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:

Distribution and Modal Split Functions in Aimsun traffic modelling software

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.

Distribution and Modal Split Functions in Aimsun traffic modelling software

Figure 2 – Distribution experiment editor

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

Distribution and Modal Split Functions in Aimsun traffic modelling software

Distribution and Modal Split Functions in Aimsun traffic modelling software

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.

Distribution and Modal Split Functions in Aimsun traffic modelling software

Figure 4 – Distribution Area editor

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

Distribution and Modal Split Functions in Aimsun traffic modelling software

Distribution and Modal Split Functions in Aimsun traffic modelling software

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.

Distribution and Modal Split Functions in Aimsun traffic modelling software

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:

Distribution and Modal Split Functions in Aimsun traffic modelling software

Distribution and Modal Split Functions in Aimsun traffic modelling software

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.

Distribution and Modal Split Functions in Aimsun traffic modelling software

Figure 8 – Modal Split Area editor

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

Distribution and Modal Split Functions in Aimsun traffic modelling software

Distribution and Modal Split Functions in Aimsun traffic modelling software

Figure 9 – Example of Modal Split Utility function