Probe Project 1121 With Table
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Nov.21 Jinguo and Cheng
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
1 / 32
Nov.21 Jinguo and Cheng
There are 116202 data used in this study. The route length is 8334 meters. The time duration is from 7:00~18:30.
2 / 32
Nov.21 Jinguo and Cheng
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
3 / 32
Nov.21 Jinguo and Cheng
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.
4 / 32
Nov.21 Jinguo and Cheng
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.
5 / 32
Nov.21 Jinguo and Cheng
Figure 2: Only Median Method Finds Congestion
6 / 32
Nov.21 Jinguo and Cheng
Location 8 plots
0.16 CDF p Median p NotApp
0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 7100
7150
7200
7250
7300
7350
7400
7450
7500
7550
7600
p-value against distance
7 / 32
Nov.21 Jinguo and Cheng
7250-8-27-784 1 0.9 0.8 0.7
F(x)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
2
4
6
8
10
12
14
16
18
x
LST plot at location 8
8 / 32
Nov.21 Jinguo and Cheng
18 16 14
Speed (m/s)
12 10 8 6 4 2 0
6
8
10
12 14 Time (Hour)
16
18
20
Scatter plot at location 8
9 / 32
Nov.21 Jinguo and Cheng
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. 8150-8-45-1778 1 0.9 0.8 0.7
F(x)
0.6 0.5 0.4 0.3 0.2 0.1 0
2
4
6
8
10
12 x
14
16
18
20
22
10 / 32
Nov.21 Jinguo and Cheng
16
14
Speed (m/s)
12
10
8
6
4
8.05
8.1
8.15
8.2
8.25 Time (Hour)
8.3
8.35
8.4
8.45
11 / 32
Nov.21 Jinguo and Cheng
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.
12 / 32
Nov.21 Jinguo and Cheng
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.
13 / 32
Nov.21 Jinguo and Cheng
Figure 3 Only LST method finds congestion
Table 1 :
Sumary of the differnt locaitons:
14 / 32
Nov.21 Jinguo and Cheng
Table 1 :
Sumary of the differnt locaitons
15 / 32
Nov.21 Jinguo and Cheng
ID
Distance
1 900~990
2 1440~15 50
3 1750~18 50
4 3150~34 10
5 3720~38 90
6 3980~40 50
Location Description After the right turn stop sign leaving parking lot on Carmack Road east bound approaching the signalized intersection on Woody Hayes Dr. crossing Campus Loop Rd east bound Approaching pedestrian crossing and bus stop on Woody Hayes after crossing Fyffe Rd.east bound Approaching intersection with W 12th Ave on Cannon Dr south bound left turn to Medical Center Dr. on Cannon south bound Medical Center Dr. east bound,
Vlow
Mean TI 4.020
7.0101
7.9508
6.6749
7.8429
Yes
Yes
Yes
Congestio n Expected Yes
4.586
4.4569
7.7759
2.8331
8.9235
Yes
Yes
Yes
Yes
We are not sure what is causing it, but we do observe it
4.2736
8.3388
8.9743
8.3965
9.1770
Yes
Yes
Yes
Yes
4.401
6.7557
8.0309
8.6203
9.4071
Yes
Yes
Yes
Yes
3.946
6.2626
7.4302
5.3415
7.9648
Yes
Yes
Yes
Yes
2.584
3.9388
4.5734
3.7294
4.3570
Yes
Yes
Yes
Yes
We may reconsider
CL
Median TI
CL
Detection of congestion LST Mean Median
16 / 32
Comments
Nov.21 Jinguo and Cheng
17 / 32
Nov.21 Jinguo and Cheng
Table 2: Reporting the percent of locations where non-parametric and ANOVA do not apply
ANOVA
vs.
Appli.
Cond.Prob
0.2483
0.2821
0.8802
43
13
96
LST
0
1
4758
166
0.0086
0.0307
64
12
Blue
%0 Non find congestion
Green
%1 only New ANOVA find congestion
18 / 32
Nov.21 Jinguo and Cheng
2
3
4
5
333
148
1739
12015
19159
0.0173
0.0616
81
1
0.0077
0.0273
25
82
0.0907
0.7178
0.1264
67
87
36
0.6271
0.8735
2
64
Light blue
%2 only LST find congestion
Yellow
%3 Both Find congestion
Pink
%4 Not Applicable and Find congestion by LST
Red
%5 Not Applicable and No congestion Found by LST
1
19 / 32
Nov.21 Jinguo and Cheng
NonPara
vs.
