We live in an era of unprecedented mobility—vehicles are much more affordable than they were at their inception in the early 20th century, and public transport provides an easy and economical means of travel for those without a personal vehicle. The latest trend in the transportation industry is that of car-sharing. 

Realizing that purchasing and owning a personal vehicle can be unnecessarily expensive, individuals are starting to turn to cheaper and more distributed means of paying for private vehicle transport. 

In order to help illuminate various aspects of the car-sharing process, our team developed mathematical models that address some of the main factors influencing car-sharing companies’ decisions. 

First, we developed a model that determines the proportion of drivers that fit into categories--low, medium, and high—for both hours driven per day and miles driven per day.

We realized that much of the information regarding these two factors depended greatly on the amount of traffic in an area or city, which subsequently depended on the population density of that region. Hence, we created a function that gives the expected number of miles driven in a day based on the population density of the city or region and the number of hours driven in a day. 

We then placed a normal distribution around this expected average value and integrated a weighted cumulative distribution function of that distribution over time to get a table of proportions of drivers in each category.