In this paper, we use Markov chains to construct a theoretical traffic system. The paper is organized into three parts: The first two deal with the construction of two spaces in which objects may interact. The third part analyzes the evolution of one particular object. Using bounds given by the law of iterated logarithm and the central limit theorem, we prove that after a large number of time steps, the probability of locating this object in the traffic network diminishes to zero. We conclude with several suggestions on the evolution of multiple objects.

Author Bio

I am currently an undergraduate at Georgia Tech and will be starting the PhD program in Mathematics at the University of Texas at Austin in Fall 2007. My current research interests lie mostly (although not exclusively) in the realm of analysis. In my free time, I like to read a variety of books, play table-tennis, and spend time with my girlfriend.