TIMED-EVENT GRAPHS WITH MULTIPLIERS AND HOMOGENEOUS MIN-PLUS SYSTEMS

The authors study fluid analogues of a subclass of Petri nets, called fluid timed-event graphs with multipliers, which are a tinted extensio n of weighted T-systems studied in the Petri net literature. These eve nt graphs can be studied naturally, with a new algebra, analogous to t he min-plus algebra, but defined on piecewise linear concave Increasin g functions, endowed with the pointwise minimum as addition and the co mposition of functions as multiplication. A subclass of dynamical syst ems in this algebra, which have a property of homogeneity, can be redu ced to standard min-plus linear systems after a change of counting uni ts. The authors give a necessary and sufficient condition under which a fluid timed-event graph with multipliers can be reduced to a fluid t imed-event graph without multipliers. In the fluid case, this class co rresponds to the so-called expansible timed-event graphs with multipli ers of Munier, or to conservative weighted T-systems. The change of va riable is called here a potential. Its restriction to the transitions nodes of the event graph is a T-semiflow.