1. Modeling Approach Direct vs. Sequenced
Meeghat Habibian

2. Outline
Introduction
Transportation Demand Analysis- Lecture note

3. Concept
predicting the number of trips made in an urban area as a function of demand and supply characteristics
Transportation Demand Analysis- Lecture note

4. Modeling Approaches Direct approach
a direct application of the concepts of microeconomic demand modeling
Sequenced choice model approach
sequencing a series of models of choice and then combining them
Transportation Demand Analysis- Lecture note

5. Direct Approach

6. Attributes that need to be identified1
purpose 4
mode 2
origin 5
route 3
destination 6
time of day

7. The Demand Function
X pijmrt: Number of trips made by an individual during a given period of time
p:purpose, i: origin, j: destination,
m: mode, r: route, t: time of day
Dp : vector of demand variables for trip purpose p
S ijmrt : vector of supply variables for trips with attributes given by i, j, m, r and t

8. Number of variables
Assuming cross-elasticities between supply variables:
d + sijmrt
In a quite realistic example:
d = 3, s=3, i= 1, j= 5, M = 3, R = 2, and T =3,
 number of variables for each trip purpose would be 273
Note: No cross-elasticity between demand and supply
Note: No cross-elasticity between trip purposes

9. Simplifications in Direct Approach
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).

10. Simplifications in Direct Approach
Aggregation on routes and modes
resulting in 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

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

12. Sequenced Choice Approach

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

14. UTPS method 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.

15. Urban Transportation Planning System (UTPS)
UTPS process:
Trip-generation model
Distributing among the available destinations
Mode spilt
Assignment

16. 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 incorporating aggregate measures of supply in the trip-generation model (e.g., accessibility index)

17. The Reverse Modeling set off all roads available for this i,j,m
vector of supply
variables
proportion of all trips, that would select route r
route choice function

18. Supply characteristics for mode m
Weighted average of the supply characteristics

19. The Conditional Choice of Mode
Mode choice function

20. Supply characteristics to destination j
The weighted average of the supply characteristics to any destination can be obtained by

21. Destination choice model
The destination choice model can now be based on these weighted supply values
Destination choice function

22. Supply value from origin i
The weighted average of all supply value from i:
A trip-generation demand model can be specified:

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

24. Reverse Modeling example
The travel times on the network
The travel costs on the network
Vector of destinations attractiveness

25. 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:

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

27. Reverse Modeling example

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

29. Reverse Modeling example2-
for example: t11=(25)(0.39)+(16)(0.61)=19.51≈20
t12=(36)(0.4)+(24)(0.6)=28.8≈30

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

31. 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)

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

33. Reverse Modeling example5-

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

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

36. 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

37. Transportation Demand Analysis- Lecture note
Finish