Document Type

Article

Source of Publication

BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN

Publication Date

12-19-2023

Abstract

In this work, we propose a mathematical model to represent traffic congestion in the street under some consideration. A congestion problem in a city highway becomes a critical issue since congestion at one point affected congestion propagation on the other points. We focus on the propagation of traffic propagation by adopting the concept of disease spread using the SIR model. We consider that the disease in traffic problems is congestion. Meanwhile, vehicles that enter the highway are susceptible to congestion. In contrast, vehicles free from traffic jams represent individuals free from disease. The SIR model can explain the spread of congestion by looking at the congestion variable as an infected variable. We discuss and analyze the existence and stability of the equilibrium points. The local stability equilibrium point is verified using the Routh-Hurwitz criteria. At the same time, the global stability is analyzed using Lyapunov function. The numerical simulation is provided in the last section to validate the discussion results.

ISSN

1978-3017

Publisher

Universitas Pattimura

Volume

17

Issue

4

First Page

2471

Last Page

2478

Disciplines

Engineering

Keywords

Traffic congestion, SIR model, Equilibrium points, Stability analysis, Numerical simulation

Creative Commons License

Creative Commons Attribution-Share Alike 4.0 International License
This work is licensed under a Creative Commons Attribution-Share Alike 4.0 International License.

Indexed in Scopus

no

Open Access

yes

Open Access Type

Hybrid: This publication is openly available in a subscription-based journal/series

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