In this project, we model the time advantage of speeding on a highway with traffic lights as a stochastic process. The object of study is the sequence of random variables $T_k$, representing the time benefit of the speeding car at the $k$ th traffic light. For simplicity, we assume identical traffic light cycles with independently distributed initial phases and constant distance between lights. With this simplified model, we investigate the distribution of $T_k$, proving results on the expected value of $T_k$ and deriving the conditional distribution $T_k|T_{k-1}$. The first result gives some intuition on the situation being modeled and the second result shows that $T_k|T_{k-1}$ and thus $T_k$ are examples of mixed distributions. Though the model serves more as a toy model, it provides an interesting example of a family of distributions having both a continuous and discrete part that arises from a simple mathematical model.