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This paper proposes modified model predictive control (MMPC) for coordinated signals, aiming to enhance a model's fidelity to the realistic traffic environment by relaxing typical assumptions. We focus on the arterial, where every intersection is equipped with a dual-ring-barrier signal controller that complies with the standards of the National Electric Manufacturers Association. MMPC employs the store-and-forward model to describe traffic flow, thereby transforming the signal control problem into a model-based rolling-horizon optimization problem, in which the prediction horizon is composed of several future sample intervals, commonly equal to the cycle length. A radar detector is used to collect vehicle data upstream of the stop line at every sampling instant. The optimization problem is solved to minimize the number of vehicles within the prediction horizon, and the next timing plan is determined based on the optimization results. Constraints are added and modified in order to incorporate the typical relaxed assumptions in the optimization process. For this purpose, MMPC introduces a transition-free ring-barrier structure, vehicle distribution ratio, and percent arrival before the end of green. Simulation results indicate that coordination can be maintained by MMPC without the need for transitions, and the estimation of current and future traffic states can be improved with the assistance of modified constraints. Compared with benchmark techniques, MMPC offers superior vehicle progression for coordinated movement and significant improvements in delays, number of stops, and total travel time from a system-wide perspective, with an acceptable small increase in runtime. [ABSTRACT FROM AUTHOR]