reliability indicators - transportation research and...
TRANSCRIPT
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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