in Figure 43. The
difference is negligible at low delay ranges. However, for
those data points in the high delay range where delays were
significantly overestimated, modeled delays are closer to
the field data than with T=0.25. In other words, using a
larger value for T tends to result in higher `1el~v
predictions than using a smaller value for T.
_ ~_ in,
The delay mode! was also validate with the site data
collected awing Phase ~ of the project. Fig,ure 44 shows the
reset. Again, each data point represents 15-n~inute interval
data The MAE for the standard sites is 9.0 sec/veh and the
MAPE is 36.2 percent. The regression and statistical
results are shown In Table 41.
Table 41. Regression Results, Phase I Validation Sites
..~.~- ''. ~',,.
Constant 4.08 -22.53
Std KIT of Y Est 13.38 10S.31
R Squared 0.37 0.19
No. of Obs 77 113
Deg of Freedom 7S 111
X Coefficient 0.92 3.39
Std KIT of Coef. 0.14 0.65
MAE 9.0 49.1
MAPE 36.2% 149.%
The mode! results in terms of LOS are given in Table 43
for the Phase ~ data.
The results indicate that the recommended delay model is
valid and provides good estimates of vehicle delays for
intersections with normal traffic and geometric
characteristics.
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Table 42. Summary of Delay Model Result in Terms of LOS as Defined in 1994 HCM
1 000
1~
10
1 10 100 1000
Field Delay, sec/veh
1 1
Figure 43. Delay Model Result for T=S min (Recommended Critical
Gap and Follow-Up Time)
1000
100
In
~ 10
a
a ~ O
-~
0~..
. .~:.
;/ · a
1 10 100 1000
Field Delay, sec/veh
0 Non Standard · Standard
Figure 44. Delay Model Validation for Phase I Sites (Recommended
Critical Gap and Follow-Up Time)
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Table 43. Summary of Delay Model Results for Phase I Validation Sites in Terms of LOS
I Car ~ ~ Cat ~ it ~mp.T. . . ~- . .
#Predicted
l :~OS ~ #shield ~ A ~ B C ~D ~E ~F
A O
B 2 ...................................... ............... ...........
C 33 . ~.: .......
D 25 1 ! ; ;!; ; ;~ ~ 2
E 11 ...... ; ;; ; ;;; ; ;;
F 6 . 3 . .
. Total 77 .
F
2
.................................. . ........
#Same #One
LOS Level
Dig
1 2
27 29
11 22
3 11
2 3
44 67
%Same
LOS
50.0%
81.8%
44.0%
27.3%
33.3%
S7.1%
%One
Level
Did.
100.0%
87.9%
88.0%
100.0%
SO.0%
87.0%
OCR for page 79
These models were tested against field data. Only those
sites that conformed with the limitations of each mode}
were selected for the test. The number of sites tested for
each mode! are as follows:
.
.
KNOSIMO, 30 sites
PICADY, ~ ~ sites
TEXAS, 64 sites,
TRAF-NETSIM, 9 sites
Figures 45 through 48 show the results of each simulation
model. Each point in these figures represents data for an
entire time period, usually ~ to 2 hours. The statistical and
regression results are shown In Table 45.
79
ASSESSMENT OF SIMULATION MODELS
Simulation techniques have been widely used In
transportation studies. A large variety of simulation
models have been develops for analyzing arterials,
signalized ~ntersechons, and freeways; however, few
simulation models are currency available for studying
unsignalized intersections. Simulation models that are
Table 44. Summary of Charact~ishcs of Simulation Models
being used for analyzing TWSC intersections include
KNOSIMO, PICADY, TEXAS, and TRAF-NETSIM.
Among these models, only the TEXAS and TRAF-
NETSIM models are able to simulate AWSC intersections.
Each of the simulation models mentioned above has its
own features and limitations. Table 44 summarizes Me
characteristics for each model.
~ ..................................
KNOSIMO Microscopic · 3 or 4 leg
Event Scan · single lane major street
· no consideration of pedestrians and cyclists
· no consideration of curve radii
· consideration of grade by adjusted I,, to values
· no consideration of upstream signals
| ?ICADY ~ Macroscopic |.b' ;edonlefr-handedtrafEic
· not based on gap acceptance
· only for British capacity experience
· maximum 6S feet width for major street
· no consideration of pedestrians and cyclists
· no consideration oftemporary blocking to major street through vehicles
by major street left tums
· no consideration of upstream signals
~.
TEXAS | Microscopic |.o'~tisnein~valofmaximurn60rninutes
Time Scan · no consideration of pedestrians and cyclists
· no consideration of upshcarn signals
rRAF-NETSIM I Microscopic ~ · nt consideration of pedestrians and cyclists
Time Scan · no consideration of grade, or curve radii
1000
100
-
o
Its 10
co
1
1
O ~
O ~
0:
0~ 00
~ °
,0
O'
O ~
,'0
0,^
~. . . . . . . . . . .....
..... , . . . · ~. . . ... ~ .
