Human sensing enables intelligent vehicles to provide driver-adaptive support by classifying perceived workload into multiple levels. Objective of this study is to classify driver workload associated with traffic complexity into five levels. We conducted driving experiments in systematically varied traffic complexity levels in a simulator. We recorded driver physiological signals including electrocardiography, electrodermal activity, and electroencephalography. In addition, we integrated driver performance and subjective workload measures. Deep learning based models outperform statistical machine learning methods when dealing with dynamic time-series data with variable sequence lengths. We show that our long short-term memory based recurrent neural network model can classify driver perceived-workload into five classes with an accuracy of 74.5%. Since perceived workload differ between individual drivers for the same traffic situation, our results further highlight the significance of including driver characteristics such as driving style and workload sensitivity to achieve higher classification accuracy.