This post originally appeared on Orphan Road.

Ever wonder how mode choice is modeled? If yes read on…

Mode choices models came to the transportation field via psychology. These models were created to account for the competing forces populations take into account when deciding between a set of options. The model essentially attempt to re-create how people weight the costs and benefits of each mode.

I would first like to walk you through utility equations for each of the modes. When mode choice models are trying to determine how a population will travel it computes the possible utility values for each mode and then compares them to each other. The larger the number (i.e. less negative) the higher the utility and the more desirable it is.

U = utility
TT = travel time

U(sov) = -0.189*TT – 0.0151*cost

The SOV is used as the baseline against which everything else is measured to. From the SOV utility equation you can determine the inferred cost of time. It is very simple and essentially takes into account how long it takes and how much it cost. The travel time includes “terminal time” i.e. getting to your car and then parking and walking to your destination. Cost includes operational cost as well as parking.

U(hov) = -4 -0.189*TT -0.0151*(cost/occupant)

The constant at the beginning of the equation shows that this mode is inherently less desirable than driving alone. The utility of time has not changed and the cost are split between the occupants of the vehicle.

U(bus) = -8 -0.189*TT -0.0151*cost – 0.291*wait -1.427*#transfers

As you can see determining transit utility is much more complicated. The inherent utility of transit is much lower. The utility of time has not changed but the value of waiting is much higher. This essentially says that waiting for the bus for 5 minutes feels like riding the bus for over 7.5 minutes. The last value is the “transfer penalty” which accounts for lower desirability of transferring even if it will be faster. In this circumstance one transfer is equal to about 7.5 minutes.

Next the utility for each mode is raised to the natural log (e^U). These values are summed and then each mode’s utility raised to the natural log is divided by the previous sum. This will give you the mode split probability. The number of trips from one place to another is multiplied by these probability and you’re done!

Below are a few graphs that I made to show what the model predicts will happen with certain changes. I purposefully did not show numbers because they are not calibrated and I only wanted to show the trends. Scenario 1 has the lowest auto cost and time while Scenario 8 has the highest auto cost and time. You can see that this models shows that SOV’s are much more sensitive to increases in prices than HOV’s. This makes sense because the utility equation divides the cost of the trip between the number of occupants. You will also notice how it takes a while to before the bus starts increasing. This is because it has such a low inherent utility. In this graph you can see how increasing travel time for SOV/HOV while keeping transit travel times constant can change mode split. You can see how both SOV and HOV shrink at the same rate because they use the same utility constant for travel time. You can also see how the change is not linear. This is a result of setting a negative number to the natural log. The last graph is a combination of the first and second graphs.

Coming Next: Delay Calculations