Lec 10, TD Part 3: ch5'4'2

1
Lec 10, TD Part 3 ch5.4.2 H/O, pp.477-491
Trip Distribution

• TD Part 3 topics

• Trip distribution why is it needed?
• The Fratar Method (read, not covered in class
  get a general idea)
• The Gravity Model
• Calibration of the gravity model

2
What is trip distribution?

• Estimates where the attraction in zone i come
  from and where do the productions go
• The decision on where the trips go is
  represented by comparing the relative
  attractiveness and accessibility of all zones in
  the area

3
The Gravity model

• Derives its base from Newtons law of gravity,
  which states that the attractive force between
  any two bodies is directly related to their
  masses and inversely related to the distance
  between them.
• Similarly, in the gravity model, the number of
  trips between two zones is directly related to
  activities in the two zones, and inversely
  related to the separation between the zones as a
  function of the travel time.

4
The gravity model formula
The friction factor is a bit confusing. Think of
a water pipe. If friction is high, then less
water passes through it. But, here a higher
friction value results in a higher number of trip
or flow of traffic.
5
The gravity model formula (cont)
Zone j gets a portion of zone Is trip
productions according to its characteristics as
compared to the characteristics of all other
zones in the study area
6
The gravity model formula (cont) a few more
things that you want to be aware

• A separate gravity model may be developed for
  each trip purpose (depending on the level of
  analytical detail you want).
• Before the number of trip interchanges can be
  computed, several parameters must be define, F(t)
  and K obviously. You may borrow these values from
  other areas.
• The travel time between each pair of zones is
  determined by the trip assignment process ?
  indicating an iterative nature of this process
  because travel time changes depending on the
  level of volume/capacity ratio.

Do Example 7.
7
Calibrating a gravity model

• Calibration is done by developing friction
  factors and socioeconomic adjustment factors.
• Travel time is more properly called impedance.
  Impedance is a weighted sum of various types of
  times (walking, waiting, riding) and types of
  cost (fares, operating cost, tolls, parking
  cost). Cost is another factor of separation.

Input Data
Compare with O-D data (Yes, we need O-D data to
calibrate the model. O-D data collection is
costly. See Example 9) Or, adjust attraction
factors (Example 10).
Outputs
8
Calibrating a gravity model what do you get out
of this?

• Using the models trip table and the O-D survey
  data, we can check how close the model is
  replicating the reality of travel making.

9
Calibrating a gravity model what do you get out
of this? (cont)

• We can get the relation between F-factor and
  travel time.
• Smoothed values are typically non-linear.

ITE Planning HB, p. 113. NCTCOG data
Impedance
Friction factor
See Example 8.
10
Example 9 and 10

• Example 9 This example shows how to adjust trip
  distributions by changing the values of friction
  factor. This method requires O-D data.
• Example 10 This example shows how to adjust
  trip distributions by modifying trip attraction
  values. This method does not require O-D data.
  (It means there is no reality check because you
  assume the values of friction factors are
  accurate.)

Attraction factor, iteration k-1 (input)
(A bit of clarification for Example 10.)
Adjusted attraction factor for zone j, iteration
k.
Computed attraction factor, iteration k-1 (output)
Given attraction factor