French Institute

of Science and Technology

for Transport, Development

and Networks

Reliability indicators

Neila BHOURI Gerard SCEMAMA Mustapha TENDJAOUI Hassan MAHDAVI Sylvain LASSARRE

Indira_B project

State of practice

Adherence to schedule indicators

GINI index in economics

Lorenz curve and GINI index

… for the analysis of waiting time

… for the analysis of the regularity of bus

service

Results and analysis on Delhi bus routes

Correlation between GI, HA, HR and STD

Conclusion 09/10/2018 2

Outlines

Measures of reliability used by

transit operators

• Distance-based

• Missed trips, and

• Distance traveled between breakdowns. • Already implemented in Claire-Diti

• Time- based

• Travel time based

• Headway based

• Adherence to schedule (Desired = Achieved)

09/10/2018 3

Lakhotia et al., IIT Delhi

?

4

STATE OF PRACTCE

International Bus

Benchmarking Group (IBBG):

Trompet et al. 2010

5

PRACTCE

International Bus

Benchmarking Group (IBBG):

Trompet et al. 2010

Headway Adherence

HA= Standard deviation (Real to Schedule) /Schedule

TCRP :Transit Cooperative Research Program

Guidebook for Developing Transit Performance Measurement System

GINI INDEX

AS A RELIABILITY INDICTOR

Gini index

8

• synthetic indicator of inequality used in

economic studies to evaluate inequality of

incomes of a population.

9

Gini index based on the Lorenz curve A Lorenz curve plots the cumulative percentages of total income received

against the cumulative number of the population, starting with the poorest

individual or household: 1

0

2 ( )GI L X dX

Maximal Inequity A=B

GI=1

G=0

Perfect equity

A=0

GI=0

10

Application to bus reliability study

On the Y axis, income is replaced by the headway:

1st Case: Scheduled headways

Measure the fairness of the waiting time

2nd Case: Ratio {Observed / Scheduled headways}

Measure the respect of the schedule

On the X axis, the population is replaced by:

1st Case: headways On all the bus route

comparison between different bus routes …

2nd Case: headways on bus stops

studying a bus route on its different stops, …

Fairness of the waiting time : Lorenz

curve based on scheduled headways

11

We show that:

When users do not plan their arrival time (Headway = 2* average waiting time);

when operators set the schedules in order to have the same number of passengers

per bus,

Where [1,i] is the interval from 1 to i. The total waiting time for the whole day on the

bus line WT, is:

the Lorenz curve based on the scheduled headways is identical to the Lorenz

curve plotting the waiting time

and is therefore a good indicator from the riders perspective.

.2

i

i P

hw N

i ij p

p j1,ij 1 j 1

h NW N . h

2 2

12

Np

T jj

NW h

1,1 1 1 1

/ . / /2 2

i N i Np p

T j j j jij j j j

N NW W h h h h

;

Lorenz curve analysis

Approximative visual interpretation

10% of intervals cumulate

30% of the sum of delays

40% of real intervals are

shorter than scheduled ones

12% of real headways are nearly

equal to scheduled headways

12

%

12

%

Bus bunching

(Hobserved/Hscheduled = 0

Hobserved=0)

Comparison between different services

50% of disturbances are due to

•45% of buses

•30% of buses

Sample Routes Selection

14

Route Length

Frequency Select Routes

Low

(> 10 min)

Short

(< 19 km)

403 CL

Long

(> 19 km)

185

High

(< 10 min)

Short

(< 19 km)

507

Long

(> 19 km)

165

0.42

0.44

0.46

0.48

0.5

0.52

0.54

DC

36

12

::A

nan

d V

ihar

Ro

ad N

o…

DC

37

72

::P

rem

Nag

ar::

41

6

DC

37

74

::C

hri

stia

n K

abri

stan

::6

72

DC

41

39

::R

oh

ini S

ec-

16

…

DC

41

41

::D

istr

ict

Par

k Se

c-1

6…

U0

09

22

::Sh

ahb

ad D

airy

::0

U0

09

96

::St

. Xav

ier

Sch

oo

l…

U0

10

61

::Sh

ahb

ad G

aon

::3

88

U0

13

43

::B

adli

Rai

lway

Sta

ion

::4

82

U0

15

32

::Sa

nja

y G

and

hi T

ran

spo

rt…

U0

16

93

::B

hal

asw

a X

ing:

