Probe Project 1121 With Table
Transcript of Probe Project 1121 With Table
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Discrepancies in Median vs. LST during 8:00~8:30..........................................2
Type A: Both median and LST method find congestion..............................2
Type B: Only median method finds congestion..........................................3
Type C: LST finds congestion but not the nonparametric method..............8
Table 1 : Sumary of the differnt locaitons:.....................................................9
Table 2: Reporting the percent of locations where non-parametric and ANOVA
do not apply....................................................................................................13
Disappearance of indication of congestion over time.....................................15
Afternoon Comparison:...................................................................................17
The bus slowing down in the early morning story?.........................................17
Comparing ANOVA results with LST results....................................................18
Comparing ANOVA results with LST results.
Rename CDF With LST method
LST: Low speed threshold method
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There are 116202 data used in this study. The route length is 8334 meters. The
time duration is from 7:00~18:30.
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Discrepancies in Median vs. LST during
8:00~8:30
Type A: Both median and LST method find congestion
There are 7 spots where both methods find congestion during 8:00~8:30am.
These 7 locations are labeled in yellow in figure 1.
Figure 1: Both Find Congestion
For location 2 ~ 7 locations, convincing explanations are found to believe that
these locations are congested during 8:00am ~8:30am. As for location 1, it might
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be congested during 8:00~8:30am because of some detour traffics trying to
avoid heavier congestion at a nearby intersection.
Type B: Only median method finds congestion
There are really only 2 spots where the median method finds congestion but no
congestion is indicated by the LST method at nearby locations. These spots are
location 8 and location 9 as labeled in figure 2. Location 8 is close to a bus stop.
Moreover, the speed distribution at location 8 shows bimodality, which cannot be
explained by our knowledge of the system. Location 9 is about 150 meters away
from an upstream major intersection. There is a right turn entering a parking lot.
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But no congestion is expected at this location during this time period. A possible
explanation of the decrease in the median speed might be related to driver
behavior.
Therefore, for the two spots where only the median method indicates congestion,
there is no convincing reason to believe that there is congestion.
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Figure 2: Only Median Method Finds Congestion
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Location 8 plots
7100 7150 7200 7250 7300 7350 7400 7450 7500 7550 76000
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
CDF p
Median p
NotApp
p-value against distance
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0 2 4 6 8 10 12 14 16 180
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
F(x)
7250-8-27-784
LST plot at location 8
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6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18
Time (Hour)
Speed
(m/s)
Scatter plot at location 8
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For location 9 , what fraction would it be to find indication of congestion
by the LST method.
At location 9 in figure 2. The original low speed threshold is 5. 6336. By
changing the threshold to 6.7344 or changing the fraction from 0.35 to 0.41839.
We obtain a p-value of 0. 09. By changing the threshold to 6.8406 or changing
the fraction from 0.35 to 0.425. We obtain a p-value of 0. 0473.
2 4 6 8 10 12 14 16 18 20 220
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0.2
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0.5
0.6
0.7
0.8
0.9
1
x
F(x)
8150-8-45-1778
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8.05 8.1 8.15 8.2 8.25 8.3 8.35 8.4 8.45
4
6
8
10
12
14
16
Time (Hour)
Speed(m/s)
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Type C: LST finds congestion but not the
nonparametric method.
There are 4 interesting locations where the LST method finds indication of
congestion but not the median method (both applicable and not applicalbe )
during 8:00~8:30am.
The indications of congestion at location 10 can be explained by the construction
on the dridge. The indications of congestion at location 11 can be explained by
left turn traffics entering a parking lot.
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Lobation 12 and 13 are around intersection with Kenny Rd. on Woody Hayes Dr..
Location 12 is east bound, and location 13 is west bound.. LST method finds
indication of congestion, but median method is not applicable in both location 12
and 13. But we do expect congetion in these two locations.
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Figure 3 Only LST method finds congestion
Table 1 : Sumary of the differnt locaitons:
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Table 1 : Sumary of the differnt locaitons
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Distance LocationDescription
Vlow Mean Median Detection of congestion CongestionExpected
Com
TI CL TI CL LST Mean Median 900~990 After the right
turn stop signleaving parkinglot on CarmackRoad eastbound
4.020 7.0101 7.9508 6.6749 7.8429 Yes Yes Yes Yes Wesureis it, do oit
1440~1550
approachingthe signalizedintersection onWoody HayesDr. crossingCampus LoopRd east bound
4.586 4.4569 7.7759 2.8331 8.9235 Yes Yes Yes Yes
1750~1850
Approachingpedestriancrossing andbus stop onWoody Hayesafter crossingFyffe Rd.eastbound
4.2736 8.3388 8.9743 8.3965 9.1770 Yes Yes Yes Yes
3150~3410
Approachingintersectionwith W 12thAve on CannonDr south bound
4.401 6.7557 8.0309 8.6203 9.4071 Yes Yes Yes Yes
3720~3890
left turn toMedical CenterDr. on Cannonsouth bound
3.946 6.2626 7.4302 5.3415 7.9648 Yes Yes Yes Yes
3980~4050
Medical CenterDr. east bound,
2.584 3.9388 4.5734 3.7294 4.3570 Yes Yes Yes Yes Wereco
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Table 2: Reporting the percent of locations where non-parametric and
ANOVA do not apply
ANOVA vs.
