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Molecular motor proteins fulfill the critical function of transporting organelles and other building blocks along the biopolymer network of the cell’s cytoskeleton, but crowding effects are believed to crucially affect this motor-driven transport due to motor interactions. Physical transport models, like the paradigmatic, totally asymmetric simple exclusion process (TASEP), have been used to predict these crowding effects based on simple exclusion interactions, but verifying them in experiments remains challenging. Here, we introduce a correlation imaging technique to precisely measure the motor density, velocity, and run length along filaments under crowding conditions, enabling us to elucidate the physical nature of crowding and test TASEP model predictions. Using the kinesin motor proteins kinesin-1 and OSM-3, we identify crowding effects in qualitative agreement with TASEP predictions, and we achieve excellent quantitative agreement by extending the model with motor-specific interaction ranges and crowding-dependent detachment probabilities. These results confirm the applicability of basic nonequilibrium models to the intracellular transport and highlight motor-specific strategies to deal with crowding.