16-Civ-A6 Highway Design, Construction, and Maintenance · May 2015

Question 3 of 7: Trip Generation — Cross-Classification and Regression

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Examination — 98-Civ-A6 Transportation Planning & Engineering, May 2015. Closed book (one two-sided aid sheet), 3 hours. Seven questions of equal value (20 marks); any five constitute a complete paper. All seven are solved here as a study resource.

Reference texts (subject):

• Papacostas, C.S. & Prevedouros, P.D., Transportation Engineering and Planning, 3rd ed. (Prentice Hall).
• Roess, R.P., Prassas, E.S. & McShane, W.R., Traffic Engineering, 4th ed. (Pearson).
• Mannering, F.L. & Washburn, S.S., Principles of Highway Engineering and Traffic Analysis, 6th ed. (Wiley).
• Ortúzar, J. de D. & Willumsen, L.G., Modelling Transport, 4th ed. (Wiley).
• Sheffi, Y., Urban Transportation Networks (Prentice Hall).

Question 3: Trip Generation — Cross-Classification and Regression (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A cross-classification trip-rate matrix (trips per household) and a matching matrix of forecast household counts, both indexed by cars (rows 0, 1, 2+) and workers (columns 0, 1, 2, 3+).

Trip rate (trips/household) — left — and forecast households — right

Cars \ Workers	0	1	2	3+		0	1	2	3+
0	0.9	2.1	3.4	5.3		120	80	60	30
1	3.2	3.5	3.7	8.5		50	210	270	240
2+	—	4.1	4.7	8.5		—	40	70	190

Find. (a) trips per cell and the zone total by cross-classification; (b) trips per cell and the total using the regression rates, with the sign/effect interpretation; (c) a comparison of the two methods.

Approach. For (a) multiply each cell's empirical rate by its household count and sum; for (b) evaluate the regression rate for each (car, worker) combination (capping the variables) then multiply by households and sum.

(a) Cross-classification (category analysis)

1. Cell trips = rate × households. The forecast trips in a cell are $$T_{c,w}=r_{c,w}\times H_{c,w}.$$ Evaluating every occupied cell (trips):

   (a) Forecast trips by household type

   Cars \ Workers	0	1	2	3+	Row total
   0	108.0	168.0	204.0	159.0	639.0
   1	160.0	735.0	999.0	2040.0	3934.0
   2+	—	164.0	329.0	1615.0	2108.0

2. Zone total. Summing the three row totals: $$T_{(a)}=639.0+3934.0+2108.0.$$ $$\boxed{T_{(a)} = 6681\ \text{trips.}}$$

(b) Regression estimate

1. Interpret the coefficients. In $r = 0.77 + 1.60\,\text{WORKER} + 1.06\,\text{CAR}$, both slopes are positive: each additional worker adds 1.60 trips/day and each additional vehicle adds 1.06 trips/day to the household rate. Workers have the stronger marginal effect. The variables are capped (WORKER at 3, CAR at 2), so a 3+/2+ household is evaluated at WORKER = 3, CAR = 2.
2. Evaluate the rate for each combination. For example $r_{1,2}=0.77+1.60(2)+1.06(1)=5.03$ and $r_{2,3}=0.77+1.60(3)+1.06(2)=7.69$. The full rate grid and the resulting trips ($r\times H$):

   (b) Regression rates and forecast trips

   Cars \ Workers	0	1	2	3+	Row total (trips)
   0 (rate)	0.77	2.37	3.97	5.57	—
   0 (trips)	92.4	189.6	238.2	167.1	687.3
   1 (rate)	1.83	3.43	5.03	6.63	—
   1 (trips)	91.5	720.3	1358.1	1591.2	3761.1
   2+ (rate)	2.89	4.49	6.09	7.69	—
   2+ (trips)	—	179.6	426.3	1461.1	2067.0

3. Zone total. Summing the occupied cells: $$T_{(b)}=687.3+3761.1+2067.0.$$ $$\boxed{T_{(b)} \approx 6515.4\ \text{trips.}}$$

(c) Comparison of the two methods

The two totals are close (6681 vs 6515), but they rest on different assumptions. Cross-classification (category analysis) uses the empirical average rate observed for each discrete household category. It makes no functional-form assumption and naturally captures non-linear and interaction effects (for example, the jump to 8.5 trips at 3+ workers, and the fact that the worker effect differs by car-ownership row). Its limitations are that it needs an adequately sampled rate for every occupied cell, it cannot produce a value for a cell it never observed (note the empty 2+ cars / 0 workers cell), the categories are coarse, and forecasting relies on the rates staying stable over time.

Regression fits one smooth linear surface with only three parameters. It is parsimonious, it can fill the missing cell by extrapolation, and it summarises the marginal effect of each variable in a single coefficient. Its cost is the built-in assumptions of linearity and additivity: it forces a constant increment per worker and per car and cannot represent interactions or saturation, so it systematically over- or under-predicts at the extremes and, being continuous, can even yield non-integer or (in principle) negative rates outside the fitted range. The small total difference here reflects exactly this smoothing.

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