Millimeter-wave (mmWave) is a promising network access technology to enable reliable communications in future vehicular networks, which is expected to be dominated by autonomous vehicles. In this study, we consider line-of- sight (LOS) communications between mmWave-enabled vehicles and roadside units (RSUs) in a highway scenario where the LOS links can potentially get blocked by blocking vehicles. We focus on two performance metrics, namely the blockage probability and the average blockage duration. We establish a continuous-time Markov chain formulation of the problem in which transition rates depend on the speed, length and intervehicle distance of blocking vehicles. By using the steady-state solution of this model, we explicitly derive the blockage probability and average blockage duration. After validating the accuracy of the analytical results by comparing with simulations, we demonstrate that the main performance limitation of mmWave systems is due to the blockage duration, not the probability of blockage events. We also discuss the implications of our results in terms of the deployment of RSUs to provide ultra-reliable and low-latency connectivity.