Fabien Leurent, Université Paris-Est, LVMT, Ecole des Ponts QUANTURB Seminar, 17 December 2014

Transcription

1 Supply and Demand Modeling of urban travel modes, housing and co Fabien Leurent, Université Paris-Est, LVMT, Ecole des Ponts QUANTURB Seminar, 17 December 2014

2 Background Personal introduction Educated as an engineer at Ecole Polytechnique (X85) then Ecole des Ponts (PC 90) PhD at Ecole des Ponts (1997) in Transportation, about the Analysis of uncertainty in a simulation model: the case of a bicriteria traffic assignment model HDR at Paris Dauphine (2006) in Informatics Operations research, about the modeling of transportation networks and the accessibility to activities Current position and duties Deputy head, LVMT a joint research lab of Ecole des Ponts, Ifsttar and UPEM Head of two chairs of research and education, in partnership with (i) STIF (ii) Vinci group (in association with MINES and Agro) Professor at Ecole des Ponts: analysis and modeling of transportation systems, of territorial systems 2

3 Scientific interest Refined modeling of Quality of Service By travel mode Supply-demand interaction Car-based systems Traffic Dynamics Parking conditions, capacity consdtraints and search traffic Disaggregated trip endpoints Transit systems Network model sensitive to a variety of traffic phenomena - In-vehicle - On track - On-platform - Regulation Vehicle-sharing systems Such as Vélib or Autolib + Spatial systems Trip distribution models Activities and accessibility Housing systems Urban economics 3

4 Systems of interest Interests and motivations Transportation systems Network traffic and operations Quality of service and user choices of path, mode, departure time Urban systems, including Housing system Quality of life, w.r.t. dwelling size and quality Real estate prices Management-oriented modeling Management issues: Traffic management, Demand mgmt, System planning Modeling: from Systems Analysis to Simulation Models, passing by Theoretical Models Evaluation methods: Cost-Benefit Analysis, Multicriteria Analysis and Life Cycle Analysis 4

5 Aims and principles Main aims to represent and understand basic phenomena and systemic effects to design tractable models applicable in the consultancy setting Main principles Economic actors and sets of actors: Supply side: suppliers of services, housing owners Demand side = a set of customers Microeconomic behavior of individual actors within the space Heterogeneity: location in space, modal options, demand segment Interaction between supply and demand induces system state Endogenous features: prices, quality of service, quantities of usage Spatial characteristics Mesoscopic features such as parking lot, or a service vehicle in the assignment of passenger traffic to a transit network 5

6 Overview of presentation Traffic on Roadway Networks: the Ladta model Partnership with Vinci Autoroutes (Cofiroute, Asf) Parking Model ParkCap Partner Vinci Park Passenger Traffic in Capacitated Transit Networks: the CapTA model Partnership with Stif, Ratp, Sncf, Rff Housing Model: DREAM Partnership with Real estate developers Discussion Conclusion 6

7 Traffic on Roadway Networks: the Ladta model 7

8 Dynamic Traffic Assignment: LadTA Model Traffic Equilibrium on a Network throughout Time Congestion phenomena in space and time Each user takes travel decision: route choice, departure time choice Demand segments: by vehicle type, by behavioral features (price-time trade-off, desired arrival time ) In order to simulate Management Policy Tariff setting, information and signalization, capacity management, speed management 8

9 Block-diagram of the LADTA model Time and price by PATH and entry time Structure of demand Service formation Transport services User choice Time and price by ARC and entry time Supply constituents Trip demand PATH volumes by entry time Structure of supply Traffic Flowing Assigned Traffic ARC volumes by entry time Volume Loading 9

10 Roadway Traffic with Pollutant Emissions 04h00 08h00 12h00 18h00 Intensité des émissions de CO en Ile-de-France, calculées à partir des débits instantanés résultant d une affectation dynamique. La matrice de demande a été construite à partir de l EGT et de matrices OD statiques HPM/HPS fournies par l ex DREIF. 10

11 The ParkCap model of Parking and Route Choice 11

12 Physiology of Parking System Microeconomic Features Tariffs of Alternative modes Quality and Cost of Travel Options Activity & Trip Options Microecomic TradeOff Utility Utility Activity Suppliers Activity Clients Land-Use and Layout Policy Spatial Configuration Trip Demand Transport Policy Recettes de Circulation Parking Revenue Physical and Technical Features Traffic Load Car Time Traffic Congestion Traffic Capacity Parking Load Parking Congestion Parking Capacity Parking Policy - Capacity - Tariffs - Control - Regulation Terminal Access Time Environnemental Impacts of roadway traffic 12

13 Principles of model Supply and Demand Interaction => usage and impacts Supply Model Parking slots in space, by management mode and number By lot, the state of occupancy: a stock whose temporal profile is driven by its inputs and outputs Demand Model Disaggregated into Segments of Users Quality of Service: tariff, search time, walk time up to activity point Choice Options: lots with access path Supply-Demand Equilibrium Initial model: a static one 13

