Probe Project 1121 With Table

8/14/2019 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

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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

0.1

0.2

0.3

0.4

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

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x

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

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Probe Project 1121 With Table