Traffic Model Based Predictive Control: A Piecewise-Affine using METANET

Musthofa, M. Wakhid · 2020 · DOAJ

DOI: 10.15408/inprime.v2i1.14332

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Summary

This paper addresses the challenge of managing freeway traffic congestion through dynamic traffic management, specifically by applying Model Predictive Control (MPC) to the macroscopic METANET traffic flow model. The primary motivation is that standard MPC applications for METANET result in nonconvex nonlinear optimization problems that are computationally difficult to solve in real-time. To overcome this, the authors propose a Piecewise-Affine (PWA) approximation of the nonlinear METANET equations. This approach allows the complex nonlinear model to be transformed into a Mixed-Integer Linear Programming (MILP) problem, enabling more efficient and intensive calculations for predictive control. The methodology involves approximating the nonlinear components of the METANET model—specifically equations governing traffic flow, density, mean speed, and queue length—using PWA functions. The authors employ techniques such as least square optimization, PWA identification, and partial constant piecewise approximation. For instance, specific parameters in the speed equation, such as free-flow speed and critical density, are fixed based on historical data to linearize the exponential terms. The resulting PWA model is integrated into an MPC framework where the objective function minimizes the Total Time Spent (TTS) in the system, which includes vehicle waiting times at on-ramps and in mainstream segments, along with penalty terms for control input deviations. The control signals include ramp metering rates and variable speed limits. Numerical simulations were conducted using MATLAB over a 2.5-hour period to evaluate the performance of the PWA-MPC controller. The simulation parameters included specific values for free-flow speed (102 km/h), critical density (33.5 vehicle/km/lane), and other model constants. The results demonstrated that the implemented control strategy effectively reduced traffic density, traffic flow, and queue lengths, with these metrics decreasing toward zero over the simulation period. Conversely, the mean speed of vehicles increased, approaching the imposed speed limit of 100 km/h in specific segments where limits were applied. The objective function values also showed a decreasing trend, indicating successful minimization of the cost function. The significance of this work lies in demonstrating that PWA approximation is a viable method for linearizing the METANET model for use in MPC. By converting the problem into an MILP format, the approach facilitates the computation of optimal control signals for traffic management. The findings confirm that this method can improve traffic efficiency by reducing congestion metrics and increasing vehicle speeds, offering a practical solution for dynamic traffic control in freeway networks.

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• mental model of traffic