Big Data techniques are essential to creating mathematical models of complex, real-world systems, as processing and analyzing such large amounts of data will require the use of complex algorithms, which will, in turn, require many parallel and distributed computations. A comprehensive model of any complex system can require tremendous computational resources. Thus, running a simulation based on such a model will require Big Data techniques.

One particular problem I am interested in is to create traffic models from collected vehicle data, and use ScalaTion to create simulations of them, with the intention of then using simulation optimization to improve the flow of vehicles in the traffic model. The models are built using geographic data to construct the physical layout of the roads, vehicle counts to construct Non-homogeneous Poisson counting processes that randomly compute interarrival times of vehicles to the system, and meta-data of the vehicle counts to construct models of vehicle behavior within the traffic system.

For simulation optimization, I am applying several different techniques in an effort to identify the most effective methods in the traffic signal context. Techniques currently being considered include gradient-based algorithms such as BFGS Quasi-Newton and the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, derivative-free methods like the Tabu Search, Nelder-Mead Simplex methods, Genetic Algorithms, and other direct search methods. Meta-modeling using Response Surface Methodology (RSM) is also an approach I am researching.

In the future, society will need traffic systems that can dynamically guide traffic flow. Self-driving vehicles are going to be arriving on many roads throughout the country in the next few years, and eventually there will be a desire to create Intelligent Traffic Systems (ITS) where route planning is controlled by the system itself so that special events such as concerts and sporting events, and unforseen events such as accidents, can be accounted for either ahead of time, or dynamically, as new information is collected by the system. Accurate, data-driven mathematical models will be needed for analysis and simulations of these traffic systems. There will also be a need to answer many "what-if" questions regarding traffic systems. An example is the analysis of physical changes to roads, such as the replacement of stop-sign controlled intersections with roundabouts. Another is the introduction of new lanes to existing highways.

I also plan to research other problem spaces in regards to mathematical modeling, simulation, and optimization. One area of interest is in finding ways to mathematically model economic systems and attempt to predict the effects of economic policy changes.

Keywords: Data-driven Mathematical Modeling, Traffic Simulation, Simulation Optimization, Big Data, Analytics, Parallel Simulation