# Modal Split Submodule of SMARTPLANS

The Modal Split Submodule uses the inter-zonal trips T_{ij|p} that are estimated via the Trip Distribution Submodule, to predict trips T_{mij|p} by transportation mode m between origin zone i and destination zone j for each trip segment p. More specifically, the Modal Split Submodule starts by predicting the probability of trips to be taken with a certain mode of transportation m based on various level-of-service (LOS) variables describing that specific mode and socio-economic characteristics describing the travelers making the trips. In the SMARTPLANS program, the multinomial logit (MNL) model is used to estimate the probability P_{mij|p} of choosing a particular mode m to make trip type p between zones i and j:

where V_{mij|p} is linear-in-parameter systematic utility that is formulated as a linear function of LOS variables influencing mode m and socio-economic variables describing the attributes of the traveler in the zone. Example of an LOS variables may include the in-vehicle travel time between zones i and j. On the other hand, an example of a socio-economic variable may include average household income in the origin zone i. Trips by transportation mode m are then calculated as follows:

In the program, the user can define the number of alternative travel modes for each trip segment p and specify the parameters of the utility function pertaining to each alternative.

The Modal Split Submodule also calculates a Logsum (i.e., transportation accessibility) variable. This variable is crucial as it integrates the Transportation Module to the Land Use Module to establish the feedback-loop between the two systems. More specifically, the Logsum value is often an influential variable in both Population Location Choice Model and Employment Location Choice Model. The program allows the user to select the trip segment p from which the logsum variable will be generated. For example, the user could choose to calculate the Logsum for only work trips only.

SMRTPLANS starts the calculation of the Logsum using the utility functions of the specified modes. At first, the program calculates matrix **L _{p}** with elements L

_{ij|p}as follows:

where V_{nij|p} is the utility of each of alternative and n is the total number of alternatives presented in the model.

Next, SMARTPLANS offers two types of zonal Logsum calculations:

- Type 1: The program here simply takes the sum of each row of matrix
**L**to create the vector containing the Logsum value of each zone i. That is:_{p}

- Type 2: The program here calculates the Logsum according to the following steps:
- Calculate matrix
**PT**with elements PT_{p}_{ij|p}from the trip matrix predicted by the trip distribution model, that is:

- Calculate matrix
**Q**with elements Q_{p}_{ij|p}as follows:

- Calculate a vector containing the Logsum value of each zone i as follows:

- Calculate matrix

Regardless of which type of Logsum calculation is chosen, the final logsum zonal values will be stored in the zonal variable specified by the user and used as input to the Land Use Module in time t+1 simulation.