Development of the Evaluation Process and Models for Metro System Service Stability and Efficiency

Railway Technology Research Center,National Taiwan University

Yung-Cheng (Rex) Lai

14th September, 2012

Presentation at the William W. Hay Railroad Engineering Seminar

• National Taiwan University– B.A., Civil Engineering, 2002

• University of Illinois at Urbana-Champaign– M.S., Civil & Environmental Engineering, 2004

• University of Illinois at Urbana-Champaign– Ph.D., Civil & Environmental Engineering, 2008

Education

2

• Rail Transportation System – Railway Capacity Analysis (Service Performance & Evaluation)

– Railway Operations and Management (Service Design)

– Railway Safety

• Techniques: – Math Programming– Heuristic or Decomposition

Methods– Simulations

Research Interests

3

Selected Research Topics on Rail Capacity• Capacity Evaluation & Computation

– Impact of Key Capacity Factors (heterogeneity, priority, etc.)– Development of Rail Capacity Models– Capacity Utilization Efficiency & Stability

• Capacity Management & Investment– Decision Support Framework for Strategic Capacity Planning– High Speed Route Improvement Optimizer – Optimization of Train Network Routing with Heterogeneous Traffic

4

Development of the Evaluation Process and Models for Metro System Service Stability and Efficiency

Glass Cup Theory – Tradeoff between Efficiency and Stability

5

• Metro System– Capacity

(Metro Assets)– Used Capacity

(Assets Utilization)– Available Capacity

(Slacks)– System Failure

(Disruption)

• Glass– Size

(Existing Resource)– Water Level

(Resource Usage)– Empty Space

(Buffer)– Vibration

(Disruption)

Higher Assets Utilization May Cause Lower System Stability

Every System has its own “optimal balance”

Evaluation Framework and Models

6

Operational Stabilityand Efficiency

System Reliabilityand Maintainability

MetroService Plan

SystemCharacteristics

System Characteristics

MetroService Plan

Historical Disturbance Data

Operational Efficiency

Operational Stability

Capacity Analysis Module Reliability Module

DowngradedCapacity

Maintainability Distribution

Reliability Distribution

NormalCapacity

Mean and Variance of the Expected Recovery Time

Percentage of the Capacity Usage

Operational Stability and Efficiency Module

UsedCapacity

Operational Efficiency- Assets Utilization Efficiency

Percentage of the Capacity Usage

NormalCapacity

Percentage of the Capacity Usage

AvailableCapacity

UsedCapacity

Normal Capacity

UsedCapacity

7

×𝟏𝟎𝟎%

Operational Stability- Expected Recovery Time

8

Disturbed Trains

Traffic Flow (Trains/hour)

T1 T2 T3 T4 T5 Time (Hour)

Normal Capacity

Downgraded Capacity

Available Capacity

Used Capacity

Disturbance

Disturbed Trains

RecoveryTime

Service Plan (headway)

RepairTime

Expected Recovery Time = Risk in Capacity Utilization

9

Metro Operation Is Not Always Under DisruptionsSystem Instability Is Introduced Through the Concept of

Expected Value in Probability Theory

ExpectedRecovery Time

RecoveryTime

Probability of System Failures

1 tF t e Failure Ratet Exposure (e.g. train-hours)

Historical Disturbance Data

Repair Time

P(x)

Repair Time Is Related to the System Maintainability• Expected recovery time inherits uncertainty from the

stochastic properties of maintainability

10

Maintainability Distribution

Evaluation Framework and Models

11

Operational Stabilityand Efficiency

System Reliabilityand Maintainability

MetroService Plan

SystemCharacteristics

System Characteristics

MetroService Plan

Historical Disturbance Data

Operational Efficiency

Operational Stability

Capacity Analysis Module Reliability Module

DowngradedCapacity

Maintainability Distribution

Reliability Distribution

NormalCapacity

Mean and Variance of the Expected Recovery Time

Percentage of the Capacity Usage

Operational Stability and Efficiency Module

UsedCapacity

A Case Study was Conducted for a Metro System• Service Plan

– Weekday service plan– Weekend service plan

• System Characteristics– 20+ intermediate stations– 2 terminal stations

12

• Historical Disturbance Data– Totally around 200 recorded

disturbances were collected for a ten-month period

Operational Stability and Efficiency

Evaluation Model

Inputs• System

Characteristics• Service Plan• Historical

Disturbance Data

Outputs• Mean and Standard

Deviation of Expected Recovery Time

• Percentage of Capacity Usage

System Map (adjusted)

13

D1 (Depot)

DR1 (Depot)

B10

B9

B9

B8

B8

B7

B7

B3

B5

B5

B4

B4

B2

B2

BR2

BR2

BR3

BR3

BR4

BR4

BR9

BR9

BR10

BR10

BR11

BR11

BR12

BR12

B6

B6

B1 BR1

BR5

BR5

BR6

BR6

BR7

BR7

BR8

BR8

Determine the Maintainability

• The classification of disturbances can facilitate the improvement of operational performance as it provides information about the sources of instability

