A critical issue facing millimeter wave (mmWave) cellular systems is channel dynamics. MmWave signals are extremely susceptible to blocking and thus may vary rapidly with motion, orientation of the handset and local blockages. In this work, we derive a Finite State Markov Channel (FSMC) model of the mmWave channel from the statistics of ray tracing simulation data, which are based on channel measurements in an urban environment. The FSMC tracks the mutual information effective SINR (MI-ESNR), which can then be used in network simulations. The FSMC model is applied to analyze queue behavior and obtain the latency, throughput, packet error and droppage statistics for mmWave links at the MAC layer, making it useful for higher-layer analysis, as well. We evaluate the accuracy of the channel model for various model complexities and packet arrival rates and show that the model performance closely matches the empirical ray tracing data.