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A thorough understanding of the fundamental relation of traffic flow variables is critical for the efficient operation of traffic systems. However, their relationships in mixed traffic are challenging to model due to the continuously changing vehicle composition. This paper proposes a composition-based approach for estimating the fundamental relationships between traffic flow variables using empirical data. The methodology seeks to eliminate the difficulties in class-specific ss identification by introducing a continuous wavelet transformation with oblique cumulative arrival and oblique occupancy time plots. We used machine learning (ML) algorithms to delineate regimes and showed the fundamental diagrams for a given location that has a composition-invariant free-flow branch but has distinct composition-specific branches in congestion. Also, it was observed that the congested regime (CR) has a wide scatter indicating possible stochastic inter-class interactions for varying vehicular composition. We proposed a distance optimization method to re-cluster the CR data and found that the proposed method improves the fit with the empirical observations. The inter-class interactions result illustrates that the heavy vehicles will dominate the high-speed vehicles with the increase of AO. It is found that beyond a critical level of AO in congestion, all vehicle class travel at the same speed. Finally, it is found that validation with different datasets shows that the proposed methodology is robust in estimating fundamental diagrams under mixed traffic conditions.

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