Table 1a. Travel Times ; HBW Ps & As ; Base and Future Demographics
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         -Base Travel Time-   -Base Trips-  -Base Demo-  -Future Demo-
 From\To  1   2   3   4   5   PROD   ATTR   WORK   EMPL   WORK   EMPL
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   1      1   3   3   6   3      0    450      0    220      0    216
   2      3   1   2   6   5      0    250      0    110      0    118
   3      3   2   1   5   6    300      0    140      0    250      0
   4      6   6   5   1   4      0    300      0    140      0    166
   5      3   5   6   4   1    700      0    360      0    472    166
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 Totals                       1000   1000    500    470    722    666
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                    Table 1b. Base HBW Trip Table
                    ------------------------------
                     FROM\TO    1    2    4  Prod
                    ------------------------------
                        3     125  125   50  300
                        5     325  125  250  700
                    ------------------------------
                      Attr    450  250  300 1000
                    ------------------------------

Problem 1. Trip Generation (10 points)
Household HBW trip production and attraction models for the region have been estimated as functions of workers per zone (WORK) and employees per zone (EMPL), respectively:

1. Estimate a measure of goodness-of-fit for each of the above models using the base data. For example, compute the root mean square error, RMSE=sqrt[(Σ(est-obs)²)/n]. Comment on the fit.
2. Use the demographic forecasts provided to predict future trip ends for the production and attraction models. These estimates will be used in the trip distribution forecast below. Tabulate.

Problem 2. Trip Distribution: Calibration (20 points)
By hand, calibrate a HBW singly-constrained gravity model for trip distribution for the base year data.

1. Develop the travel time frequency distribution based on one minute travel time intervals. Set all initial friction factors equal to one. Complete a minimum of 3 iterations, using a 5 percent convergence tolerance. Apply "Attraction Factoring" or "Column and Row Factoring" at each iteration. Show all work.
2. How close are the trip matrix cells to the base distribution? How could you adjust the cells for a better fit? What are the limitations of your adjustment process?
3. Estimate the mean trip length (time) for the base trip distribution results (note: these estimates do not reflect congested travel times).

Problem 3. Trip Distribution: Application (10 points)
Using future forecasts from the trip generation models in Problem 1 and an effective change in travel time to 2 minutes for Zone 3 to Zone 1, estimate the future trip distribution. Estimate the mean trip length (time) for the future distribution and compare to the base mean trip length.

• [cee223 only] Do Either Problem 4a or 4b •

Problem 4a. Trip Distribution: DCGM (10 points)
Using the calibrated friction factors from the HBW Singly-Constrained Gravity Model of Problem 2, complete one iteration of a Doubly-Constrained Gravity Model application.

1. Compute the balancing terms (a_i and b_j) and estimate the trip matrix.
2. Determine the corresponding Trip Length Frequency Distribution. Is the DCGM within the final convergence tolerance of the SCGM in Problem 2?

Problem 4b. Trip Distribution: Growth Factors (10 points)
Using future forecasts from the trip generation models in Problem 1, estimate future HBW trip distribution using the Furness growth factor model (Row and Column Factoring). Use a 5 percent convergence tolerance or a maximum of two iterations. Growth Factor Models cannot project growth in zones where no base activity exists, so ignore the added future employment in Zone 5. Hint: Simply use future productions and attractions to "column and row factor" the base trip matrix.

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 only households 10 through 12 in this exercise.

1. 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.
2. 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.
3. Calculate the associated OD trip table and the PA trip table.