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This paper addresses the computational intractability of traffic control when applying the integrated METANET freeway traffic model and the VT-macro emission model in a model-based predictive control (MPC) framework. To facilitate real-time implementation, a piecewise-affine (PWA) approximation of the nonlinear METANET model is proposed. While a direct MPC approach based on the full PWA model is intractable for online applications, a conversion to a mixed-logical dynamical (MLD) model description is made instead. The resulting MLD-MPC problem, which is written as a mixed-integer linear program (MILP), can be solved much more efficiently as it does not explicitly state all model equations for each particular region. As a benchmark, the computational efficiency and accuracy of the MLD-MPC approach is tested on a case study including variable speed limits and a metered on-ramp while optimizing the total time spent (TTS) and taking into account emissions and fuel consumption of the vehicles. The performance is evaluated against the original nonlinear and nonconvex MPC problem and shows an improved computational speed at the cost of some deviation in the cost function values.