Public Transportation Models I: Framework and Low Frequency Services

Transcription

1 Public Transportation Models I: Framework and Low Frequency Services Ennio Cascetta Modeling and Simulation of Transportation Networks Boston, July 30, 2015 Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-Demand Interaction (Assignment) models Applications 2 1

2 Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications 3 INTRODUCTION Types of transportation services In relation to space & time dimensions, Transportation Systems can be classified in: Continuous services are available at every instant and can be accessed from a very large number of points (e.g. individual modes: car, walking,.) Discrete services (e.g. Scheduled Services) can be accessed only at given points and are available only at given times Passengers services Bus Plane Train Freight services Railway Combined transport Maritime Transport: Ro- Ro 4 2

3 INTRODUCTION Scheduled Services modelling approaches Scheduled Services can be modelled using two different approaches: Frequency-based approaches line-based representation of services modal choice and path choice models that give the mode and the line probability in relation to service frequency assignment models that give the average flow of each line Schedule-based approaches run-based supply models with explicit consideration and representation of services timetable modal choice and path choice models give the mode and the run choice probability in relation to run attributes assignment models that give the average flow of each run 5 INTRODUCTION Definitions Run r individual connection among s with a given scheduled arrival/departure time at each A run is defined by the route and the (scheduled) arrival and departure times at s run Line AA BB AA CC service type INTERCITY REGIONAL INTERCITY INTERCITY initial station depart ure time Intermediate Stops terminal station Line l set of runs with the same characteristics (route and s, average travel times, quality of services, etc.). A line is defined by the route and the frequency (average number of runs in the unit of time) A A A A B/C - D D D D E 6 3

4 Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications 7 SUPPLY MODELS Definitions Line-based supply models Run-based supply models services are represented by lines services are represented by runs 8 4

5 SUPPLY MODELS Line-based approach line 1 line 2 line 1 E line 3 line 4 line 2 A C F o B G d line 5 line 5 line 5 line 5 D line 6 line 7 line 7 line 7 line 8 line 8 line 8 taken from: Cascetta (2009). Transportation System Analysis: models and applications. 2 nd edition. Springer. centroids pedestrian nodes pedestrian nodes nodes line nodes pedestrian links boarding/alighting links line links 9 SUPPLY MODELS Run-based approach Diachronic graph: nodes representing events taking place at a given instant (nodes have explicit time coordinate); allows using network algorithms similar to those used for static continuous networks. 10 5

6 TRANSIT SUPPLY MODELS Run-based models Diachronic graph - Definition The diachronic graph consists of three different sub-graphs in which each node has an explicit time coordinate: temporal centroids temporal centroids d a service sub-graph s ; p b rs a b rs a temporal centroids sub-graph d ; Di Dis s s an access-egress sub-graph ae. s s centroid centroid DIACHRONIC SUPPLY MODELS Service sub-graph Definition The service sub-graph s represents transit services, in which each run of each line is defined both in space, through its s, and in time, according to its arrival/departure times at s. 6

7 DIACHRONIC SUPPLY MODELS Service sub-graph Representation TIMETABLE run Terminal s arr. dep. Terminal s arr. dep. line 1 - run 5 line 1 - run 6 line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s DIACHRONIC SUPPLY MODELS Service sub-graph Representation TIMETABLE run line 1 - run 5 Terminal s arr. dep Terminal s arr. dep s s line 1 - run 6 line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s 7

8 DIACHRONIC SUPPLY MODELS Service sub-graph Representation TIMETABLE run line 1 - run 5 Terminal s arr. dep Terminal s arr. dep s s line 1 - run 6 line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s DIACHRONIC SUPPLY MODELS Service sub-graph Representation TIMETABLE run line 1 - run 5 Terminal s arr. dep Terminal s arr. dep s s line 1 - run line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s 8

9 DIACHRONIC SUPPLY MODELS Service sub-graph Representation TIMETABLE run line 1 - run 5 Terminal s arr. dep Terminal s arr. dep s s line 1 - run line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s DIACHRONIC SUPPLY MODELS Service sub-graph Representation run line 1 - run 5 TIMETABLE Terminal s arr. dep Terminal s arr. dep s s line 1 - run line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s 9

10 DIACHRONIC SUPPLY MODELS Service sub-graph Representation run line 1 - run 5 line 1 - run 6 TIMETABLE Terminal s arr. dep Terminal s arr. dep s s line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s DIACHRONIC SUPPLY MODELS Service sub-graph Representation TIMETABLE run line 1 - run 5 line 1 - run 6 Terminal s arr. dep Terminal s arr. dep s s line 1 - run boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s 10

11 DIACHRONIC SUPPLY MODELS Service sub-graph Representation run line 1 - run 5 line 1 - run 6 line 1 - run 7 TIMETABLE Terminal s arr. dep Terminal s arr. dep s s boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s DIACHRONIC SUPPLY MODELS Service sub-graph Representation run line 1 - run 5 line 1 - run 6 line 1 - run 7 TIMETABLE Terminal s arr. dep Terminal s arr. dep s s boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s 11

