Traffic Model Based Predictive Control: A Piecewise-Affine using METANET
Abstract
Traffic congestion on the freeway is a serious problem for modern society. Dynamic traffic management is a good alternative solution to improve efficiency on congestion problems. This article aims to analyze parts of freeway traffic network by using METANET model which is part of macroscopic traffic flow model that describes a set of parameters such as mean speed, traffic flow, and density of a traffic system. The piecewise-affine (PWA) approximation on METANET model is used to design traffic predictive controls and test them on a traffic model structure. This approach guarantees more intensive calculation for METANET traffic flow model in nonlinear form in the context of model predictive control (MPC). Some equations in the METANET model will be approximated by PWA function. With PWA-MPC approximation as direct calculation, equation of PWA model can be transformed into mixed-integer linear programming (MILP). Furthermore, to see the control of the model with MPC control, numerical simulations will be carried out on mean speed, traffic density, traffic flow, queue length, and MPC control. We use time 0 – 2.5 hours. Simulation result shows that the density of traffic, traffic flow, and queue length decreased in this time period, while the mean speed increased.
Keywords: traffic control; model predictive control; piecewise-affine model; METANET; mixed-integer linear programming (MILP).
Abstrak
Kemacetan lalu lintas di jalan bebas hambatan merupakan masalah yang sangat serius bagi masyarakat modern. Pengelolaan lalu lintas yang dinamis merupakan solusi alternatif yang baik untuk meningkatkan efisiensi pada masalah kemacetan. Artikel ini bertujuan untuk menganalisis bagian jaringan pada jalan bebas hambatan dengan mengkaji model METANET yang termasuk bagian dari model arus lalu lintas secara makroskopik yang menggambarkan kumpulan parameter seperti kecepatan rata-rata, arus lalu lintas, dan kepadatan. Pendekatan piecewise-affine (PWA) pada model METANET digunakan untuk mendesain kendali prediktif lalu lintas dan mengujinya pada suatu struktur model lalu lintas. Pendekatan ini menjamin penghitungan yang lebih intensif untuk model arus lalu lintas METANET yang berbentuk nonlinear dalam konteks kendali model prediktif (model predictive control/MPC). Beberapa persamaan pada model METANET akan didekati oleh fungsi PWA. Dengan pendekatan PWA-MPC sebagai perhitungan secara langsung, persamaan model PWA dapat diubah menjadi program linear bilangan bulat campuran (mixed- integer linear programming/MILP). Selanjutnya untuk melihat keterkendalian model dengan kendali MPC, simulasi numerik akan dilakukan terhadap kecepatan rata-rata, kepadatan lalu lintas, arus lalu lintas, panjang antrian, serta kendali MPC. Waktu yang digunakan pada simulasi adalah 0 – 2.5 jam. Hasil simulasi menunjukkan bahwa kepadatan lalu lintas, arus lalu lintas, panjang antrian mengalami penurunan dalam kurun waktu tersebut, sedangkan kecepatan rata-rata mengalami peningkatan.
Kata Kunci: endali lalu lintas; model lalu lintas berbasis kendali prediktif; pendekatan model piecewise-affine; METANET; program linear bilangan bulat campuran.
Keywords
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DOI: 10.15408/inprime.v2i1.14332
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