Gravity model

The gravity model is a method for distributing trips between origins and destinations based on their characteristics and the distance between them, analogous to Newton’s law of gravitation.

The gravity model operates on the analogy of gravitational force, considering factors such as trip production and attraction along with travel costs to estimate trip distribution. Balancing factors are introduced to ensure that the total trips produced and attracted are maintained in the model.

Gravity Model

The gravity model for trip distribution draws an analogy from Newton's gravitational law, which states that gravitational force is proportional to the product of the masses involved and inversely proportional to the square of their distance apart. This model represents the interaction between origins (trip producers) and destinations (trip attractors) based on their respective sizes and the cost associated with travel between them.

Key Points:

• Formulation: The basic formula is expressed as:

  $T_{ij} = C \times O_i \times D_j / c_{ij}$

  where:

  • T_{ij} = trips from origin i to destination j
  • O_i = number of trips produced in zone i
  • D_j = number of trips attracted to zone j
  • C = constant, and c_{ij} is the generalized cost of travel from i to j.

• Balancing Factors: To maintain the integrity of the model with total trip productions and attractions, balancing factors A and B are applied:

  $T_{ij} = A \times O_i \times B \times D_j \times f(c_{ij})$

  where $f(c_{ij})$ is a deterrent function representing disincentives to travel as cost or distance increases. Different versions of this function include:

  • Exponential: $f(c_{ij}) = e^{-\beta c_{ij}}$
  • Power: $f(c_{ij}) = c_{ij}^{-n}$
  • Combination: $f(c_{ij}) = c_{ij}^{-n} \times e^{-\beta c_{ij}}$

• Constrained Models: The model can be singly or doubly constrained, allowing flexibility based on available data. For a doubly constrained model, both productions and attractions are considered, ensuring that:

  • $\Sigma T = D$

• Iterative Process: Solving for A and B is done iteratively, ensuring the trip distributions balance according to the observed data.

Significance of the Gravity Model:

The gravity model is significant as it provides a theoretical foundation for understanding travel patterns. By factoring in the characteristics of zones and the costs of travel, planners can reliably predict the distribution of trips, thereby guiding transportation planning and assessments. This model is especially useful in the context of urban design and policy formation.