Spring 2021: Michael G. McNally (mmcnally-at-uci-dot-edu) [15460]
Homework #6 -- Trip Distribution Modeling [ S O L U T I O N S ]
The following problems deal with a hypothetical, 4-zone region (this data will be used in a subsequent trip assignment homework). Table 1 summarizes surveyed activity system and trip generation data (productions and attractions) for 2020 and estimates of activity system variables for 2030.
Table 1. Base and Future HBW Trips and Demographic Data Summary
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HBW HH(i) C(i) W(i) E(j) I(i)
P(i) A(j) Households Cars Workers Empl. Inc.
Zone '20 '20 ---------- ---------- ---------- ---------- -----
'20 '30 '20 '30 '20 '30 '20 '30 both
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1 825 710 321 330 447 460 390 395 300 300 Low
2 775 800 402 470 360 420 345 480 360 450 Med
3 910 970 330 300 396 375 582 570 600 690 High
4 865 895 375 420 450 465 399 450 456 455 Med
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Tot 3375 3375 1428 1520 1653 1720 1716 1895 1716 1895 N/A
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Problem 1. Trip Generation [10 points]
Household HBW trip production and attraction models for the
region as a whole have been estimated and found to be significant.
Pi = 34.8 + 0.59 HHi + 0.80 Ci + 0.63 Wi
Aj = 485.1 + 0.84 Ej
- Using the base data, apply the models and estimate a goodness-of-fit measure for each model. For example, compute the root mean square error, RMSE=sqrt[(1/n)Σ(est-obs)^2]. Comment on the fit.
- Use the demographic forecasts provided to predict and tabulate future trip ends for the production and attraction models. These estimates will be used in the trip distribution forecast.
Solution:
Analysis is best accomplished via a spreadsheet.
Problem 2. Trip Distribution: Calibration (20 pts)
By hand, calibrate a singly-constrained trip distribution model for the base
year data. Show ALL calculations for three iterations. Does the model converge?
Use 5-minute time categories and Attraction Factoring.
Table 2. Base Travel Time and Trip Distribution Matrix (2020)
---------------------------------------------------------------
BASE Travel Times BASE Trip Interchanges
---------------- --------------------- P(i)
From\To 1 2 3 4 From\To 1 2 3 4
---------------------------------------------------------------
1 5 16 13 18 1 250 125 375 75 825
2 16 7 20 12 2 100 400 50 225 775
3 13 20 2 9 3 205 60 225 420 910
4 18 12 9 3 4 155 215 320 175 865
---------------------------------------------------------------
A(j) 710 800 970 895 3375
---------------------------------------------------------------
Solution: The FHWA production-constrained gravity model is calibrated via the standard friction factor method. Table 2a below summarizes only the results of the estimated trip length frequency distribution at each interation. Attraction Factoring was performed at each iteration. A minimum of 3 iterations was required and the model did converge within 5 percent in 3 iterations (within 1 percent by the 5th iteration).
Table 2a. SCGM Friction Factor Calibration Iterations
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Travel OD Pairs Observed Iter # 1 Iter # 2 Iter # 3
k Time in Time ----------------- ---------- ---------- ----------
Interval Interval Trips (%) Fk (%) Fk (%) Fk (%) Fk
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1 0 - 5 11,33,44 650 19.3 1.00 19.7 0.98 19.1 0.99 19.7 0.96
2 6 - 10 22,34,43 1140 33.8 1.00 20.0 1.69 31.6 1.81 32.3 1.89
3 11 - 15 13,31,24,42 1020 30.2 1.00 24.9 1.22 31.3 1.17 30.5 1.16
4 16 - 20 12,21,14,41,23,32 565 16.7 1.00 35.5 0.47 17.9 0.44 17.6 0.42
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Converged after 3 Iteration (all F-bins +/- 5%)
Table 2b. SCGM Calibration Iterations Trip Matrices and Adjusted Attractors
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----- Iter 1 ----- ----- Iter 2 ----- ----- Iter 3 -----
i\j 1 2 3 4 i\j 1 2 3 4 i/j 1 2 3 4 Pi
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1 174 195 237 219 1 215 116 364 130 1 268 118 323 116 825
2 163 184 223 205 2 80 324 110 261 2 90 363 91 231 775
3 191 216 261 242 3 212 93 233 372 3 246 91 208 365 910
4 182 205 249 229 4 76 220 371 198 4 88 228 361 188 865
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Aj 710 800 970 895 Aj 583 753 1078 961 Aj 692 800 983 900 3375
Wj 710 800 970 895 Wj* 865 850 873 834 Wj* 888 850 861 829
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Problem 3. Trip Distribution: Application (10 points)
In response to identified problems in the base network and to anticipated traffic
volumes from future growth, a network infrastructure project has been planned that
would change base travel times between some zones. In general, infrastructure would
be improved around Zone 1 (low income with little projected growth) while problems
identified in Zone 4 would not be addressed.
Forecast the future total trip matrices using the trip generation forecast from Problem 1, the calibrated model from Problem 2, and the original (A0) and new (A1) skims given in Table 3. Utilize column/row factoring on the final trip table.
