Estimating gravitation parameters (KALIBRI)

The Estimate gravitation parameters function (short KALIBRI) allows you to calibrate two different utility functions (determine parameters a, b and c) for the gravity model used for trip distribution.

1.  

where

Uij	Value of the utility (for example distance or travel time) between zone i and zone j
a,b,c	Parameters to be estimated

2.  

where

Uij	Value of the utility (for example distance or travel time) between zone i and zone j
a,c2	parameters to be estimated

The KALIBRI function adjusts these utility functions to a given trip length distribution.

Then the Trip distribution function calculates the traffic flow Fij (from zone i to zone j) with the aid of the gravity model and known data, namely the source traffic Qi (of zone i), destination traffic Zj (of zone j) and the parameters a, b, c (or a,c) specified here (Gravity model calculation).

The KALIBRI function provides two options that allow you to estimate the parameters for the gravity model.

• Singly-constrained production
• Doubly-constrained (Multi procedure)

Parameters a, b, c or a, c respectively are determined in an iterative process. The utility function is transformed during this process; with

[2]

or

[3]

Within each KALIBRI iteration a temporary demand matrix is calculated (for example via Multi procedure with option doubly-constrained gravity model). The resulting values of the utility function are smoothed by linear regression until the maximum number of KALIBRI iterations is reached or the values do not change anymore. The smoothed values then describe a function of type [2] or [3].