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

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 Newton’s 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 I’s 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 model’s 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 Friction factor Impedance 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