1. Trip Distribution Lecture 8 Norman W. Garrick and Hamed Ahangari

2. Socio-Economic and Demographic
Land Use
Socio-Economic and Demographic
# Trip
Trip Generation
# Trip
O-D
Trip Distribution
Mode Choice
# of Trips by Modes
Transportation
Network
Trip
Assignment
Traffic volumes

3. i i j j Tij Trip Generation Production Attraction Pi Aj
Trip Distribution
Tij i j

4. Trip Generation Input: Socioeconomic Data Land Use Data Output:1 2 3 4 5 6 8 7
Output:
Trip Ends by trip purpose

5. Trip Generation Trip Distribution
The question is… how do we allocate all the trips among all the potential destinations?
Trip Matrix or Trip Table
Zone 1

6. STORRS Buckland Hill Westfarms Mall Eastbrook Mall Production
Attraction

7. Trip Distribution

8. Trip Distribution
We link production or origin zones to attraction or destination zones
A trip matrix is produced
The cells within the trip matrix are the “trip interchanges” between zones

9. Trip Distribution: Theory
Trip interchange between two zones depends on:
Type of land use
Costs of travel between zones

10. Basic Assumptions of Trip Distribution
Number of trips decrease with COST between zones
Number of trips increase with zone “attractiveness”

11. Methods of Trip Distribution
Growth Factor Models
Gravity Model

12. Growth Factor Assumptions
1. Future travel pattern would be the same as the existing pattern (distribution of future trips from an origin is a proportion of the present trip distribution)
2. The growth factor allow us to adjust future interchanges

13. Growth Factor Models
Growth Factor Models assume that we already have a basic trip matrix
Usually obtained from a previous study or recent survey data

14. Growth Factor Models
The goal is then to estimate the matrix at some point in the future
For example, what would the trip matrix look like in 2 years time?
Trip Matrix, t (2008)
Trip Matrix, T (2018)

15. Some of the More Popular Growth Factor Models
Uniform Growth Factor
Singly-Constrained Growth Factor
Average Factor
Detroit Factor
Fratar Method

16. Uniform Growth Factor Model

17. Uniform Growth Factor tij = Base-year Trip Matrix
i = I = Production Zone
j = J = Attraction Zone
Tij = τ tij for each pair i and j
Tij = Future Trip Matrix
tij = Base-year Trip Matrix
τ = General Growth Rate

18. Uniform Growth Factor Tij = τ tij
If we assume τ = 1.2 (growth rate), then…
Trip Matrix, t (2013)
Tij = τ tij
= (1.2)(5)
= 6
Trip Matrix, T (2018)

19. Uniform Growth Factor
The Uniform Growth Factor is typically used for over a 1 or 2 year horizon
However, assuming that trips grow at a standard uniform rate is a fundamentally flawed concept

20. Pros and Cons of Growth Model
Advantages:
Simple
Easy to balance origin and destination trips at any zone
Disadvantages:
Does not reflect changes in the land use
Does not reflect changes in the network

21. The Gravity Model

22. The Inspiration for the Gravity Model
The big idea behind the gravity model is Newton’s law of gravitation…
The force of attraction between 2 bodies is directly proportional to the product of masses between the two bodies and inversely proportional to the square of the distance
M1 M2
F = k r2

23. Some of the Variables Tij = Qij = Trips Volume between i & j
Fij =1/Wcij = Friction Factor
Wij = Generalized Cost (including travel time, cost)
c = Calibration Constant
pij = Probability that trip i will be attracted to zone j
kij = Socioeconomic Adjustment Factor
Tij = Trips between i & j
i = production zone
j = attraction zone
Tij = f (Pi, Aj, Cij)
Cij = Generalized cost of trip from i to j

24. The Gravity Model
Pi Aj FijKij
Tij = Qij =
= Pipij
ΣAjFijKij
(Productions)(Attractions)(Friction Factor)(K-factor) =
Sum of the (Attractions x Friction Factors x K-factor) of the Zones
Fij = 1 / Wcij
or ln F = - c ln W
The bigger the friction factor, the more trips that are encouraged

