CIE4801 Transportation and spatial modelling Modal split

Transcription

1 CIE4801 Transportation and spatial modelling Modal split Rob van Nes, Transport & Planning Delft University of Technology Challenge the future

2 Content Nested logit part 2 Modelling component 3: Modal split Your comments/questions on Chapter 6 Practical issues 2

3 1. Comments/questions last lecture 3

4 Comments/questions Trip distribution Trip distribution models Growth factor Gravity model and Entropy model Choice modelling Iterative algorithm Singly, doubly and triply constrained Calibration methods Hyman, Poisson 4

5 Estimation of the distribution function Hyman s method Given: Cost matrix Production and atraction Mean trip length Assumed: Type of distribution function Estimated: Q i, X j and parameter distribution function Poisson model Given: Cost matrix (partial) observed OD-matrix Thus also known: (partial) production and attraction Totals per bin for the travel costs Estimated: Q i, X j and F k 5

6 Solution methods: overview Hyman s method 1. Set parameter α of the distribution function equal to 1/MTL 2. Determine values for f(c ij ) 3. Balance the matrix for the productions and attractions (i.e. apply gravity model) 4. Determine new estimate for α based on observed MTL and computed MTL and go to step 2 until convergence is achieved Poisson model 1. Set values for F k equal to 1 2. Balance the (partial) matrix for the (partial) production 3. Balance the (partial) matrix for the (partial) attraction 4. Balance the (partial) matrix for the totals per cost class (i.e. correction in iteration i for estimate of F k ) 5. Go to step 2 until convergence is achieved i observed totalk Fk = Õ j computed total j 6 k

7 Practical issues Distribution function and trip length distribution Intra-zonal trips External zones: through traffic All trips or single mode? 7

8 2. Nested logit part 2 8

9 Recall the example Car Transit Nests k Scale parameter β Car driver Carpool Bus Rail Alternatives i Scale parameter λ k P i e = å bv j e i bv j Pi () Pi ( kpk ) ( ) l V bv k ik k = = å l V e å jîk lîk e e e bv k jk l 9

10 Decomposition in two logits Split utility in two parts: variables describing attributes for nests (aggregate level): W k variables describing attributes within nest: Y j U = W + Y + e iîb i k i i k Probability alternative is product of probability of alternative within nest and probability of nest P = P P i ib B k k 10

11 Decomposition in two logits Resulting formulas P P I k = å l = 1 1 ln k Yj e l = å j Bk l Î k e ( W I ) b + k k ( ) Bk K b Wl+ Il ib e = å Î e l Y k k j j B k k i e l Y Probability of choosing a nest Probability of an alternative within a nest Utility of a nest Main concept is I k ³ max ( Y ) i, thus having alternatives can have benefits 11

12 Example route choice with 2 routes Travel time route 1 is 40 minutes, travel time route 2 varies Aggregated travel time Travel time route 2 Added value of having two alternatives TT Mean TT Min TT Logsum 12

13 Why is there an added value? Everyone opts for alt 1 Travellers opt for the alternative having the lowest travel time Everyone opts for alt 1 PU ( U) 1 = PU2 ( = U) Probability distribution of the perceived travel time Travel costs 13

14 Typical conditions for nested logit P k i e P = æ 1 l Y ln k j ö b ç Wk + e l Y l å jîb è k k ø ib k Bk å lk Yj æ 1 l Y ln l j ö e b Wl e j B K ç + j B k l Î Î å å è l l ø e l= 1 e Define the parameter b µ k = l It is required that µ k 1 If µ k =1 this expression collapses to the standard logit model If µ k 0, the nest is reduced to the alternative having the highest utility, i.e. the other alternatives in the nest have no additional value k 14

15 Example for P+R facility Car Origin Walk1 Train 40 min 5 min 25 min, 5 Walk2 5 min Walk 5 min Destination Parking: 4 See spreadsheet on Blackboard Analyse the spreadsheet and experiment with the values of β and λ 15

16 Other examples of nested models Logsum over routes in mode choice Logsum over modes in destination choice Dutch National Model considers nesting when modelling destination and mode choice (and tour generation) 16

17 Four stage model and logsums Trip generation Destination A Destination B Destination C Mode 1 Mode 2 Mode 1 Mode 2 Mode 1 Mode 2 Route I Route I Route II Route II 17

18 Nested logit: to conclude Nested logit modelling proved to be a powerful tool for travel behaviour modelling Limitations: an alternative can only be allocated to a specific nest Possible extensions: Cross-nested logit Generalised nested logit Network GEV (Generalised Extreme Value) 18

19 3. Mode choice: what s it about? 19

20 Introduction to modal split Zonal data Trip generation Trip frequency choice Transport networks Trip distribution Destination choice Travel resistances Modal split Mode choice Period of day Time choice Assignment Route choice Travel times network loads etc. 20

21 Modal split (Netherlands) Trips and trip kilometres for an average day Walk Bicycle Car driver Car passenger Bus Tram/metro Train Other 21

22 Topics to study sections What does this modelling component do? What s its output and what s its input? How does it fit in the framework? Do you agree with the influencing factors? For the trip maker, trip, and transport service Do you understand the modelling methods? Empirical curves Entropy based simultaneous distribution/modal split model For a method to solve it, see these slides! Choice model approach Nested logit model Are these models appropriate? 22

23 3.1.1 Modal split models Method 1: Empirical curves 23

24 Travel time ratio (VF) Ratio between travel time by public transport and by car: t VF = t PT car Data used: observed trips where PT might be attractive i.e. train service or express service available Public transport: Access and egress time to main PT mode, waiting time first stop, in-vehicle time of main PT mode, waiting time transfer Car: travel time based on fixed speeds per area and period of day, parking Basic version: Elaborate model: P e - pt 0.45 VF = VF 0.17 N t 0.23 F P = e pt N t =transfers, F=frequency 24