:69

4

U0

19

41

::M

uku

nd

Pu

r C

ho

wk:

:73

3

U0

23

38

::C

V R

aman

ITI:

:57

9

U0

26

43

::G

op

al P

ur

Cro

ssin

g::8

06

U0

29

45

::G

uru

dw

ara…

U0

31

27

::K

haj

uri

::6

24

U0

32

84

::Ya

mu

na

Vih

ar B

rij P

uri

::5

19

U0

34

11

::B

R A

mb

ed

kar

Co

llege

…

U0

34

78

::M

eet

Nag

ar::

54

1

U0

35

98

::G

TB H

osp

ital

Xin

g::4

54

U0

36

27

::N

and

Nag

ari T

erm

inal

::3

86

U0

36

44

::D

ilsh

ad G

ard

en

…

U0

36

61

::G

agan

Cin

ema:

:65

7

U0

36

95

::Jh

ilmil

Xin

g::8

96

U0

37

15

::R

am P

rast

ha

Tem

ple

::4

27

U0

37

46

::Sh

ahd

ra B

ord

er::

61

1

Gini Index 165 Down

Ligne : Indice 0,506

Regularity at stops

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

DC

41

41

::D

istr

ict

Par

k Se

c-1

6…

U0

13

43

::B

adli

Rai

lway

Sta

ion

::4

82

U0

25

38

::G

and

hi V

ihar

::1

23

8

U0

30

39

::R

aje

ev N

agar

::9

17

U0

36

61

::G

agan

Cin

ema:

:65

7

U0

36

22

::G

TB H

osp

ital

::5

00

U0

16

04

::O

ute

r R

ing

Ro

ad…

U0

37

12

::R

am P

rast

ha…

U0

10

94

::En

gg C

olle

ge…

DC

36

12

::A

nan

d V

ihar

Ro

ad N

o…

U0

34

11

::B

R A

mb

ed

kar

Co

llege

…

U0

37

28

::Su

rya

Nag

ar::

10

09

U0

09

22

::Sh

ahb

ad D

airy

::0

U0

37

46

::Sh

ahd

ra B

ord

er::

61

1

U0

13

90

::Sa

may

pu

r Sc

ho

ol:

:74

6

U0

10

30

SB::

Shah

bad

Sch

oo

l::4

21

U0

23

38

::C

V R

aman

ITI:

:57

9

U0

36

95

::Jh

ilmil

Xin

g::8

96

DC

41

40

::R

oh

ini S

ec-

16

Po

cke

t-…

U0

21

81

::B

ura

ri C

ross

ing:

:91

6

U0

26

43

::G

op

al P

ur

Cro

ssin

g::8

06

U0

34

78

::M

eet

Nag

ar::

54

1

U0

18

40

::Ja

han

gir

Pu

ri O

ute

r…

U0

36

79

::A

nan

d V

ihar

ISB

T…

U0

35

80

::N

and

Nag

ari D

epo

t::7

98

DC

41

42

::R

oh

ini S

ec-

15

::5

99

U0

09

57

::Sh

ahb

ad D

airy

A…

165 Down

Sunday, 18th

Tuesday, 20

Sunday vs Tuesday

STD = Standard Deviation

HR= Headway Ratio

HA= Headway Adhrence

20

Data problems

Data problems and the reconstitution

approach

Ti=Ti-1+Di/Vi Ti=Ti+1-Di/Vi

• Ti=Ti+1-Di/Vi

• Ti=Ti-1+Di/Vi

• Ti=Ti-1+(TN-Ti1)/(N+1)

22

Bus route 165 DOWN. Before and after data reconstitution

ρ=0.3536

ρ=0.5407

ρ=0.3374

HR-before

HR-After HA-before

HA-After

STD-before

STD-After

ρ=0.6378

GI-before

GI-After

Robustness of the indicators face to data errors

23

Advantages of the Gini index

• Based on the Lorenz curve: visual information easily interpreted

a detailed analysis of compliance with schedule

• Standardized value normalized scale: independence from the headway length

comparison between different bus routes or different

stops for the same route.

Allow to make a detail analysis about a bus line

(central part vs periphery, bus stop meeting other

buses or not …

Difficulty : Needs both Scheduled and Observed Headway data

Thank you for your attention

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