I will introduce some possible models and then focus on a model proposed by Joseph Keller in two papers written in the early 1970s. I will discuss some calculus of variations and optimal control theory and use those tools to derive Keller's solution. Then I will discuss some short comings, what others have done, and where I would like to go. That will probably include some of the following topics: probability, stochastic calculus of variations, simulation.
(Basic Calculus and ODE knowledge is required.)