Bus schedule modelling in Bandung, Indonesia, using max-plus algebra

Abstract

Congestion has been a big problem in many big cities in the developing countries. One of the main factors causing traffic congestion is the lack of use of public transportations. The network problems related to synchronization problems, e.g. scheduling of public transportation, can be modeled and solved using the Max-plus algebra. Bandung as the capital and the biggest city in the West Java has also faced such a problem, that is congestion. In this paper, the scheduling of DAMRI bus, one of public transportation in Bandung will be modelled using the Max-plus algebra. We choose two DAMRI routes in Bandung, those are Dipatiukur - Leuwi Panjang and Ledeng - Leuwi Panjang. Both routes are transformed into a directed graph with the bus stops as the nodes. The Max-plus algebra is applied to develop the bus scheduling. In the developed model, the eigenvalues and eigenvectors of the system are calculated. The eigenvalues represent the period of departure at each bus stops and the eigenvectors represent the initial time of departure of the DAMRI bus. The results show that for every 3.7492308 minutes a bus will depart at each bus stop. If the DAMRI bus operation starts at 05.00, then the first departure should be from the bus stop in Pasir Kaliki to the bus stop in Hasan Sadikin Hospital.