Transportation Modeling Approach Direct vs. Sequence

1. Transportation Modeling ApproachDirect vs. Sequence Modeling approach Meeghat Habibian

2. Approaches in travel demand modeling MODELING APPROACHES (2) the sequenced choice model approach. sequencing a series of models of choice and then combining them the direct approach. a direct application of the concepts of microeconomic demand modeling

3. Approaches in travel demand modeling MODELING APPROACHES (2) the structured choice model approach. the direct approach. predicting the number of trips made in an urban area as a function of demand and supply characteristics

4. The Direct Approach: The following attributes need to be identified: purpose mode 1 4 origin 2 route 5 3 destination 6 time of day

5. The Direct Approach: X pijmrt the number of trips made by an individual during a given period of time, p=purpose, origin=i, destination=j, mode=m, route =r, and at time of day= t demand function: all the attributes of all the alternatives simultaneously

6. The Direct Approach: Dp = vector of demand variables for trip purpose p Sijmrt= vector of supply variables for trips with attributes given by i, j, m, r and t

7. The Direct Approach: the total number of variables in the demand function: d + ijmrt In the quite realistic situation when d = 3, i= 3, j= 5, M = 3, R = 2, and T =3, the number would be 273

8. Simplifications in the Direct Approach models: • Elimination of the cross-elasticities of demand for different trip purposes, p, which has been assumed. • Eliminating the t index and constructing demand functions for trips over all time periods (i.e., typical weekday).

9. Simplifications in the Direct Approach models: • Simplifications in The Direct Approach models: • Another level of simplification is when origins and destinations are left in the model (*aggregation on route and modes), resulting in the origin-destination demand model or • a generation-distribution model: • The extreme of such a simplification is when all attributes are suppressed except the trip origin or • a trip-generation model:

10. Example of The Direct Approach: One of the earliest direct demand models for an urban freeway bridge in the San Francisco Bay Area, The Kraft-Wohl model (1967) : income measure Population measure Trip volume purpose And … time of day

11. The Sequenced Choice Approach: The Direct Approach: All the attributes of all the alternatives simultaneously The Sequenced Choice Approach: The number of trips is first decided, and then the other attributes . Sequential process

12. Sequenced Choice Approach Reverse modeling UTPS The Sequenced Choice Approach Methods: Two methods which are different in modeling trip generation

13. The first method in sequence approach (UTPS) • This method is common in practice: • Urban Transportation Planning System (UTPS) • A trip-generation model is defined Xpi, then distributed among the alternatives available for mode, destination and route choices, using models of travel choice.

14. Urban Transportation Planning System (UTPS) UTPS process: trip-generation model distributing among the available destinations Mode spilt Assignment

15. UTPS major drawback • The total travel demand is not elastic with respect to the attributes of the supply system and that trips are generated on the basis of demand variables only. • Attempts to correct this are made by either incorporating aggregate measures of supply in the trip-generation model (e.g., accessibility index)

16. The second method in sequence approach (Reverse modeling) set off all roads available for this i,j,m proportion of all trips, that would select route r vector of supply variables route choice function

17. Reverse Modeling Using previous, provide a: weighted average of the supply characteristics modeling the conditional choice of mode: Mode choice function

18. Reverse Modeling The weighted average of the supply characteristics to any destination can be obtained: The destination choice model can now be based on these weighted supply values: Destination choice function

19. Reverse Modeling the weighted average of all supply value from i: a trip-generation demand model can be specified:

20. Reverse Modeling example A transportation system serving an area: Purpose a given trip purpose Mode two modal networks 1 4 origin One origin Route two routes 2 1 5 Destination 3 possible destinations time of day -------------- 3 6

21. Reverse Modeling example The travel times on the network The travel costs on the network vector of destinations attractiveness

22. Reverse Modeling example Amounts of traffic flows from an origin i to destinations j by each of the modes and routes? The hierarchy assumed is, destination choice is first, and using that, the choice of mode is made on the basis of which route is chosen . 1-modeling the choice of route conditional on mode choice:

23. Reverse Modeling example bases route choice only on travel times Invariant respect to route

24. Reverse Modeling example

25. Reverse Modeling example 1- choice of route conditional on mode choice: 2-calculation of weighted average travel time for each mode and destination combination:

26. Reverse Modeling example 2- for example: t11=(25)(0.39)+(16)(0.61)=19.51≈20 t12=(36)(0.4)+(24)(0.6)=28.8≈30

27. Reverse Modeling example 3-A logit mode choice model: Where V(m, j) is a linear choice of travel time & cost:

28. Reverse Modeling example 3-computation of The weighted average values of the time and cost functions Vˆ(j) for each destination: Vˆ(j)=Σm V(m,j) p(m│j) 5.19=(5)(0,62)+(5.5)(0.38)

29. Reverse Modeling example 4- A gravity destination choice model: 5- calculating p(m,r,j) matrix: Stage 4 Stage 1 Stage 3

30. Reverse Modeling example 5-

31. Reverse Modeling example 6-Trip generation Xi =681 measure of generalized transport cost

32. Reverse Modeling example 7-allocating 681 trips among all the modes, routes, and destinations according to the p(j,m,r) matrix

33. Example summary 1- choice of route conditional on mode choice. 2-calculation of weighted average travel time for each mode. and destination combination. 3-modeling mode choice (a logit) . 4- modeling destination choice (a gravity). 5- calculating p(m,r,j) matrix. 6-computing Trip generation. 7-allocating all trips among all the modes, routes, and destinations .