10 100 1000
Field Delay, sec/veh
Figure 45. Sumulation Results Dom KNOS~O
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two
~ 1~
~10
10
Fh d Delay, Ah
100 1000
Figure 46. Simulation Results from PICADY
~wv
~ 1=
~10
o
~°
1
1
10
held Dekly, "c~h
r ~ ....
100 1000
Figure 47. Simuladon Results fLom TEXAS
1000
~ 1~-
10
. . . . . . . .
., r~ ~r
10 100
Hed Dday, ~hh
Figure 48. Simuladon Results from TRAF-NETSIM
Table 45. Regression and Stabshcal Results for Different Simulation
Models
Constant l.S9 -0.14 ~-47.74
Std E'r of Y 6.8S 6.18 72.37
R Squamd 0.72 0.80 0.44
No. Obs 30 11 68
Deg Freedom 28 9 66
X Coef. 0.96 O.S4 7.76
Std Err CoeŁ 0.11 0.09 7.08
MAE 4.S 11.2 36.4
MAPE 30.2% 41.4% 126.S%
S.63
2.30
0.12
9
7
0.03
0.03
19.8300.1
Eleven intersections were tested with PICADY, and
average delay values for the complete observation and
simulation p~iods were compared. The simulation results
show~atPICADYundereshmates the measured delays ~n
each case. It is likely ~at ~e emp~ncaBy based capacity
formulas used by ~e program, and developed in the Un~ted
Kingdom, are not calibrated to U.S. conditions.
Nine intersections were s~mulated w~th the program
TRAF-NETSIM. In all cases NETSIM underestimated the
measured delays when using the default values for the
"acceptable gap in near-side cross traff~c". The simulated
delays did not exceed Il seconds even though the
measured delays were much hither. Even w~th ~ncreased
default values the results could not be ~mproved. In some
cases ~e s~mula~ delays rema~ned low, in o~er cases ~e
delays became unrealistically high.
TEXAS can only consider one time intenal wi~ a
max~mum duration of one hour. Altogether s~xtr-four
intersections were ~nvestigated. The simulation results
show that the qualit,,r of the s~mulation results varies
widely. A veIy important factor is the trailic volume on the
minor approach. For medium to high traffic volumes on
the minor approaches (above 280 vehicles per hour)
TEXAS produces an unrealistic overestimation of the
measured delays. This behavior was only observed for
intersections wi~ single-lane minor approaches. For
intersechons with lower trafflc volumes on the minor
approaches, TEXAS generally underestimates the
measured delays when using the default values of 8
seconds for parameters TLEAD and TLAG. The quality of
the results can be improved by va~ying the values of
TLEAD/TLAG; never~eless it is not possible to assign
correct consistent TLEAD/TLAG values to specif~c traff~c
situations.
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KNOSIMO can only consider Intersections with one lane
In each direction. Because of this limitation, only 30
intersections could be investigated. For Me simulation
studies, the site-specific gap data were used. The results
show that In most cases KNOSIMO simulated realistic
delays. No systematic over- or underestimation could be
observed. When companog the delays for the whole
simulation and observation penods, the standard deviation
between the delays generated by KNOSIMO and the
measured delays is about 6.S seconds. The average
deviation is about 30.1 percent.
In Sumner, Me best correlation between field conditions
and simulation results is g~venbyKNOSIMO. The general
gap acceptance concept of KNOSIMO is recomb ended for
further application. Nevertheless, the KNOSIMO program
in its present version does not Fife all needs of U.S.
practice. Therefore, an expansion of this or over gap
acceptance based simulation programs may be desirable.
The following features should be considered:
more variations of intersection geometry, e.g.,
multi-lane major streets, central refuge areas,
flared approaches..
modified major street headway distribution to
account for signal control at adjacent
intersections.
SUMMARY AND CONCLUSIONS
Some of the major conclusions of the delay mode! testing
results are given below:
The acc~acyofdela`,reshmabon is closely related
to the accuracy of capacity estimation. Delay
.
.
.
.
cannot be correctly estimated unless the correct
capacity is determined.
Similar to the capacity mode} testing results, using
site-specific critical gap and follow-up time
always yields the best delay forecast results. If
site-specif~c critical gap and follow-up time
information are not available, the recommended
critical gap and follow-up time discussed in
chapter five can also provide good capacity and
delay estimates.
Using Harders' basic capacity mode} and the
1994 HEM procedure, the delay mode} can
predict He same LOS as observed In He field for
more Can 50 percent of the cases, and predict
LOS within one level difference for about 90
percent of the cases.
The recommended capacity mode! and delay
mode} cannot be directly used for analyzing
intersections with unusual geometry and traffic
flow conditions. Special considerations are
necessary for analyzing these special conditions.
Simulation may be the best solution when these
special conditions exist. However, existing
simulation programs need further improvements
to adequately mode] conditions commonly
encountered.
Testing of the KNOSIMO, PICADY, TEXAS,
and TRAF-NETSIM simulation models showed
that only the KNOSIMO mode! provided good
correlation with field data. However, some of its
limitations need to be resolved before the mode!
can be used over a wide range of conditions. The
mode} should tee modified to address intersections
with conditions such as a multi-lane major street,
and two-stage gap acceptance.
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. .
,...
Representative terms from entire chapter:
critical gap
