# Distribution and Modal Split Functions

### Technical Note #29

*January 2018*

*By Margarida Delgado*

Since version 8.2 of Aimsun, the Distribution and Modal Split steps have been separated into two different processes, each with their own Scenario and Experiment. Each of these two steps needs its own set of two types of function:

*Figure 1 – Distribution functions and Modal Split functions*

#### Distribution

The Distribution process implements a gravity model, where you need to specify (a function to model) the resistance for making a trip between each particular OD pair, given the (combined skim costs or) impedance for that OD pair.

– Distribution Deterrence functions model the reluctance to make a trip given its impedance. You select the Deterrence function in the Distribution Experiment, so if you want to set up different discrete choice functions, such as per trip purpose, you will need to define a distribution scenario and experiment per purpose, changing the distribution deterrence function that you want to use each time.

*Figure 2 – Distribution experiment editor*

An example of Distribution Deterrence function could be a Gamma function:

*Figure 3 – Example of Distribution Deterrence function*

– Distribution Impedance functions give the formula that combines the different available costs (distance, travel time, price, etc.) to take into account.

*Figure 4 – Distribution Area editor*

An example of Distribution Impedance function is a linear function that combines distance and travel time:

*Figure 5 – Example of Distribution Impedance function*

#### Modal Split

The Modal Split step calculates, for each OD pair, the probability of use for each transportation mode available, based on the utilities per transportation mode.

– Modal Split Discrete Choice functions calculate the probabilities within the available transportation modes. You select the Discrete Choice function in the Modal Split Experiment, so if you want to set up a different discrete choice function, e.g., per trip purpose, you will need to define a modal split scenario and experiment per purpose, changing the discrete choice function that you want to use each time.

*Figure 6 – Modal Split experiment editor*

An example of a Discrete Choice function is the Multinomial Logit, where probabilities are calculated according to the utilities, following the formula:

*Figure 7 – Example of Modal Split Discrete Choice function*

– Modal Split Utility functions represent the utility of each transportation mode according to the values of different variables, usually in linear form.

*Figure 8 – Modal Split Area editor*

Utility functions are usually linear functions depending on different cost variables (xi):

*Figure 9 – Example of Modal Split Utility function*