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The asynchronous parallel painting of vehicles in modern vehicle assembly facilities provides flexibility to handle variations in mix, quality and equipment uptimes. However this results in an unpredictable output sequence of vehicles leading to problems in material flow, especially in plants that have gone JIT. We develop a flow model that captures the relationship between processing time, system throughput, loading mix, system size, and output sequence number.The model provides several insights for design, configuration and setting operating policies. It was validated by performing spectral analysis using plant data. We will be extending the model to handle dynamic loading and updates on controls.