CE 326:

Transportation

Planning TRIP DISTRIBUTION

Goal of Trip Distribution

To distribute productions among attractions

To obtain inter-zonal flows

Trip Conservation

Production Conservation

𝑇𝑖𝑗 = 𝑃𝑖 ∀ 𝑖

𝑗

where Tij is the trip interchange from zone i to zone j

Pi is the total number of productions from zone i

Attraction Conservation

𝑇𝑖𝑗 = 𝐴𝑗 ∀𝑗

𝑖

Aj is the total number of attractions to zone j

Trip Distribution Models

Growth Factor Model (e.g. Fratar model)

Gravity Model

Growth Factor Model

Theory: Preserves historical relationships

Often used to estimate external trips (those either

produced and/or attracted outside of study region)

Fratar Model Steps

1) Given: Observed average interzonal trips from zone i to zone j (𝑇𝑖𝑗0)

2) Compute zonal growth factors based on expected changes in land use (𝐺𝑖

𝑜 = 𝐺𝑗𝑜)

3)Estimate expected future trips per zone

𝑇𝑖𝐸 = 𝑇𝑖

0𝐺𝑖𝑜

4) Apply growth factors directly to observed trips to estimate expected

trips for each zone pair

𝑇𝑖𝑗𝑛 = 𝑇𝑖

0𝐺𝑖𝑜𝑇𝑖𝑗0𝐺𝑗𝑜

𝑇𝑖𝑗0𝐺𝑗𝑜

𝑗

5) Estimate expected trips for individual zone pairs

𝑇𝑖𝑗𝑛 =𝑇𝑖𝑗𝑛 + 𝑇𝑗𝑖

𝑛

2

6) Calculate new Growth Factor; stop when sufficiently close to 1

𝐺𝑛+1 =𝑇𝑖𝐸

𝑇𝑖𝑛

Limitations of Growth Factor

Models

Advantages

Simple

No LOS information needed

Disadvantages

May break down mathematically when a new zone is added

Convergence to the target-year generation totals is not always possible

The model is not sensitive to impedance (No project/policy effect)

No congestion impact

Newton’s Law of Gravitation

“The force of attraction between two bodies is

directly proportional to the product of the masses of

the two bodies and inversely proportional to the

square of the distance between them”

Trip Distribution Formula

“The interchange volume between a trip-producing zone i and

a trip-attracting zone j is directly proportional to the magnitude

of the trip productions of zone i and the trip attractions of zone j

and is inversely proportional to a function of the impedance Wij

between the zones”

Dependent variable: i to j volume

Independent variables: Productions, attractions, impedance

Model Parameters: k, c; estimated through calibration

Friction Factor

Friction factor (or travel time factor)

Fij is a measure of the impedance from i to j

We need to know the relative impedance to zone j compared

to all zones

Socioeconomic Adjustment Factors

Fij is often estimated as a function of only one variable (usually

travel time)

Kij incorporates the effects not captured by the limited number

of independent variables in the model

Relative attractiveness

of zone j compared to

all other zones

Limitations of the Gravity

Model

Does not consider individual user or household characteristics in trip

decision-making process (although separate models can be

developed for stratified groups)

K-factors difficult to interpret, may not remain constant between

observed and predicted years