14 Parking and Routing Choice Near of Destination The user is a Candidate to a lot of slots By lot, a success probability In case of failure: diversion to a neighboring lot On average: each lot has a terminal generalized cost with respect to the final destination of the trip Path from Origin to Destination Decomposed into a main path towards a target lot chosen exante and a terminal path (possibly including loops) Option cost = Main path cost (classical approach) Plus Terminal cost of target lot 14

15 Formation of traffic and its equilibrium Formation of traffic Local flow = volume due to main paths, plus the cruising traffic from initial target lots to allocated lots Load Y m of parking lot m = aggregate of candidates. Success Probability: α m = min{1, K m / Y m } Traffic Equilibrium Path choice to optimize the individual generalized cost Local diversion: a stochastic model of random utility (DCM) => probability p m,n (s) to divert from lot m to lot n for demand segment s 15

16 Model Structure Q S f SR ĝ SR Route demand Local demand p ST ĝ SL c SL f SA q SL y SL α L v SA Traffic t SA x ST Γ AST Search & Park κ L t SR c ST g SR m SR m SA Costing Route demand Local demand Search and Park Traffic Costs 16

17 Application instance Parking and car traffic at Cité Descartes (Marne-la-Vallée)

18 A 5 step model 1. Generators by function: specific factor 2. Local demand for activity, in proportion to generator Demand generation 3. Demand for parking space, according to the modal share of Car driver 4. Occupancy load: time assignment w.r.t. time-of-day and activity duration 5. Modal and spatial split of parking load And also O-D structure Manage filling Cité Descartes Based on activity location and dimension F. Leurent, QUANTURB Seminar, LVMT Supply-Demand Models Workshop, September 2012

19 Passenger Traffic in Capacitated Transit Networks: the CapTA model 19

20 Systems analysis 20

21 Principles of the CapTA Model A static, frequency-based transit assignment model Passenger route choice Individual optimization of generalized cost along travel hyperpath from origin to destination Traffic phenomena Two levels of traffic units: passenger / vehicle A wide range of Capacity constraints are addressed in a coherent way, on the basis of the line sub-model Traffic equilibrium of supply and demand Passenger routes give rise to local passenger flows, which in turn determine traffic phenomena, from which stems the quality of service hence the chosen routes 21

22 In-vehicle traffic Traffic phenomena Comfort states (sitting vs standing under crowding density) => generalized cost per unit of physical time Passenger physical time depends on vehicle time Station platform: passenger storage and waiting From stop station & by exit station: Residual passenger capacity determines # of passengers stored on platform, hence the waiting time Infrastructure track as a scarce resource By station track: dwell times, clearance times and safety margins determine the frequency effectively delivered A revised frequency propagates downstream. It induces a delay upstream 22

23 Capacity phenomena Platform track Occupancy i. Track capacity ii. Route K in veh runs/time unit iii. Veh K, in passengers iv. Service K, in pass v. K of Pedestrian element (station) vi. Station K for vehicle storage vii. K in private vehicles 23

24 Overview of Line model 24

25 A Bilevel Model Architecture Upper layer: Macro assignment model integrating modes Trip matrix Service level matrix Lower layer: Meso or Micro model of modal sub-system Upper level: passenger route choice On a network of pedestrian links and transit line legs (from entry station to exit station) Lower level: traffic operations by average service run Based on line topological ordering of stations along line of operations 25

26 Application to Greater Paris Input Data DRIEA Network of Greater Paris Capacity data Passenger layer Network of ~300k arcs and 160k nodes Trip matrix Morning Peak hour OD * 1,3 26

27 Passenger Flows along Network 27

28 Frequency modulation when boarding and alighting flows face insufficient exchange capacity e.g. Frequency of Westbound RER A is reduced from Nominal (30 veh/h) by 9% Network performance 28

29 Quality of service outcomes 29

30 Some comments The CapTA model: CAPacitated Transit Assignment A wide range of features Modular architecture based on Systems analysis It still requires to be calibrated Stochastic features in space: heterogeneity of passenger load along a given train and also along a given platform Stochastic features in time: heterogeneity of vehicle headways, hence of passenger load between successive trains Estimation of Passenger route choice: the valuation of service attributes (run time, wait time, comfort, reliability) Complexity => Need for a Transit Lab 30

31 Housing Model: DREAM Disaggregate Residential Equilibrium Assignment Model 31

32 Housing System Housing supply Housing type: surface area, quality, location, price Total housing stock disaggregated by type and location By type and location: elastic supply function Transportation supply Travel conditions for O-D pairs Activity supply Essentially job supply Jobs disaggregated by type, wage and location Joint housing and travel demand By household: one housing unit with a given job (and workplace)

33 Housing option Main principles in DREAM One housing type in a given zone, characterized by a given size, quality and price Travel option By O-D pair, travel conditions in price and time For a given job (characterized by type, wage and location) The household holding the job chooses a housing option that maximizes its utility Supply demand equilibrium Prices are endogenous. They determine how households are assigned to options