25 Travel time ratio (basic version) 100% 90% 80% 70% Percentage PT 60% 50% 40% 30% 20% 10% 0% Travel time ratio PT t = car t 25

26 3.1.2 Modal split models Method 2: Simultaneous distributionmodal split 26

27 Gravity model and distribution functions Using distribution functions per mode å å T = rq X F with F = f ( c ) = F ij i j ij ij v ijv ijv v v Note that this formula also holds per mode f T = rq X F = rq X f ( c ) = rq X f ( c ) = T ij i j ij i j v ijv i j v ijv ijv v v v bike å å å train car 10km 50km distance 27

28 Distribution functions per mode Car PT Bike 12 Distribution function Note that each mode has its own travel time! Travel time (min) 28

29 Example mode choice Zoetermeer - TU Delft Car: 30 min PT: 50 min Bike: 45 min Function values Car: 1.12 PT: 0.43 Bike: 0.04 Total: 1.59 Result Car: 71% PT: 27% Bike: 2% 29

30 Doubly constrained simultaneous distribution/modal split model T = ab PA F with F = f ( c ) ijv i j i j ijv ijv v ijv åå åå T = P and T = A ijv i ijv j j v i v zone 1 zone 2 zone 3 car PT car PT car PT S zone 1 Can be solved zone 2 in a similar way as the standard doubly constrained model zone 3 S 30

31 Simultaneous distribution/modal split model Most of the time, destination choice and mode choice are made simultaneously instead of sequentially. Combined choices (e.g. for going shopping): Take the train to the center of Amsterdam Take the bike to the center of Delft Take the car to the center of Rotterdam General gravity model for simultaneous trip distribution/modal split: T rq X F with F f c = =å ( ) ij i j ij ij ijv v Does simultaneous imply that you cannot compute it sequentially? 31

32 3.1.3 Modal split models Method 3: Choice modelling 32

33 Mode choice model j car share: P ij1 i all modes PT share: bike share: P ij 2 P ij3 P ijv bv e = å e w ijv bv ijw V = q + q X + q X + q X v v v v v v v ijv 0 1 ij1 2 ij 2 3 ij3 33

34 Mode choice model A B C A B C car train A 3 2 P B 2 C car train car CA = = P ijv V V car CA train CA V ijv e =, i.e. = 1 å Vijw e w e e + e 62% =- 0.6 c car CA = c train CA ( b ) car train 34

35 Derivation nested distribution-modal split model c ik k c ik k i c ijv j i c ij j ( ) P w ij = exp å v exp Probability of choosing alternative j? Let s first look at the mode choice for j (-bmcijw ) (-bmcijv ) Translate attractiveness of all alternatives back into costs Attractiveness of alternative w Attractiveness of all alternatives Þ c 1 ij =- b ln exp( -bmcijv ) m å v 35

36 Derivation nested distribution-modal split model c ik k c ik k i c ijv j i c ij j ( ) P j = Probability of choosing alternative j : æ æ öö expç bd ç å( qa X ja ) -cij è è a øø æ æ öö æ æ öö expç bd ç å( qa X ja ) - cij + åexpç bd ç å( qa Xka ) -cik è è a øø k¹ j è è a øø c 1 ij =-b ln exp( -bmc b ijv ) Note: d µ m å 1 b = v m 36

37 Difference simultaneous distribution model and nested logit model? Assume exponential deterrence functions: v cijv ( ijv ) = F c e b - For trip distribution you use: For nested logit you use: ij v ijv v cijv ( ) å F = F c = e b - With F d being an exponential function as well: å æ-1 æ c ln ijv Fij Fd e b - öö = ç b ç å è è v øø -1 æ b - ö bd - ln e b -c ö ijv b ç å è v ø c ijv æ-1 æ ö Fij = Fd ç ln e = e b ç å è è v øø bd æ b b - c d ln e ijv ö æ b ç å ö b ç è v ø æ b -c ö ç å è v ø ijv = e = ç e è ø Thus only similar if scale parameters are identical v 37

38 3.2 Practical topics 38

39 Practical topics Role of constraints: Car ownership Car passenger Parking What comes first: destination choice or mode choice? Multimodality 39

40 Car ownership How is that accounted for so far? Implicit Mode specific constant Distribution functions Explicit approach Split demand matrix in matrix for people having a car and people not having a car available and apply appropriate functions 40

41 Car passenger Why is this relevant? Simple approach Exogenous car occupancy rate per trip purpose Comprehensive approach Car passenger and car driver as separate modes Problem in both cases? No guarantee for consistency in trip patterns car driver and car passenger 41

42 Parking Would you include it, and if so, how? How would you do it in case of tours? How would you do it in case of trips? What about morning and evening peak? Assign half of parking costs to a trip (origin and destination)? 42

43 What comes first: trip distribution or mode choice? What is the order we discussed so far? Swiss model: Mode preferences appear to be pretty strong 43

44 Multimodality? Approach so far: clear split between car, public transport (and slow modes) Special case: separate modes for train and BTM 80% of train travellers use other modes for access and/or egress Bus/tram/metro, but also bike and car So where do we find the cyclist to the station? 44

45 Multimodal trips car network public transport network origin pedestrian network destination 45

46 Simultaneous route/mode choice car super network train bus bike 46

47 Alternative model structures Production/attraction Production/attraction Production/attraction Distribution Distribution Distribution Modal split Modal split Modal split Assignment Assignment Assignment 47