Abstract: In this paper we propose a modelling technique for the control of computational processes. The Petri Net model, particularly a Timed Event Graph (TEG) can be used for analyzing. The proposed model enables the determination of state equations. The max-plus algebra represents linear algebraic form of discrete systems and supplies new tools to their modelling. We develop a linear mathematical model under constraints in the Max-plus algebra. When using max-plus algebra with TEG, the arc weights are kept equal to one in order to be able to resolve the state equations. Structure of max-plus algebra is equipped with maximization and addition operations over of the real numbers and minus infinity. It can be used appropriately to determine marking times within a given Petri net and a vector filled with marking state at the beginning. Tools of max-plus algebra are useful to investigate properties of network models. Finally, numerical examples show the use of this model.

Keywords: Max-Plus-Linear? Systems, Petri Nets, Discrete Systems, Modelling Technique

ACM Classification Keywords: H. Information Systems, H.1 MODELS AND PRINCIPLES, H.1.1 Systems and Information Theory; D. Software D.4, OPERATING SYSTEMS, D.4.1 Process Management, Multiprocessing/multiprogramming/multitasking, Synchronization.

Link:

MODELLING AND CONTROL OF COMPUTATIONAL PROCESSES USING MAX-PLUS ALGEBRA

Jerzy Raszka, Lech Jamro

http://foibg.com/ibs_isc/ibs-23/ibs-23-p14.pdf