Routing game presents an interesting framework to analyse the practical problem of source routing in the Internet. It is particularly useful in quantifying the inefficiency of selfish user behavior that results in any transportation network without any central authority. This game assumes that the only user criteria for decision making is path cost. In this work, we take a step further, and model a routing game where user decision is based not only on path but also on time. We show that, under convex cost functions, this new routing game over time can be mapped to the classical routing game, thereby presenting a model that can exploit well-established results in the subject. Using a simple example, we demonstrate the usefulness of the model, and motivate the need for resource coordination to minimize inefficiency or cost.