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All Journal Prosiding Seminar Nasional MIPA CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Pendidikan Matematika RAFA EDU-MAT: Jurnal Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Zero : Jurnal Sains, Matematika, dan Terapan Square : Journal of Mathematics and Mathematics Education Jurnal Pendidikan Matematika Unpatti
Dewa Putu Wiadnyana Putra
Universitas Sanata Dharma
Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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Designing an Optimal Route Network for the Synchronized Trans Gadjah Mada Electric Bus (TGMEB) using Max-Plus Algebra Franciscus Budi Pranatta; Marcellinus Andy Rudhito; Dewa Putu Wiadnyana Putra
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i2.25392

Abstract

We develop an optimal route network and synchronized timetable for the Trans Gadjah Mada Electric Bus (TGMEB), designed to cover the entire campus with 4 buses and 28 stops. Using literature review, field observation, and online mapping, we create three network candidates-one-, two-, and three-terminal-and model each as a max-plus linear discrete-event system. Service period and periodic departures are derived from eigenvalue-eigenvector analysis and implemented in Scilab 5.5.2 with a max-plus toolbox. The two-terminal layout performs best: its average inter-stop travel time is 32% faster than the other alternatives while keeping departures synchronized and coverage intact. The results confirm that jointly selecting the network architecture and its timetable yields superior campus operations. This is the first campus-scale study that co-designs a multi-terminal electric-bus route network and synchronized timetable via max-plus algebra, optimizing departure throughput and average inter-stop travel time. Unfortunately, this design has not been tested on the field.
Delay Tolerance Thresholds and Natural Recovery in a Fork-Join Production System over Max-Plus Algebra Dewa Putu Wiadnyana Putra; Marcellinus Andy Rudhito
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.45031

Abstract

This study investigates server-specific delay tolerance and natural recovery in a three-server fork--join production system modeled with max-plus algebra. The system has two parallel servers synchronized by a join server and is analyzed in the canonical regime where the second-server self-loop is the unique critical circuit. Using max-plus spectral theory, critical-circuit margins, relative-delay recurrences, and computational validation, we examine a single additive event-time delay introduced after the nominal trajectory has entered the eigenvector regime. Every positive delay at the critical server propagates permanently, so its tolerance threshold is zero. At the two non-critical servers, exact finite thresholds are determined by the available margins between the critical circuit and competing non-critical paths. Delays not exceeding these thresholds are naturally absorbed without switching or control intervention, and a finite upper bound on the recovery time is established from a two-cycle contraction argument. Numerical tests across three admissible parameter sets confirm below-threshold recovery, boundary recovery, above-threshold propagation, and invariance with respect to the delay cycle and eigenvector translation. These results provide a precise event-level robustness characterization for the stated canonical fork--join regime.
Co-Authors Ayuningtyas, Lusia Diva Eko Budi Santoso Franciscus Budi Pranatta Gede Suweken Herwidasari, Maria Priska Marcellinus Andy Rudhito Nugraha, Adhi Surya Pratiwi, Ni Putu Ayu Dias Ruditho, Marcellinus Andy Septicitaningtyas, Damiana Dewi Susanto, Anindito Wisnu Yovela, Christabel Yulia, Vista Putri