Reliability indicators

Transcription

1 French Institute of Science and Technology for Transport, Development and Networks Reliability indicators Indira_B project Neila BHOURI Gerard SCEMAMA Mustapha TENDJAOUI Hassan MAHDAVI Sylvain LASSARRE

2 Outlines 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

3 Measures of reliability used by transit operators Distance-based Missed trips, and Distance traveled between breakdowns. Time- based Already implemented in Claire-Diti Travel time based Headway based Lakhotia et al., IIT Delhi Adherence to schedule (Desired = Achieved)? 09/10/2018 3

4 STATE OF PRACTCE International Bus Benchmarking Group (IBBG): Trompet et al

5 PRACTCE International Bus Benchmarking Group (IBBG): Trompet et al

6 Headway Adherence HA= Standard deviation (Real to Schedule) /Schedule Guidebook for Developing Transit Performance Measurement System TCRP :Transit Cooperative Research Program

7 GINI INDEX AS A RELIABILITY INDICTOR

8 Gini index synthetic indicator of inequality used in economic studies to evaluate inequality of incomes of a population. 8

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: GI 1 2 L( X ) dx 0 Maximal Inequity A=B GI=1 Perfect equity G=0 A=0 GI=0 9

10 Application to bus reliability study On the Y axis, income is replaced by the headway: 1 st Case: Scheduled headways Measure the fairness of the waiting time 2 nd Case: Ratio {Observed / Scheduled headways} Measure the respect of the schedule On the X axis, the population is replaced by: 1 st Case: headways On all the bus route comparison between different bus routes 2 nd Case: headways on bus stops studying a bus route on its different stops, 10

11 Fairness of the waiting time : Lorenz curve based on scheduled headways We show that: When users do not plan their arrival time (Headway = 2* average waiting time); w i N P hi. 2 when operators set the schedules in order to have the same number of passengers per bus, i i j p W N. h 1,i p j j j 1 h N Where [1,i] is the interval from 1 to i. The total waiting time for the whole day on the bus line W T, is: N N W W h h h h 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. W i N i N p p /. / / 1, i T j j j j 2 j 1 2 j 1 j 1 j 1 ; T N 2 p N j 1 h j 11

12 Lorenz curve analysis Approximative visual interpretation 10% of intervals cumulate 30% of the sum of delays 12 % 12% of real headways are nearly equal to scheduled headways 12 % Bus bunching (Hobserved/Hscheduled = 0 Hobserved=0) 40% of real intervals are shorter than scheduled ones

13 Comparison between different services 50% of disturbances are due to 45% of buses 30% of buses

14 Sample Routes Selection Frequency Select Routes Route Length Low (> 10 min) High (< 10 min) Short Long Short Long (< 19 km) (> 19 km) (< 19 km) (> 19 km) 403 CL

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16 DC3612::Anand Vihar Road No DC3772::Prem Nagar::416 DC3774::Christian Kabristan::672 DC4139::Rohini Sec-16 DC4141::District Park Sec-16 U00922::Shahbad Dairy::0 U00996::St. Xavier School U01061::Shahbad Gaon::388 U01343::Badli Railway Staion::482 U01532::Sanjay Gandhi Transport U01693::Bhalaswa Xing::694 U01941::Mukund Pur Chowk::733 U02338::CV Raman ITI::579 U02643::Gopal Pur Crossing::806 U02945::Gurudwara U03127::Khajuri::624 U03284::Yamuna Vihar Brij Puri::519 U03411::B R Ambedkar College U03478::Meet Nagar::541 U03598::GTB Hospital Xing::454 U03627::Nand Nagari Terminal::386 U03644::Dilshad Garden U03661::Gagan Cinema::657 U03695::Jhilmil Xing::896 U03715::Ram Prastha Temple::427 U03746::Shahdra Border::611 Regularity at stops 0.54 Gini Index 165 Down Ligne : Indice 0,506

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18 DC4141::District Park Sec-16 U01343::Badli Railway Staion::482 U02538::Gandhi Vihar::1238 U03039::Rajeev Nagar::917 U03661::Gagan Cinema::657 U03622::GTB Hospital::500 U01604::Outer Ring Road U03712::Ram Prastha U01094::Engg College DC3612::Anand Vihar Road No U03411::B R Ambedkar College U03728::Surya Nagar::1009 U00922::Shahbad Dairy::0 U03746::Shahdra Border::611 U01390::Samaypur School::746 U01030SB::Shahbad School::421 U02338::CV Raman ITI::579 U03695::Jhilmil Xing::896 DC4140::Rohini Sec-16 Pocket- U02181::Burari Crossing::916 U02643::Gopal Pur Crossing::806 U03478::Meet Nagar::541 U01840::Jahangir Puri Outer U03679::Anand Vihar ISBT U03580::Nand Nagari Depot::798 DC4142::Rohini Sec-15::599 U00957::Shahbad Dairy A Sunday vs Tuesday Down Sunday, 18th Tuesday, 20

19 STD = Standard Deviation HR= Headway Ratio HA= Headway Adhrence

20 Data problems 20

21 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 Robustness of the indicators face to data errors Bus route 165 DOWN. Before and after data reconstitution GI-before GI-After ρ= STD-before STD-After HA-before HA-After HR-before HR-After ρ= ρ= ρ=

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 23

24 Thank you for your attention IFSTTAR Bld. Newton Cité Descartes Champs sur Marne Marne-la-Vallée Cedex 2 France Ph +33 (0)