The Traffic Management Software System developed in this study is a vast improvement upon existing systems, as it makes use of Braess' paradox to individualize and optimize the routes drivers take to their destination. Braess' paradox states that, as drivers tend to make selfish decisions regarding their path, drivers will all elect to take any faster, more efficient path opened - thus increasing travel time on that path, and our traffic management software system makes use of this paradox by individualizing routes for drivers so that they do not all take the same shortcut or, in the event of construction or an accident, the same detour, thereby clogging it. This is an improvement on existing traffic management systems because existing traffic management systems will direct all drivers to the same route, which increases the volume of traffic on these routes and the amount of time it takes to travel on them. If there is construction or a car accident on a given road, all cars will be directed to the same detour route, which will create a high volume of traffic on that road. If a new, shorter road is opened, drivers will all be directed to use it, and the road will become clogged. These roads are always suggested to drivers no matter what the traffic volume is. However, our traffic management software disincentivizes, or renders temporarily unusable, high traffic roads due to the high amount of congestion. However, this problem is solved with the customization of routes for individual drivers, and the opening and closing of certain routes to drivers based on their traffic volume. Routes are output by the software system by using the demand and capacity of these routes, and the travel time on them, to generate 'Braess routes', which are routes deemed efficient by the software and a function of route demand and travel time. When a Braess route becomes congested, it is disincentivized, thus eventually eliminating the high traffic. This is achieved using the Frank Wolfe algorithm, which formulates and minimizes linear approximations of the route demand and travel time functions used to output the Braess routes. The use of these individualized Braess routes that don't direct all drivers to the same shortcut or the same detour, and the disincentivization of congested routes both help to reduce road congestion and travel time. A SUMO GUI is specifically a visual interface that was able to be implemented when models of the traffic system were present. This indicates that our software was able to correctly identify the Braess routes as they continually changed, as well as that our original hypothesis, that applying Braess' paradox to a traffic management software and customizing routes to maximize efficiency for individual drivers would decrease overall travel time. Therefore, we have developed a system that can apply the Frank-Wolfe Algorithm and Braess' paradox in order to identify new or changing Braess routes. Our findings have also shown that the use of our software does in fact slightly shorten travel time for drivers.