Appli.
Cond.Prob
0.5451
0.6782
0.8037
75
71
71
LST
0
1
2
10445
973
995
0.0507
0.0748
86
75
0.0519
0.0765
34
68
Blue
%0 Non find congestion
Green
%1 only New ANOVA find congestion
Light blue
%2 only LST find congestion
20 / 32
Nov.21 Jinguo and Cheng
3
4
5
582
643
5521
19159
0.0303
0.0447
77
86
0.0335
0.3217
0.1043
61
29
15
0.2881
0.8956
67
85
Yellow
%3 Both Find congestion
Pink
%4 Not Applicable and Find congestion by LST
Red
%5 Not Applicable and No congestion Found by LST
1
21 / 32
Nov.21 Jinguo and Cheng
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
22 / 32
Nov.21 Jinguo and Cheng
100
200
300
400
500
600
700
800 50
100
150
200
250
300
350
400
Figure 4 Congestion map for LST method during 8:00~8:30
23 / 32
Nov.21 Jinguo and Cheng
100
200
300
400
500
600
700
800 50
100
150
200
250
300
350
400
24 / 32
Nov.21 Jinguo and Cheng
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.
25 / 32
Nov.21 Jinguo and Cheng
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.
26 / 32
Nov.21 Jinguo and Cheng
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
27 / 32
Nov.21 Jinguo and Cheng
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
28 / 32
Nov.21 Jinguo and Cheng
8300-8-18-537 1 0.9 0.8 0.7
F(x)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
2
4
6
8
10
12
14
16
18
x
LST plot at location 8300 during 8:00~8:30 and during whole day
29 / 32
Nov.21 Jinguo and Cheng
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
2
4
6
8
10
12
14
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
30 / 32
Nov.21 Jinguo and Cheng
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.
31 / 32
Nov.21 Jinguo and Cheng
Figure 6 Type A, B, C locations for ANOVA vs. LST
32 / 32
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
1 / 32
Nov.21 Jinguo and Cheng
There are 116202 data used in this study. The route length is 8334 meters. The time duration is from 7:00~18:30.
2 / 32
Nov.21 Jinguo and Cheng
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
3 / 32
Nov.21 Jinguo and Cheng
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.
4 / 32
Nov.21 Jinguo and Cheng
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.
5 / 32
Nov.21 Jinguo and Cheng
Figure 2: Only Median Method Finds Congestion
6 / 32
Nov.21 Jinguo and Cheng
Location 8 plots
0.16 CDF p Median p NotApp
0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 7100
7150
7200
7250
7300
7350
7400
7450
7500
7550
7600
p-value against distance
7 / 32
Nov.21 Jinguo and Cheng
7250-8-27-784 1 0.9 0.8 0.7
F(x)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
2
4
6
8
10
12
14
16
18
x
LST plot at location 8
8 / 32
Nov.21 Jinguo and Cheng
18 16 14
Speed (m/s)
12 10 8 6 4 2 0
6
8
10
12 14 Time (Hour)
16
18
20
Scatter plot at location 8
9 / 32
Nov.21 Jinguo and Cheng
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. 8150-8-45-1778 1 0.9 0.8 0.7
F(x)
0.6 0.5 0.4 0.3 0.2 0.1 0
2
4
6
8
10
12 x
14
16
18
20
22
10 / 32
Nov.21 Jinguo and Cheng
16
14
Speed (m/s)
12
10
8
6
4
8.05
8.1
8.15
8.2
8.25 Time (Hour)
8.3
8.35
8.4
8.45
11 / 32
Nov.21 Jinguo and Cheng
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.
12 / 32
Nov.21 Jinguo and Cheng
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.