12 DIACHRONIC SUPPLY MODELS Service sub-graph Representation run line 1 - run 5 line 1 - run 6 line 1 - run 7 TIMETABLE Terminal s arr. dep Terminal s arr. dep s s = avg section speed boarding/alighting run arrival/departure time run/dwell link boarding/alighting links transfer link s s DIACHRONIC SUPPLY MODELS Temporal centroids sub-graph Definition The temporal centroids sub-graph d represents user departure/arrival times or an user target times (DDT - Desired Departure Time and Desired Arrival Time - DAT). 12

13 DIACHRONIC SUPPLY MODELS Temporal centroids sub-graph Representation temporal centroid t D i space centroid DIACHRONIC SUPPLY MODELS Access-Egress sub-graph Definition The access-egress sub-graph ae represents the connection between centroids and s, and among s. It allows the connection between the demand sub-graph and the service sub-graph. 13

14 DIACHRONIC SUPPLY MODELS Access-Egress sub-graph Representation temporal centroids centroid s s centroid DIACHRONIC SUPPLY MODELS Access-Egress sub-graph Representation tempotal centroids access link egress link t Di t Dis centroid s s centroid 14

15 DIACHRONIC SUPPLY MODELS The diachronic graph temporal centroids = s d ae temporal centroids d centroid origin departure time destination arrival time arrival time boarding/alighting run arrival/departure time run/dwell link boarding/alighting links Di p b rs a b rs Dis s access/egress link s transfer link,... example of path s s centroid centroid Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications 30 15

16 DEMAND MODELS Services classification Frequency: Low: av. headway > 30 mins (e.g. non-urban transit services) High: av. headway <12-15 mins (urban transit) Regularity: Low (e.g. urban transit services): average delays large compared to the average headways High (e.g. airlines, intercity train services) : average delays small compared to the average headways Frequency High Low Irregular URBAN Service Regular Service REGIONAL INTERCITY 31 DEMAND MODELS Modelling approaches Different specifications for modal choice, path choice and assignment models: Frequency-based approach for High-frequency services Schedule-based approach for High-frequency services See lecture Public transportation II: Schedule-based Models for High Frequency Services for Low-frequency services 32 16

17 DEMAND MODELS Schedule-Based models for low frequency services Behavioural assumptions pre-trip choice of the (station, airport) and of the run users segmentation according to the user target time (TT), i.e.: - desired departure time (DDT) or - desired arrival time (DTT) 33 DEMAND MODELS Schedule-Based models for low frequency services User Target Time Times in which users desire/need to start or to complete their trips : desired departure times (DDT) times in which users would like to depart from their origin desired arrival times (DAT), times in which users would like to arrive at their destination user target times (TT), due to low frequency, generate early or late schedule delays, producing a further disutility component (early/late schedule penalty) in mode and path choice 34 17

18 users DEMAND MODELS Schedule-Based models for low frequency services Example of early/late schedule delay IR 312 railway terminal 2.30 late departure penalty delay (40min) 1.50 DDT IR 310 early departure penalty delay (20min) DEMAND MODELS Schedule-Based models for low frequency services Example of User Target Time distribution Regional trips arrival departure time slice 36 18

19 DEMAND MODELS Schedule-Based models for low frequency services Demand Temporal Segmentation Time-dependent O/D matrix 37 DEMAND MODELS Schedule-Based models for low frequency services O-D segmentation: other criteria Trip purposes: Home-based (from/to) work business study other Non home-based secondary Users segmentation: Income level; Reimbursement or not; Party size; Car availability

20 Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications Commercial software packages Application example to Regione Veneto 39 DEMAND MODELS Path choice models estimate the probability of choosing a path on the diachronic network given the origindestination pair and the user s target time DESIRED DEPARTURE TIME DESIRED ARRIVAL TIME 40 20

21 DEMAND MODELS Path choice models Path choice set Choice set defined by the following rules: maximum earliness and lateness band (e.g. all the runs within a given temporal band) feasibility rules (e.g. max schedule delay, max number of interchanges) Dominance rules (e.g. no paths leaving earlier and arriving later) j = departure target time K s = path choice set a1 b1 a2 b2 a s K s K run departure times 41 DEMAND MODELS Path choice models Example of Random Utility path choice model Pre-trip choice of run r with maximum perceived utility U r in relation to target time TT U r TT = TB TB r + TC TC r + MC MC r + CFB CFB r + ESP ESD r + LSP LSD r + r where: TB r on-board time; TC r transfer time; MC r monetary cost; CFB r on-board comfort; ESD r early schedule delay; LSD r late schedule delay; 42 21

22 Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications 43 DEMAND MODELS Mode-service choice models estimate the joint probability of choosing a mode and a service (e.g. train-first class) on a given OD pair for a given user s target time Service characteristics single or multiclass on the same vehicle or group of vehicles (e.g. business and economy for plane, First and second class for train)) single or multiservice on different vehicles (train) (e.g. High-speed, Intercity, Interregional) different fare structures (e.g. different prices for O/D pair, service and class) 44 22