Table 3. Base and Future Transportation System Skims
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BASE Travel Times FUTURE Travel Times
2020 ---------------- 2030 -----------------
From\To 1 2 3 4 From\To 1 2 3 4
------------------------------------------------------
1 5 16 13 18 1 6 14 11 14
2 16 7 20 12 2 14 8 17 15
3 13 20 2 9 3 11 17 3 11
4 18 12 9 3 4 14 15 11 5
------------------------------------------------------
Solution:
Forecasted P's and A's (balanced) are utilized, first, with existing skims (A0),
and then with future skims (A1). Since travel times have changed for some zone pairs,
associated friction factors will also change (e.g., trips from 1 to 2 used F4 in the
base but F3 in the future). Forecast trip tables were Column & Row Factored. Note
that column sums do not exactly match but are within one percent of the forecasted
Trip Generation results. The spreadsheet output is provided for A0 and A1. Note the
changes in the forecast P/A trip table for the two future scenarios.
A0. Future Ps and As with Base Skims
-s21k.png)
A1. Future Ps and As with Future Skims
-s21k.png)
Comments: What changes can you notice? WHile it's easier to look for link volume changes after trip assignment is completed, you can notice differences in the two trip tables (for A0 and A1). From the skims, travel times to and from TAZ 1 have been reduced, while most times to and from TAZ 4 have deteriorated. The resulting A1 volumes, compared to A0 volumes, show decreases in intrazonal trips in TAZ 1 and 2, and increases in trips between TAZs 1 and 4. Demographic changes also come into play. What changes do you think multiply the impacts of travel time? A full analysis would \ compare both A0 and A1 to the base year, as well as A1 to A0.
Problem 4. Trip Distribution: Performance (10 points)
Summary statistics help describe the overall flow pattern at the end of trip
distribution. Using skim tree times for the base and future networks, and
the base and estimated future trip distribution matrices, compute the average
trip travel times for 2020 and 2030. Tabulate total trips, total time, and
average travel times for each year.
Solution:
Calculation Results: results.
Summary results are provided in Table 4. In A0, average travel times increase,
particularly for interzonal trips. In A1, the increase is somewhat less for
interzonal but greater for intrazonal. The results vary geographically (see below).
Table 4. Summary Statistics for Base and Future Trips ----------------------------------------------------------- Performance BASE A0 A1 Measure (observed) (est.) (est.) ----------------------------------------------------------- Total Trips 3375 3606 3606 - Interzonal 2325 2474 2482 - Intrazonal 1050 (31%) 1132 (31%) 1124 Total Travel Time 34445 37249 39030 - Interzonal 29420 31647 32670 - Intrazonal 5025 5602 6360 Average Travel Time 10.21 10.33 10.82 - Interzonal 12.65 12.79 13.17 - Intrazonal 4.79 4.95 5.66 -----------------------------------------------------------
Problem 5. Travel Surveys (20 points)
The spreadsheet provides 2020 household socio-economic and
travel diary data for a sub-sample of Miasma Beach households. Use households 4 through 6.
- Calculate the trip travel time, activity duration, and trip purpose
classification (HBW, HBO, or NHB) for each trip and append to the table.
Compute the mean travel time by mode and mean activity duration by
purpose. Submit a hardcopy (e-copy optional) of the updated spreadsheet.
SOLUTION: Calculation results.
Note: All times expressed as hours:minutes. Mean travel time was 12 minutes (9 min for 7 walk trips (19%); 10 min for 6 bike trips (16%); 25 minutes for 4 bus trips (11%); and 11 min for 20 car trips (54%)). Mean activity duration was 2:50, with 6:36 for work/school activities and 0:41 for non-work activities (durations not computed for return home trips). Note activity types do not follow the trip type classification (e.g., the first two work activities are actually at the end of, first, an HBW trip and, second, a NHB trip).
- Plot the travel patterns on a Miasma Beach network map. Label each trip end
as a production (P) or attraction (A) and label the trip type (HBW, HBO, NHB).
Use color and/or line types to distinguish individuals and/or trip types. You
may need to plot households on separate maps.
Solution Map not shown in this solution key. Trips can be drawn as straight lines between the origin and destination centroids, and should be color-coded by trip type (e.g., HBW).
- Calculate the associated OD trip table and the PA trip table.
Solution S'2021 (All trip types)
PA Table 1 2 3 4 5 6 Pi OD Table 1 2 3 4 5 6 Oi
======== === === === === === === === ======== === === === === === === ====
1 1 1 - - - - 2 1 1 2 - - - 2 5
2 3 4 - - - - 7 2 2 4 1 - - 1 8
3 - 2 5 - - 6 13 3 - 1 5 - - 7 13
4 - - - - - - 0 4 - - - - - - 0
5 - - - - - - 0 5 - - - - - - 0
6 4 2 8 - - 1 15 6 2 1 7 - - 1 11
======== === === === === === === === ======== === === === === === === ====
Aj 8 9 13 0 0 7 37 Dj 5 8 13 0 0 11 37
If you've correctly plotted the Os and Ds in part (c), the total Os and Ds in each zone should match. Try to code each trip by Ps and As and you'll see that this will match the PA trip table.
Last Updated: 19 May 2021