13 / 32
Nov.21 Jinguo and Cheng
Figure 3 Only LST method finds congestion
Table 1 :
Sumary of the differnt locaitons:
14 / 32
Nov.21 Jinguo and Cheng
Table 1 :
Sumary of the differnt locaitons
15 / 32
Nov.21 Jinguo and Cheng
ID
Distance
1 900~990
2 1440~15 50
3 1750~18 50
4 3150~34 10
5 3720~38 90
6 3980~40 50
Location Description After the right turn stop sign leaving parking lot on Carmack Road east bound approaching the signalized intersection on Woody Hayes Dr. crossing Campus Loop Rd east bound Approaching pedestrian crossing and bus stop on Woody Hayes after crossing Fyffe Rd.east bound Approaching intersection with W 12th Ave on Cannon Dr south bound left turn to Medical Center Dr. on Cannon south bound Medical Center Dr. east bound,
Vlow
Mean TI 4.020
7.0101
7.9508
6.6749
7.8429
Yes
Yes
Yes
Congestio n Expected Yes
4.586
4.4569
7.7759
2.8331
8.9235
Yes
Yes
Yes
Yes
We are not sure what is causing it, but we do observe it
4.2736
8.3388
8.9743
8.3965
9.1770
Yes
Yes
Yes
Yes
4.401
6.7557
8.0309
8.6203
9.4071
Yes
Yes
Yes
Yes
3.946
6.2626
7.4302
5.3415
7.9648
Yes
Yes
Yes
Yes
2.584
3.9388
4.5734
3.7294
4.3570
Yes
Yes
Yes
Yes
We may reconsider
CL
Median TI
CL
Detection of congestion LST Mean Median
16 / 32
Comments
Nov.21 Jinguo and Cheng
17 / 32
Nov.21 Jinguo and Cheng
Table 2: Reporting the percent of locations where non-parametric and ANOVA do not apply
ANOVA
vs.
Appli.
Cond.Prob
0.2483
0.2821
0.8802
43
13
96
LST
0
1
4758
166
0.0086
0.0307
64
12
Blue
%0 Non find congestion
Green
%1 only New ANOVA find congestion
18 / 32
Nov.21 Jinguo and Cheng
2
3
4
5
333
148
1739
12015
19159
0.0173
0.0616
81
1
0.0077
0.0273
25
82
0.0907
0.7178
0.1264
67
87
36
0.6271
0.8735
2
64
Light blue
%2 only LST find congestion
Yellow
%3 Both Find congestion
Pink
%4 Not Applicable and Find congestion by LST
Red
%5 Not Applicable and No congestion Found by LST
1
19 / 32
Nov.21 Jinguo and Cheng
NonPara
vs.
Appli.
Cond.Prob
0.5451
0.6782
0.8037
75
71
71
LST
0
1
2
10445
973
995
0.0507
0.0748
86
75
0.0519
0.0765
34
68
Blue
%0 Non find congestion
Green
%1 only New ANOVA find congestion
Light blue
%2 only LST find congestion
20 / 32
Nov.21 Jinguo and Cheng
3
4
5
582
643
5521
19159
0.0303
0.0447
77
86
0.0335
0.3217
0.1043
61
29
15
0.2881
0.8956
67
85
Yellow
%3 Both Find congestion
Pink
%4 Not Applicable and Find congestion by LST
Red
%5 Not Applicable and No congestion Found by LST
1
21 / 32
Nov.21 Jinguo and Cheng
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
22 / 32
Nov.21 Jinguo and Cheng
100
200
300
400
500
600
700
800 50
100
150
200
250
300
350
400
Figure 4 Congestion map for LST method during 8:00~8:30
23 / 32
Nov.21 Jinguo and Cheng
100
200
300
400
500
600
700
800 50
100
150
200
250
300
350
400
24 / 32
Nov.21 Jinguo and Cheng
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.
25 / 32
Nov.21 Jinguo and Cheng
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.
26 / 32
Nov.21 Jinguo and Cheng
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
27 / 32
Nov.21 Jinguo and Cheng
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
28 / 32
Nov.21 Jinguo and Cheng
8300-8-18-537 1 0.9 0.8 0.7
F(x)
0.6 0.5 0.4 0.3 0.2 0.1 0
0
2
4
6
8
10
12
14
16
18
x
LST plot at location 8300 during 8:00~8:30 and during whole day
29 / 32
Nov.21 Jinguo and Cheng
0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0
0
2
4
6
8
10
12
14
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
30 / 32
Nov.21 Jinguo and Cheng
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.
31 / 32
Nov.21 Jinguo and Cheng
Figure 6 Type A, B, C locations for ANOVA vs. LST
32 / 32
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