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

(1) Universitas Gadjah Mada
(*) Corresponding Author


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.


max-plus algebra, schedules, train, synchronization

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Baccelli, F., Cohen, G., Olsder, G.J., dan Quadrat, J.P., 2001, Synchronization and Linearity, New York. De Schutter, B., 1996, Max-Algebraic System Theory for Discrete Events Systems, Katholieke Universiteit Leuven, Belgium. De Schutter, B. dan Van Den Boom, T., 2008, Max-Plus Algebra and Max-Plus Linear Discrete Event System: An Introduction, Proceeding of The 9th International Workshop on Discrete Event Systems (WODES'08), Goteborg, Sweden, pp. 36-42. Goverde, Rob M. P. , 2005, Railway Timetable Stability Analysis Using Max-Plus System Theory, Transportation Research Part B 41 (2007) 179-201. Heidergott, B., Olsder, G.J., dan Van Der Woude, J., 2006, Max-Plus at Work, Princeton University Press, New Jersey. Kasie G. Farlow, 2009, Max-Plus Algebra, Virginia Polytechnic Institute and State University, Virginia. Rudhito M. Andy, 2016, Aljabar Max-Plus dan Penerapannya, Universitas Sanata Dharma, Yogyakarta. Subiono, 2015, Aljabar Min-Max Plus dan Terapannya, Institut Teknologi Sepuluh Nopember, Surabaya. Subiono, dan Van Der Woude, J., 2000, Power Algorithms for (max,+) and bipartite (min,max,+) systems, Journal of Discrete Event Dynamic Systems: Theory and Applications, 369-389. Stanczyk Jarosław, 2016, Max-Plus Algebra Toolbox for Matlab


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