34 Household behavior Utility function For a household m, housing option r yields utility U m ( s, q, z, τ) Monetary budget constraint p r s r + c ( q, s, ν ) r r r m + t rj + z ρ m Time budget constraint ρ ~ ~ m + trj + τ θm Depending on prices and travel conditions U ~ m ( r) = U m ( s r, q r, ~ z mr, ~ τ mr ) ~ z = ρ p s c ( q, s, ν ) mr m r r mr = θm ~ ρ ~ m t rj ~ τ r r r m t rj

35 Impact of income Small, B Small, C Large, B Large, C

36 Mathematical model By demand segment = type and location of the job, one income distribution Cf. one demand segment on a O-D pair for price time assignment For each housing option, the segment competes for a certain number of dwelling units (which may be 0) By housing option: total demand (aggregated over the various segments) sets the price Elastic supply function Cf. a time flow function in traffic assignment Equilibrium conditions between supply and demand They make a primal dual problem of constrained non linear optimization Solved by a convex combination algorithm

37 Case study Set-up Two residential zones: downtown / suburbs Two dwelling sizes: small / big Two household sizes: small / big Equilibrium: prices and quantities No Small No Large Price ( /m2 per day) Small Suburbs Small Centre Large Suburbs Large Centre 0,90 0,80 0,70 0,60 0,50 0,40 0,30 0,20 0,10 0,00

38 1,0 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0,0 Sensitivity analysis Price Small B Price Small C Price Large B Price Large C Elasticity1 Restructuration Homothetic Recomposition IsoGini Dispersion Elasticity1 Restructuration Homothetic Recomposition IsoGini Dispersion Elasticity0 Elasticity0 Increment Increment Reference No small hh, Sm B No small hh, sm C No small hh, Lg B No small hh, Lg C No Large hh, Lg B No Large hh, Lg C Reference

39 Housing prices: 5+ rooms, IdF 2001

40 Housing prices 3-4 rooms, IdF 2001

41 Housing prices 1-2 rooms, IdF 2001

42 Discussion 42

43 Spatial shape as basis for modeling Network structure Links and nodes Sequential composition of paths for networks users Some parallel composition induced by users choice of path And more => Hierarchical modeling Transit line and complex traffic interactions / operations Parking basin of a destination place within walking reach The attractiveness of places for location choice, for destination choice 43

44 Physical relevance Aggregation issues Some traffic variables are intrinsically aggregate quantities: flowing capacities and the associated flows, storage capacities and the associated stocks, spatial densities, average speeds Mathematical payback Smooth behavior of aggregate variables yields properties for system state, especially so for equilibrium states: existence In some cases: property of uniqueness Probabilistic modeling An aggregate quantity may be disaggregated at a finer level of detail: e.g. capacity of a parking lot as a set of parking spaces, or link time as the sum of elementary times along it Details and aggregation to be captured in probabilistic framework 44

45 Urban issues Urban travel modes are specific The parking issue in individual, motorized modes Car mode in the urban setting: the importance of node traversal and performance, also of link disruptions Transit modes: Bus <> Railway modes Vehicle sharing systems Walking, cycling, the cab The specificities involve Supply side: traffic performance Demand side: quality of service, mode choice, intermodality Planning trade-offs Users vs. Residents: Access vs. impacts 45

46 Economic patterns and issues Demand side Microeconomic agents and behaviors. Elasticity Supply side Traffic performance. Capacity issues? Elasticity? Management? Supply and demand in equilibrium Users rivalry for scarce capacity Market price (housing price or travel cost) Economic fabric (for evaluation of transportation plans) The propagation of value flows in the socio-economic circuit 46

47 Salient features Conclusion: summary Economic representation Spatial features, with emphasis on specific forms such as parking lot, transit line, transit vehicle, station platform, location of a given household option and its access cost from a given job Mathematical formulation and statement in a typical form A Variational Inequality Problem or a Fixed Point Problem. Solution schemes involve classical algorithms of traffic network assignment, or ad-hoc adaptations Macroscopic representation to benefit from the mathematical form and its theoretical properties It involves probabilistic models in several respects Systemic Analysis Upstream of Modeling Sub-System Modularity 47

48 Bottom-up From micro to macro From local to global Top-down On system modeling Systems analysis: patterns and structural relationships: Supply and Demand, Urban features System state determines microeconomic situations Classroom case as basis for generalization 48

49 i. Semantic model ii. The four facets of models Physics, economics, systems analysis Mathematical formulation Mathematical statement of assumptions and causalities Mathematical analysis of system state iii. Technical solver E.g. computation algorithm iv. Empiric relationship between model and system under study Econometrics 49

50 Short run On-going work Multimodal: the transit and parking models are under integration into a refined model of mode choice Space disaggregation of trip endpoints Dynamics of transit, of parking Elasticity of supply: the inclusion of supply management in system planning and operations beginning with transit Medium run To integrate the housing model as a driver of mode choice so as to capture the fact that housing prices that may well dominate those of transit season tickets 50