25. Steps Step 1- Calculate Friction Factors, {Fij}
Step 2- Find Denominator of Gravity Model Equation {AjFijKij}
Step 3- Find Probability that Trip i will be attracted to Zone j, {pij}
Step 4- Find Trip Interchanges, {Tij}

26. To Apply the Gravity Model
What we need…
Productions, {Pi}
Attractions, {Aj}
Skim Tables {Wij)
Target-Year Interzonal Impedances

27. Gravity Model Example 8.2 Given: Find: Target-year Productions, {Pi}
Relative Attractiveness of Zones, {Aj}
Skim Table, {Wij}
Calibration Factor, c = 2.0
Socioeconomic Adjustment Factor, K = 1.0
Find:
Trip Interchanges, {Qij}

28. Find Trip Interchanges, {Qij}
Find Denominator of Gravity Model Equation {AjFijKij}
Calculate Friction Factors, {Fij}
Find Probability that Trip i will be attracted to Zone j, {pij}
Given…
Given…
Target-Year Inter-zonal Impedances, {Wij}
Calibration Factor c = Socioeconomic Adj. Factor K = 1.0
Calculate Friction Factors, {Fij} 1
F11= 1 52 =
0.04
Fij = =
Wcij
Find AjFijKij
AjFijKij=A2F12K12
(3)(0.01)(1.0) = 0.03
Find Probability that Trip from i will be attracted to Zone j, {pij}
A2F12K12
0.03
p12 = = =
Σ(AjFijKij)
0.0514
Find Trip Interchanges, {Qij}
Q12 = P1p12 = (1500)(0.5838) = 876

29. Find Trip Interchanges, {Qij}
Find Denominator of Gravity Model Equation {AjFijKij}
Calculate Friction Factors, {Fij}
Find Probability that Trip i will be attracted to Zone j, {pij}
Given…
Given…
Target-Year Inter-zonal Impedances, {Wij}
Calibration Factor c = Socioeconomic Adj. Factor K = 1.0
Calculate Friction Factors, {Fij} 1
F23= 1
102 =
0.01
Fij = =
Wcij
Find AjFijKij
AjFijKij=A3F23K23
(2)(0.01)(1.0) = 0.02
Find Probability that Trip from i will be attracted to Zone j, {pij}
A3F23K23
0.02
p23 = = =
Σ(AjFijKij)
0.1622
Find Trip Interchanges, {Qij}
Q12 = P2p23 = (0)(0.1233) = 2

30. Find Trip Interchanges, {Qij}
Find Denominator of Gravity Model Equation {AjFijKij}
Calculate Friction Factors, {Fij}
Find Probability that Trip i will be attracted to Zone j, {pij}
Given…
Given…
Target-Year Inter-zonal Impedances, {Wij}
Calibration Factor c = Socioeconomic Adj. Factor K = 1.0
Calculate Friction Factors, {Fij} 1
F23= 1
102 =
0.01
Fij = =
Wcij
Find AjFijKij
AjFijKij=A3F23K23
(2)(0.01)(1.0) = 0.02
Find Probability that Trip from i will be attracted to Zone j, {pij}
A3F23K23
0.02
p23 = = =
Σ(AjFijKij)
0.1622
Find Trip Interchanges, {Qij}
Q12 = P2p23 = (0)(0.1233) = 2

31. Keep in mind that the socioeconomic factor, K, can be a matrix of values rather than just one value

32. The Problem with K-Factors
Although K-Factors may improve the model in the base year, they assume that these special conditions will carry over to future years and scenarios
This limits model sensitivity and undermines the model’s ability to predict future travel behavior
The need for K-factors often is a symptom of other model problems.
Additionally, the use of K-factors makes it more difficult to figure out the real problems

33. Limitations of the Gravity Model
Too much of a reliance on K-Factors in calibration
External trips and intrazonal trips cause difficulties
The skim table impedance factors are often too simplistic to be realistic
Typically based solely upon vehicle travel times
At most, this might include tolls and parking costs
Almost always fails to take into account how things such as good transit and walkable neighborhoods affect trip distribution
No obvious connection to behavioral decision-making