Common car-following models for microscopic traffic simulation assume a time advancement using fixed-sized time steps. However, a purely time-driven execution is inefficient when the states of some agents are independent of other agents and thus predictable far into the simulated future. We propose a method to accelerate microscopic traffic simulations based on identifying independence among agent state updates. Instead of iteratively updating an agent’s state throughout a sequence of time steps, a computationally inexpensive “fast-forward” function advances the agent’s state to the time of its earliest possible interaction with other agents. We present an algorithm to determine independence intervals in microscopic traffic simulations and derive fast-forward functions for several well-known traffic models. In contrast to existing approaches based on reducing the level of detail, our approach retains the microscopic nature of the simulation. An evaluation is performed for a synthetic scenario and on the road network of Singapore. At low traffic densities, maximum speedup factors of about 2.6 and 1.6 are achieved, while at the highest considered densities, only few opportunities for fast-forwarding exist. We show that the deviation from purely time-driven execution is reduced to a minimum when choosing an adequate numerical integration scheme to execute the time-driven updates. Verification results show that the overall deviation in vehicle travel times is marginal.