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16-Civ-A6 Highway Design, Construction, and Maintenance · May 2013

Question 5 of 7: Trip distribution by the gravity model

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

Notes on this paper

Paper format. National Examination, 98‑Civ‑A6 Transportation Planning & Engineering (May 2013). Closed book, one two‑sided aid sheet, 3 hours. Seven questions; any five constitute a complete examination and each is of equal value (20 marks). All seven are solved below as a study resource.

Reference texts (subject).

Question 5: Trip distribution by the gravity model (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. Attraction of zone 8 and productions/travel times of the three origin zones.

Given data
Zone $i$Travel time $t_i$ (min)Production $P_i$ (now)Production $P_i$ (target)
12050005850
22565007475
34080009200
Zone 8 attraction $A_8$—20002500

Find. Trips $T_{i8}$ from each origin zone to zone 8, now (a) and in the target year (b); and other trip‑distribution factors (c).

Zone 1P=500020 minZone 2P=650025 minZone 3P=800040 minZone 8A=2000 trips
Singly‑constrained gravity model: the 2000 (later 2500) attractions of zone 8 are allocated to origin zones 1–3 in proportion to $P_i/t_i$.

Approach. With the friction factor $F_i=1/t_i$, the attraction of zone 8 is shared among the origins in proportion to the product $P_iF_i=P_i/t_i$ (a gravity model constrained to reproduce the attraction total).

  1. Gravity allocation formula. With friction $F_i=1/t_i$,
    $$T_{i8}=A_8\,\frac{P_i/t_i}{\sum_j P_j/t_j}.$$
  2. Weights for the base year (a).
    $$\frac{P_1}{t_1}=\frac{5000}{20}=250,\quad \frac{P_2}{t_2}=\frac{6500}{25}=260,\quad \frac{P_3}{t_3}=\frac{8000}{40}=200,\quad \sum=710.$$
  3. Base‑year trips (a). Multiply each weight share by $A_8=2000$:
    $$T_{18}=2000\tfrac{250}{710}=704,\quad T_{28}=2000\tfrac{260}{710}=732,\quad T_{38}=2000\tfrac{200}{710}=563.$$
    $$\boxed{T_{18}\approx704,\ T_{28}\approx732,\ T_{38}\approx563\ \text{trips/day}\ (\Sigma=2000).}$$
  4. Weights for the target year (b). Travel times are unchanged, so recompute $P_i/t_i$ with the new productions:
    $$\frac{5850}{20}=292.5,\quad \frac{7475}{25}=299.0,\quad \frac{9200}{40}=230.0,\quad \sum=821.5.$$
  5. Target‑year trips (b). Share the new attraction $A_8=2500$:
    $$\boxed{T_{18}\approx890,\ T_{28}\approx910,\ T_{38}\approx700\ \text{trips/day}\ (\Sigma=2500).}$$
Question 5 — trips to zone 8 (trips/day)
Origin(a) Base year(b) Target year
Zone 1704890
Zone 2732910
Zone 3563700
Total20002500

(c) Other factors affecting trip distribution

Besides travel time, the number of trips between zones depends on: the generalized cost of travel (fuel, fares, tolls, parking) rather than time alone; the attractiveness and size of the destination (floor area, mix and quality of shops, employment); socioeconomic characteristics of the travellers (income, car ownership, household size); the competition among alternative destinations (intervening opportunities); trip purpose; comfort, reliability and safety of the route; land‑use and demographic patterns; and the quality and connectivity of the transportation network and available modes.