LST
Appli. Cond.Prob
0 4758 0.2483
43
0.2821
13
0.8802
96
Blue %0 Non find congestion
1 166 0.0086
64
0.0307
12
Green %1 only New ANOVA find congestion
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2 333 0.0173
81
0.0616
1
Light blue %2 only LST find congestion
3 148 0.0077
25
0.0273
82
Yellow %3 Both Find congestion
4 1739 0.0907
67
0.7178
87
0.1264
36
Pink %4 Not Applicable and Find congestion by LST
5 12015 0.6271
2
0.8735
64
Red %5 Not Applicable and No congestion Found by LST
19159 1
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NonPara vs.
LST
Appli. Cond.Prob
0 10445 0.5451
75
0.6782
71
0.8037
71
Blue %0 Non find congestion
1 973 0.0507
86
0.0748
75
Green %1 only New ANOVA find congestion
2 995 0.0519
34
0.0765
68
Light blue %2 only LST find congestion
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3 582 0.0303
77
0.0447
86
Yellow %3 Both Find congestion
4 643 0.0335
61
0.3217
29
0.1043
15
Pink %4 Not Applicable and Find congestion by LST
5 5521 0.2881
67
0.8956
85
Red %5 Not Applicable and No congestion Found by LST
19159 1
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Disappearance of indication of congestion over
time.
The locations where congestion is indicated during 8:00~8:30 within the 4 red
frames in figure 4 disappear during 9:00~9:30. This is consistent with our
knowledge of the CABS system.
8:00~8:30
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50 100 150 200 250 300 350 400
00
00
00
00
00
00
00
00
Figure 4 Congestion map for LST method during 8:00~8:30
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50 100 150 200 250 300 350 400
100
200
300
400
500
600
700
800
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Figure 5 Congestion map for LST method during 9:00~9:30
Afternoon Comparison:
As for the afternoon period, there is no eye-bow evidence of locations where
the nonparametric method finds congestion but not the LST method.
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The bus slowing down in the early morning
story?
It can be found that, at some locations, the speeds obtained during
7:00am~7:30am are pretty high, which does not seem to be a good indication
of congestion. Nevertheless, there does exist a significant decrease in the
mean or median speed during time intervals 7:00am~7:30am. This decrease
in the mean or median speed is probably caused by the fixed bus schedule as
explained in the following paragraph.
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Let locations where recurrent congestions occur during peak hours be type C
locations. Let locations where recurrent congestions never occur be type D
locations. Usually, bus schedules are set by taking into account higher
demands of passengers and lower speeds at some locations (usually type C
locations) during peak hours. During 7:00am~7:30am, the campus is nowhere
congested and the passenger demand is relatively low. Therefore, the buses
tend to get overhead the schedule when there are very few passenger
demands and very few traffic demands. As a result, buses may travel at a
relatively slow speed at some locations in order to avoid going overhead the
schedule. Especially for type D locations, during peak hours, buses are more
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likely to drive faster and more aggressively in order to catch up the schedule.
Therefore, when the buses are not driving as aggressive as they do during
peak hours, there would be a decrease in the speeds. Case B1 occurs at one
of the type D locations and the time intervals 7:00am~8:00am and
7:00am~7:30am are not peak hours.
Comparing ANOVA results with LST results.
ANOVA finds but not LST during 8:00~8:30
Only one location after 3-space rule.
1340 1350 4200 8290 8300 8310
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0 2 4 6 8 10 12 14 16 180
0.1
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1
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F(x)
8300-8-18-537
LST plot at location 8300 during 8:00~8:30 and during whole day
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0 2 4 6 8 10 12 140
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
p-value against low speed threshold plot
From figure 6 in the following page, it can be found that there are 4 type A
locations labeled in yellow, i.e. both find congestion. Congestions at Location 2,
3, and 4 are explainable. As for location 1, similar to the case in comparing the
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median method to the LST method, cut through traffics might explain the
congestion.
Type B location labeled in green indicates only the ANOVA method finds
congestion. However, it is clear that location 5 in green is very close to location 4
in yellow where both find congestion.
Type C location labeled in light blue are locations only the LST finds congestion.
Location 6 in light blue is explained by the entrance to a parking lot as in the
case for comparing the median method to the LST method. Location 7 in light
blue is similar to location 1 in green. They are very close to location 4 in yellow.
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Figure 6 Type A, B, C locations for ANOVA vs. LST