Parameters of the Equilibrium_Lohse assignment

Equilibrium_Lohse: Basis tab

Element	Description
Route volumes	Route volumes are calculated according to the method of successive averages (MSA). Therefore, you need to define the exponent (value range 0 – 4). Notes For smoothing the route volumes, we recommend an exponent between 1 and 1.5. With exponent = 1 the formula complies with the formula used by the method of successive averages (MSA). This ensures a safe but slow convergence. A greater value normally reduces the number of iteration steps, but does not necessarily lead to convergence.
Estimated impedance	In the selection list, select the method for smoothing the estimated impedance. The methods provide different input options for the Delta value computation. Notes We recommend to test the three smoothing methods prior to the actual calculation. Heuristic rule Lotka-Volterra rule Note In most cases, the Lotka Volterra method is faster than the heuristic method; however, the quality of the calculation results depends on the used network. Method of successive average With this selection you define the exponent (value range 0 – 1). Notes For the exponent, we recommend a value close to 0.15. With parameter value = 1 the formula complies with the formula used by the method of successive averages. This ensures a safe but slow convergence. Do not smooth impedances This selection is used to obtain convergence faster if exponential smoothing of impedance values impairs the convergence of a procedure instead of improving it. If this entry has been selected, the currently estimated impedance equals the current impedance.

Element

Description

Route volumes

Route volumes are calculated according to the method of successive averages (MSA). Therefore, you need to define the exponent (value range 0 – 4).

Notes

For smoothing the route volumes, we recommend an exponent between 1 and 1.5.

With exponent = 1 the formula complies with the formula used by the method of successive averages (MSA). This ensures a safe but slow convergence. A greater value normally reduces the number of iteration steps, but does not necessarily lead to convergence.

Estimated impedance

In the selection list, select the method for smoothing the estimated impedance. The methods provide different input options for the Delta value computation.

Notes

We recommend to test the three smoothing methods prior to the actual calculation.

Heuristic rule

Lotka-Volterra rule

Note

In most cases, the Lotka Volterra method is faster than the heuristic method; however, the quality of the calculation results depends on the used network.

Method of successive average

With this selection you define the exponent (value range 0 – 1).

Notes

For the exponent, we recommend a value close to 0.15.

With parameter value = 1 the formula complies with the formula used by the method of successive averages. This ensures a safe but slow convergence.

Do not smooth impedances

This selection is used to obtain convergence faster if exponential smoothing of impedance values impairs the convergence of a procedure instead of improving it.

If this entry has been selected, the currently estimated impedance equals the current impedance.

Equilibrium_Lohse: Convergence criteria tab

Element	Description
Use classical convergence criteria	If this option is selected, the classic criteria described below are taken into account.
Use extended convergence criteria	If the option is selected, you can define additional termination conditions in addition to the classic convergence criteria. These are described further down in the table in the Extended section. The extended criteria can be used to check which links and turns show greater deviations in volume and/or impedance between iterations, and a minimum percentage of converged links and turns can be used as an additional convergence criterion (Fundamentals: Convergence criteria of assignment quality). Note The shares of network objects based on the extended convergence criteria are always calculated, regardless of the option set, and output in the PrT assignment quality data list.
Termination conditions	Maximum number of iterations Specify the maximum number of iterations after which the procedure ends if no convergence occurs. Maximum gap Measure of the difference between the current loaded state and the balanced state. The procedure terminates as soon as the value falls below.
Classical	Convergence statistics The settings you make here only take effect for the output of the shares in the PrT assignment quality data list. Relative difference between previous and current iteration Enter the desired value for the relative difference for link volume/impedance and turn volume/impedance for comparing results of successive iterations. The input values for links apply to the output of the shares of the connectors. Ignore links and turns with a volume < Network objects whose volume is beneath the defined threshold are not taken into account.
Extended	Relative difference between previous and current iteration For the comparison of results of successive iterations, a value for the relative difference must be defined for each convergence criterion. The calculation of the share of objects is based on the links or turns/main turns open in the network. Link volume <=/Link impedance <= Enter a numerical value and define the Share of links in percent that meet the respective condition. Turn volume <=/Turn impedance <= Enter a numerical value and define the Share of turns in percent that meet the respective condition. Note The input value for the share applies to both the turn and the main turn together. Ignore links and turns with a volume < Network objects whose volume is beneath the defined threshold are not taken into account. Consider only active links and turns If the option is selected, the termination is based on the relative differences for the active links, turns, and main turns. Number of iterations taken into account for convergence Enter the number of iterations to be taken into account. Notes The assignment is considered converged if the condition for link volume or link impedance, the condition for turn volume or turn impedance, and the condition for the gap are fulfilled. In addition, these criteria must be fulfilled in the specified number of consecutive iterations. The convergence attributes of the assignment are always stored at links, turns, main turns, and connectors.