Max-Plus Linear Equation System and Its Application on Railway Network System

Abstract

Max-Plus algebra is the set of R U {-~} with R is the set of all real numbersthat are equipped with maximum operation and addition. Max-Plus algebra is able tomodel 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.