Calibration of a metro-specific trip distribution model with smart card data

Transcription

1 Calibration of a metro-specific trip distribution model with smart card data Jan-Dirk Schmöcker, Saeed Maadi and Masahiro Tominaga Department of Urban Management Kyoto University, Japan

2 PT Fares Public transport fare levels and structures are considered to be an important tool to manage demand: Demand generation Temporal demand spreading Spatial demand spreading Though fare sensitivity has been widely discussed, there appears to be few literature directly discussing the effect of fare structures on spatial demand spreading. 2

3 Spatial PT fare structures Fare Flat Distance depending (degressive) Step function Distance 3

4 Spatial PT fare structures Radial zones with sectors Barcelona Radial zones Areal zones Oslo region Berlin-Brandenburg (Berlin area) Berlin-Brandenburg (Potsdam area) 4

5 Fare structures in Japan: Example JR East 1. Basic fare table (all JR lines) 1) Main lines ( 幹線 ): Table A 2) Local lines ( 地方交通線 ): Table B 2. Tokyo area fare table 1) Tokyo area: Table A + cheapest route 2) Specific area: Table C 3) Inner Yamanote area only: Table D plus exceptions. 5

6 London s zonal fare system 6

7 Possible effect of zonal fares (1) More expensive fare Cheaper fare Origin Zone 1 Zone 2 Alight walk Destination 7

8 Possible effect of base fare and access/egress O2 PT D2 Zone 1 O1 walk D1 Zone 2 8

9 Zonal effect? Example Central Line, Oyster data from Oct, 2011 Station specific production/attraction conscious design of zonal boarders fare effect 9

10 Research objectives Do fares influence boarding and alighting station choice? Develop an approach distinguishing the effect of fares on distribution from those on trip generation. 10

11 Hypothesised metro impedance Impedance g ij metro trips only Impedance considering all modes distance 11

12 Impedance function (general concept) g ij = α c ij + β f ij d ij + γ c ij + δ f ij For too close trips metro is not taken 1 2 All else equal, closer destinations are preferred c ij : Travel time f ij : Fare d ij : Crow-fly distance α, β, γ, δ : Parameters to be estimated 12

13 Obtaining the required data (1) 1. Trip matrix t ij Obtained from Oyster smart card data: possible to distinguish groups: pre-paid, travel pass, freedom pass. Only considering underground stations. 2. Distance d ij Should be a proxy of travel time by competing modes, i.e. minimum travel time by any other modes: approximated by crow-fly distance. 13

14 Obtaining the required data (2) 3. Travel time by metro c ij Unconstrained frequency-based transit assignment model 4. Fare f ij Publically available table of fares between zones. Assumptions for trips within same zone: If travel time longer than 45min assume that travelers must have gone via zone 1 through other side of circle. 14

15 Impedance function: Distance-Fare correlation 15

16 Ƹ Estimation by Regression Assume classic gravity model: t ij = k O i r D j g ij u s Log transform does not lead to linear model due to form of g ij. Estimation by non-linear heuristic optimisation. 16

17 Regression Results (1) tƹ ij = k O i r s D j u γ c ij Impedance funtion Parameter Estimate R2 Travel time only k r s u γ

18 Regression Results (2) Ƹ t ij = k α c ij d ij O i r D j s + γ c ij u Impedance function Parameter Estimate R2 Travel time and travel time /distance k r 0.81 s 0.81 u α 2001 γ

19 Regression Results (3) Ƹ t ij = k α c ij d ij O i r D j s + δ f ij u Impedance funtion Parameter Estimate R2 Fare and travel time/distance k r s u 2.09 α 2004 δ

20 Regression Results (4) Ƹ t ij = k O i r D j s α c ij d ij + γ c ij + δ f ij u Impedance funtion Parameter Estimate R2 Fare, travel time and travel time/distance k r s u α γ δ

21 Regression Results: Summary R 2 values in between 0.45 and 0.56 depending on model specification. Inclusion of term travel time /distance important for model fit and to explain that metro is not taken for short trips. Inclusion of fare does not significantly increase model fit. small negative value if travel time is included indicating that metro is underpriced? 21

22 Results Estimated Trips Observed Trips

23 Estimation by Regression Few parameters Easily interpretable and transferable? Does not guarantee that sum of estimated trips is equal to sum of observed trips. 23

24 Estimation by Heuristic + Iterative balancing (1) Assume: tƹ ij = r is j g ij Furness procedure Initialise s j = 1 j Repeat r i = O i / σ j s j g ij s j = D j / σ i r i g ij Until convergence 24

25 Estimation by Heuristic + Iterative balancing (2) Load matrices C, D, F, T Modify impedance parameters α, β, γ, δ Estimate G Furness procedure to obtain r, s Obtain T and R 2 Update max R 2 Repeat until convergence; no further improvements in R 2 can be found. 25

26 Iterative Balancing: Results (1) Ƹ t ij = r is j γ c ij Impedance funtion Parameter Estimate R2 Travel time only γ (plus vectors r and s for all 255 stations) 26

27 Iterative Balancing: Results (2) Ƹ t ij = α c ij d ij r i s j + γ c ij Impedance funtion Parameter Estimate R2 Travel time and travel time /distance α γ (plus vectors r and s for all 255 stations) 27

28 Iterative Balancing: Results (3) Ƹ t ij = α c ij d ij r i s j + γ c ij + δ f ij Impedance funtion Parameter Estimate R2 Fare, travel time and travel time/distance α γ δ (plus vectors r and s for all 255 stations) 28

29 Result Discussion Better model fit obtained by iterative balancing Unfair comparison? Iterative balancing using a large number of origin and destination specific parameters Direct interpretation of these parameters as station attractiveness. Results regarding importance of travel time/distance as well as minimal role of fares confirmed again negative parameter for fare! 29

30 Conclusions Smart card data allow for (or limit) analysis to mode selective trip distribution models Travel distance and travel speed both of critical importance for such a models Zonal pricing appears to have small effect on trip distribution: Desired? Negative fare coefficient suggesting that, in fact, there is a fare advantage for metro compared to other modes Further work: Sensitivity/stability, user groups, Models for innovative pricing schemes: price capping, route specific fares, mileage cards. 30

31 Thank you 31

32 Further work Obtaining t-values (for both estimation procedures) Use gradients and Hessian for estimation Patterns in r and s parameters? Estimation for different population groups: Freedom pass (elderly, disabled); travel card holders Stability of results over different days Sensitivity of results to changing value of waiting and walking? Obtain fare matrix directly from smart card data? Omit some OD pairs in estimation for forecasting. Would iterative balancing still work Use model to predict effects of network/fare changes? 32