<title>Reduced Petri nets model of scheduling problems</title>

Abstract

ABSTRACT In order to model and solve scheduling problem, a new Petri Nets Model--Reduced Petri Nets (RePN)model is introduced. Compared with previous Petri Nets models of scheduling problem, RePN model notonly has strong ability of analysis but also reduces the number ofplaces and transitions in a great amount. Sothe reachable set of RePN model is much smaller,which makes it more convenient to search the optimal ornear-optimal solution of scheduling problem.Keywords: scheduling problem, Marked Graph(MG), Reduced Petri Nets(RePN), reachable set, combinedplace, operation. 1.DTRODUCTION Petri nets, which was introduced by CA. Petri in 1962, is a mathematical and graphical tool of systems.After 30 years of development, Petri nets has become a powerful tool for system modeling and analyzing.Many successful applications of Petri nets in computer science, automated control and communication haveproven its strong ability[1].Scheduling problem concentrates on how to optimize some evaluating parameters of a job which consistsof a series of operations without disturbing some constraints such as resource constraints, the relationship ofoperations, etc. . Many applied problems in robotics, automation and computer architecture can be classifiedas scheduling problem[2,3].Some methods using Petri nets in modeling and analyzing of scheduling problem have been introducedafter 1980's, many of them adapted Marked Graph or P/T nets as the model of scheduling problem. Althoughthese models can represent scheduling problems in details, the complexity of them make analysis becomevery difficult. High_Level nets are also used to model scheduling problem, but the analyzing and simulatingabilities of HighLevel nets are weak. Therefore the suitable Petri nets model of scheduling problem is stillin demanding.In order to compromise the precision of representation and abilities of analysis, we build a Petri netsmodel, called RePN(Reduced Petri Nets), by reducing the original Marked Graph model of scheduling