MAX-PLUS LINEAR EQUATION SYSTEM AND ITS APPLICATION ON RAILWAY NETWORK SYSTEM

Andro Kurniawan; Ari Suparwanto

doi:10.22146/jmt.55316

MAX-PLUS LINEAR EQUATION SYSTEM AND ITS APPLICATION ON RAILWAY NETWORK SYSTEM

https://doi.org/10.22146/jmt.55316

Andro Kurniawan^(1*), Ari Suparwanto⁽²⁾

(1) Universitas Gadjah Mada
(2)
(*) Corresponding Author

Abstract

Max-Plus algebra is the set of R U {-~} with R is the set of all real numbers
that are equipped with maximum operation and addition. Max-Plus algebra is able to
model several types of Discrete Event System (DES) which are nonlinear in conventional algebra to be linear in Max-Plus algebra, so we can do further analysis of the system. Types of DES will be linear in the form of Max-Plus algebra which only synchronizes without any concurrency such as railway network systems, production systems, traffic lights, etc. This research discusses the application of the linear Max-Plus equation in the train schedules and involves synchronization between trains. The result of this study are obtained DAOP VI Yogyakarta rail network system model in the form of x(k + 1) = A otimes x (k) which is then used to determine the departure period and the time of initial train departure. The departure period is obtained from the eigenvalue (lambda) from the A matrix and the initial departure is obtained from the eigenvector corresponding to lambda. The calculation shows that the train departure period is T = 588 minutes.

Keywords

max-plus algebra, schedules, train, synchronization

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References

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DOI: https://doi.org/10.22146/jmt.55316