Delay Tolerance and Recovery Control in a Synchronized Electric Bus Network using Max-Plus Algebra

Marcellinus Andy Rudhito (Department of Mathematics Education, Sanata Dharma University, Yogyakarta, 55281, Indonesia)
Dewa Putu Wiadnyana Putra (Department of Mathematics Education, Sanata Dharma University, Yogyakarta, 55281, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 10, No 2 (2026): Zero: Jurnal Sains Matematika dan Terapan

This study analyzed delay tolerance, normalization time, and recovery control in the two-terminal Trans Gadjah Mada Electric Bus network using max-plus algebra. An analytical-computational approach was applied by representing the nominal route times as a weighted directed graph and transforming them into a max-plus linear system. The max-plus eigenvalue, critical arcs, component-wise delay thresholds, excess delays, and recovery horizons were then computed. The nominal synchronized period was 21 minutes. The Terminal 1 and Terminal 2 local routes had delay thresholds of 2 and 3 minutes, respectively, whereas both interterminal corridors were critical arcs with zero delay tolerance. Thus, any positive delay on a critical corridor directly disturbed synchronization. Service-operational delays changed route weights, while departure-time delays shifted terminal event times. The resulting threshold and excess-delay measures provided the mathematical basis for a simple recovery-mode switching rule, whose parameters remain illustrative and require empirical calibration before operational deployment.