The Estimate gravitation parameters function (short KALIBRI) allows you to calibrate two different utility functions (determine parameters 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 |
|
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 |
|
c2 |
Parameter 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 b, c (or just c) specified here (Gravity model calculation).
The KALIBRI function provides two options that allow you to estimate the parameters for the gravity model.
Parameters b, c or c respectively are determined in an iterative process. The utility function is transformed during this process; with
or
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].
If a log file is generated (option on the Output tab), you can find a summary of the estimation results in it. The quality of the estimate is also indicated. It is defined by
and represents the average relative deviation of the shares in the model from the empirically measured target shares. Ideally, the quality is 1 (perfect match) and decreases with decreasing values. A negative quality is equivalent to very strong deviations and thus a rather poor parameter estimation.