14

Disturbance Mean Time to Repair

Train Failure Level 1 3.10 Train Failure Level 2 8.62

Loss of Electrical Power 11.01

Line Obstruction 7.89 Signal Failure 4.67

Communication Failure 13.98

Others 3.65

Probability of System Failure

• The operational stability is composed of– Severity of disturbances (Maintainability)– Frequency of disturbances (Reliability)

15

Disturbance (failure/train-hour)

Train Failure Level 1 2.00E-04

Train Failure Level 2 2.18E-04

Loss of Electrical Power 3.12E-05

Line Obstructed 4.01E-05Signal Failure 1.42E-04

Communication Failure 7.26E-05

Others 1.58E-05

1 tF t e Failure Ratet Exposure (e.g. train-hours)

Overall Evaluation Results

16

Weekday Service Plan Weekend Service Plan

D1-bound DR1-bound Overall D1-bound DR1-

bound Overall

Expected Recovery

Time (min)

Mean 0.677 0.679 1.356 0.220 0.219 0.438

Standard Deviation 0.016 0.016 0.023 0.005 0.005 0.006

Average Operational Efficiency (%) 30.37 31.53 30.95 20.81 21.60 21.21

+210%

+46%

Substantial Increase (>200%) in Operational Instability with Relatively Small Increase (46%) in Operational Efficiency

Operational Efficiency3D-histograms (Weekend)

17

Relatively High Operational Efficiency happen at Terminal Sections and Sections near Station BR4

D1-bound DR1-bound

Relatively High Expected Recovery Time is observed at Terminal Sections and Sections near Station BR4

Expected Recovery Time3D-histograms (Weekend)

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D1-bound DR1-bound

Operational Efficiency3D-histograms (Weekday)

19

High Operational Efficiency happen at Terminal Sections and Sections near Station BR4

D1-bound DR1-bound

Expected Recovery Time3D-histograms (Weekday)

20

Terminal Sections and Sections near Station BR4 have High Expected Recovery Time, particularly in Peak Hours

D1-bound DR1-bound

Operational Stability and EfficiencySection Perspective (Weekday)

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DR1 = BR13

BR13 = BR12

BR12 = BR11

BR11 = BR10

BR10 = BR9

BR9 = BR8

BR8 = BR7

BR7 = BR6

BR6 = BR5

BR5 = BR4

BR4 = BR3

BR3 = BR2

BR2 = BR1

BR1 = B1

B1 = B2

B2 = B3

B3 = B4

B4 = B5

B5 = B6

B6 = B7

B7 = B8

B8 = B9

B9 = B10

B10 = B11

B11 = D10

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35Average Expected Recovery Time 2 Standard Deviaiton from the AverageOperational Efficiency

Expe

cted

Rec

over

y Ti

me

(min

)

Ope

ratio

nal E

ffici

ency

Highest Instability and Efficiency Occur at Sections near Station BR4;Uncertainty Increases with Expected Recovery Time (Variance Increases)

Operational Stability and EfficiencyTime Perspective (Weekday)

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0:0~1:0

1:0~2:0

2:0~3:0

3:0~4:0

4:0~5:0

5:0~6:0

6:0~7:0

7:0~8:0

8:0~9:0

9:0~10:0

10:0~11:0

11:0~12:0

12:0~13:0

13:0~14:0

14:0~15:0

15:0~16:0

16:0~17:0

17:0~18:0

18:0~19:0

19:0~20:0

20:0~21:0

21:0~22:0

22:0~23:0

23:0~24:00

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7Average Expected Recovery Time 2 Standard Deviation from the AverageOperational Efficiency

Expe

cted

Rec

over

y Ti

me

(min

)

Ope

ratio

nal E

ffici

ency

Highest Instability and Efficiency Occur During Peak Hours

Means to Improve System Stability

Operational Stabilityand Efficiency

System Reliabilityand Maintainability

MetroService Plan

SystemCharacteristics

Improve Capacity (Upgrade System)

AdjustService Plan

Improve System Stability &

Maintainability

23

Evaluation of Improvements

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.550

0.5

1

1.5

2

2.5

3

3.5

Daily Operational Efficiency

Daily

Exp

ecte

d Re

cove

ry T

ime

(min

)

1.356

1.083

-20%

0.31

Original

Communication System Upgraded

Conclusions

• With the proposed method, metro operators can examine and monitor the stability and efficiency of their operational plan

• Operational instability usually increases with operational efficiency, and the proposed method can help users establish and understand this relationship between stability and efficiency

• This methodology can also be used to justify whether improvement strategies are cost effective

25

Future Work

• An operational database should be established to record and continuously update the disturbance data and system characteristics so as to understand the most up-to-date system reliability status

• Future studies should focus on the determination of the optimal balance in operational stability and efficiency

26

Operational Stabilityand Efficiency

System Reliabilityand Maintainability

MetroService Plan

SystemCharacteristics

Thank you & Questions?Yung-Cheng (Rex) Lai

Assistant ProfessorRailway Technology Research Center

Department of Civil EngineeringNational Taiwan University

E-mail: yclai@ntu.edu.twPhone: +886-2-3366-4243