23 DEMAND MODELS Mode-service choice model Example of model structure O / D pair User Target Time od, TT Early Run Late Run Individual Mode k Mode j Mode n Mode j Mode n 45 DEMAND MODELS Example of mode-service choice model Model specification exp(v j / θ0 ) p(j/k) exp(vm / θ0 ) m I k V j βi Xij i i model parameters X ij i-th attribute of j-th alternative p(j) p(j/k) p(k) = systematic utility of j-th alternative exp(θy k / θ0 ) p(k) exp(θy / θ ) h h 0 exp(v Y h ln m / θ ) = logsum variable of h-th group m I h 46 23

24 DEMAND MODELS Example of Mode-service choice model Model Structure O/D, target time EARLY RUNS LATE RUNS Car Early Bus Early Train (bus+train) Early Park-Ride Late Bus Late Train (bus+train) Late Park-Ride 47 DEMAND MODELS Example of Mode-service choice model Alternatives & Attributes ALTERNATIVES CAR EB ET EPR LB LT LPR description car early bus early train early park & ride late bus late train late park & ride TB transit travel time X X X X X X A T T R I B U T E S TC car travel time X C travel cost X X X X X X X EP early schedule Delay X X X LP late schedule Delay X X X A/E access/ egress time X X X X X X HI high income user X PR park&ride dummy X X CAR car dummy X EBUS early bus dummy X 48 24

25 DEMAND MODELS Example of mode-service choice model Estimation results Attribute t Stud On board time Car time Monetary cost High income Park&Ride Purpose Center Center Car Early arrival penalty Late arrival penalty Urban acc/egr Early bus log-likelihood Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications 50 25

26 ASSIGNMENT MODELS Demand-Supply interaction models Classification DDP 51 Schedule-based Assignment Models for low frequency services DEMAND MODEL OD demand flows Path/Departure time choice model Path Flows (h) Path cost (g) within-day dynamic network loading model (WD-DNL) Network Flow Propagation Model Link flows (f) Path Performances Model Link costs (c) Link Performances Model SUPPLY MODEL Within-day Dynamic Systems 52 26

27 ASSIGNMENT MODELS Within-day Dynamic Network Loading B C The within-day dynamic network loading model (WD-DNL) allows to obtain the network loading map, i.e. loads f,t at each time on day t A space 53 Outline Introduction Types of transportation services Supply models Definitions and modeling approaches Demand models Users behavior assumptions Path choice models Mode-service choice models Supply-demand interaction (assignment) models Applications 54 27

28 Application example The Italian High Speed Railways 55 APPLICATION EXAMPLE The base scenario The methodology for demand forecasting - Modeling specifications - Validation Simulation of strategic operations of a new entrant The opening of competition the HSR 56 28

29 APPLICATION EXAMPLE The base scenario 57 APPLICATION EXAMPLE Current Scenario The study area: The catchment area of the station of the Italian HSR 28 trains *37 trains 50 trains 23 trains 48 trains HSR daily services frequency 98 trains 98 trains 48 trains 22 trains 58 29

30 APPLICATION EXAMPLE December 2009:was completed and opened to the public the director High Speed Turin-Milan-Naples-Salerno ; 1,000 km long Distance Travel time before HSR Travel TIME after HSR Δ Δ% Torino-Milano 125 1h % Torino-Roma 640 6h 30 4h 30 2h -31% Milano-Roma 515 4h 30 3h 1h 30-33% Milano-Napoli 720 6h 30 4h 55 1h 35-31% Milano-Bologna 182 1h % Bologna-Firenze % Roma-Napoli 205 1h 45 1h % 59 APPLICATION EXAMPLE 2012 incoming of a new operator o TRENITALIA : (Italian National Operator) o NTV : (expect entry time : Dec 2001) 60 30

31 APPLICATION EXAMPLE The base scenario The methodology for demand forecasting - Modeling specifications - Validation Simulation of strategic operations of a new entrant The opening of competition the HSR 61 APPLICATION EXAMPLE 62 31

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33 APPLICATION EXAMPLE 65 APPLICATION EXAMPLE Space 66 33

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40 APPLICATION EXAMPLE The base scenario The methodology for demand forecasting - Modeling specifications - Validation Simulation of strategic operations of a new entrant The opening of competition the HSR 79 APPLICATION EXAMPLE 80 40

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44 APPLICATION EXAMPLE 87 HSR supply growth Runs/day Trains-km/day Università di Napoli Federico II Dipartimento di Ingegneria dei Trasporti L. Tocchetti E. Cascetta Framework and Low Frequency Services 44

45 HSR demand growth Passengers/day Passengers-Km/day induced demand Intercity Air Motorway Università di Napoli Federico II Dipartimento di Ingegneria dei Trasporti L. Tocchetti Mil. Passenger/ year induced demand demand diversion from other rail services demand diversion from other modes (motorway, AIR) E. Cascetta Framework and Low Frequency Services APPLICATION EXAMPLE Modal shares between