Probe Project 1121 With Table

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

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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.

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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

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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.

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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.

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Nov.21 Jinguo and Cheng

Figure 2: Only Median Method Finds Congestion

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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

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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

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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

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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

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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

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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.

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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.

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Figure 3 Only LST method finds congestion

Table 1 :

Sumary of the differnt locaitons:

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Nov.21 Jinguo and Cheng

Table 1 :

Sumary of the differnt locaitons

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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　

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Comments

Nov.21 Jinguo and Cheng

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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

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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

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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

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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

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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

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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

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Nov.21 Jinguo and Cheng

100

200

300

400

500

600

700

800 50

100

150

200

250

300

350

400

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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.

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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.

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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

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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

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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

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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

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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.

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Figure 6 Type A, B, C locations for ANOVA vs. LST

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