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All Journal Indonesian Journal of Applied Statistics BAREKENG: Jurnal Ilmu Matematika dan Terapan
Rafsanjani, Zani Anjani
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Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Earth & Planetary Sciences Economics, Econometrics & Finance Energy Engineering Environmental Science Mathematics Mechanical Engineering Physics Transportation

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TRAFFIC CONGESTION ANALYSIS USING SIR EPIDEMIC MODEL Rafsanjani, Zani Anjani; Herdiana, Ratna; Tjahjana, R Heru; Erlangga, Yogi Ahmad
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 4 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss4pp2471-2478

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.
Estimator Cramer Von Mises bagi Parameter Distribusi Kumaraswamy-Lindley Saputra, Bagus Arya; Rafsanjani, Zani Anjani
Indonesian Journal of Applied Statistics Vol 7, No 1 (2024)
Publisher : Universitas Sebelas Maret

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.13057/ijas.v7i1.79911

Abstract

The Kumaraswamy-Lindley (KL) distribution is a combination of the Lindley distribution and the Kumaraswamy distribution. The KL distribution is widely used to examine lifetime data. The importance of the application of the KL distribution in explaining lifetime data makes it necessary to estimate distribution parameters well. Therefore, this research will discuss the Cramer Von Mises Estimator (ECM) for the Kumaraswamy-Lindley distribution parameters. The formula for the ECM is obtained and the simulation is carried out using the same initial parameters with different generation sample sizes. The simulation results show that for the same initial parameters, estimation with a larger sample size has better results.
Co-Authors Erlangga, Yogi Ahmad Herdiana, Ratna Saputra, Bagus Arya Tjahjana, R Heru