A generalized eigenmode algorithm for reducible regular matrices over the max-plus algebra with applications to the Metro-bus public transport system in Mexico city

In this paper, an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to the Metro-bus public transport system in Mexico city. A timed event Petri net model is constructed from the data table that characterizes the transport system. A max-plus recurrence equation, with a reducible and regular matrix, is associated with the transport system timed event Petri net. Next, given the reducible and regular matrix, the problem consists of giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence equations. In fact, by transforming the reducible regular matrix into its normal form, and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is constructed. The generalized eigenmode obtained sets a timetable for the transport system.