TY - JOUR
T1 - 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
AU - Königsberg, Zvi Retchkiman
PY - 2008/11
Y1 - 2008/11
N2 - 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.
AB - 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.
KW - Algorithm
KW - Eigenmode
KW - Max-plus algebra
KW - Metro-bus
KW - Recurrent equations
KW - Reducible matrices
UR - http://www.scopus.com/inward/record.url?scp=56649097334&partnerID=8YFLogxK
U2 - 10.1016/j.nahs.2008.09.019
DO - 10.1016/j.nahs.2008.09.019
M3 - Artículo
SN - 1751-570X
VL - 2
SP - 1205
EP - 1216
JO - Nonlinear Analysis: Hybrid Systems
JF - Nonlinear Analysis: Hybrid Systems
IS - 4
ER -