Modeling and Scheduling Design for a Class of Queuing Systems by means of timed Petri Nets and Max-Plus Algebra
نویسنده
چکیده
A queuing system, is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Placetransitions Petri nets (commonly called Petri nets) are a graphical and mathematical modeling tool applicable to queuing systems in order to represent its states evolution. Timed Petri nets are an extension of Petri nets, where now the timing at which the state changes is taken into consideration. Scheduling is a key concept in queuing systems and it refers to the way the queuing system should run to work properly. This work proposes a new methodology for modeling and scheduling design for a class of queuing systems using timed Petri nets and maxplus algebra. An algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to the reducible and regular matrix of the recurrence equation associated to the timed Petri net that models the queuing system. The generalized eigenmode obtained sets a schedule for the queuing system. Mathematics Subject Classification: 90B22, 15A80, 68W01, 34H15
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