MAX-PLUS LINEAR SYSTEM IN CONTROL OF DATA PROCESSING

Jerzy Raszka,

Lech Jamroż

Abstrakt

The increasing complexity of information processing in distributed computer systems and microprocessors requires the use of time-saving devices and extended capacities of transmission channels. Processes in computers systems need effective processing time. This article describes an application of the theory of the Max Plus Linear System (MPLS) to controlling digital information processing and transmission time in information systems. System processes are described by an MPLS state equation and an MPLS output equation. The MPLS model makes use of formal mathematical methods of max-plus algebra which include maximization and addition operations in the domain of non-negative real numbers with the addition of minus infinity. The input data and the structure of the processes under consideration are represented by the Timed Event Graph (TEG) formalism constituting a special case of Timed Petri Nets. The suggested MPLS methods are useful for investigating selected properties of network models. They may be applied, among others, to evaluate performance criteria, cycle time, predictive control etc. This article presents the theoretical considerations used to determine the input signals controlling discrete processes, which are then illustrated with examples of numerical computations.

Słowa kluczowe: max-plus algebra, Petri nets, data processing, discrete processes
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