A model for correcting the initial marking of a classical Petri net based on solving a discrete programming problem


DOI: 10.34759/trd-2023-131-22

Аuthors

Pavlov D. A.*, Popov A. M.*, Tkachenko V. V.

Mlitary spaсe Aсademy named after A.F. Mozhaisky, Saint Petersburg, Russia

*e-mail: vka@mil.ru

Abstract

Apparatus based on the classical Petri net is being employed quite often while modeling various parallel asynchronous processes. This apparatus allows demonstrating the system transition from state to event, establishing cause-and-effect relations between the states of the system being modeled. It offers an opportunity to perform formal analysis of the model properties and reflect the results of the obtained analysis on the real properties of the system. However, when the modeled system volume is large enough, and Petri net properties analysis produces incorrect result, changes should be introduced into the formed model, though detecting the place, which requires correction, is not an easy task. It will be necessary to analyze relations between all positions and transitions together with initial, intermediate and final marking stage-by-stage, namely from the initial to the final state.

This article proposes a formal approach to the initial marking correction of the Petri net so as the network would reach the final state, i.e. correct fulfilling of the reachability property of the network by solving the discrete programming problem.

The discrete programming problem will be solved in the case of the Petri net reachability property unfulfillment, i.e. when the reachability equation solution will differ from X ∈ Zn. After the necessary solution finding, the reverse conversion operation of the system of linear equations into the reachability equation is being accomplished to discriminate the corrected vector of the initial marking from it. Correction of the initial marking vector is necessary for the net transition to the required (final) state.

The said approach may be employed for various type initial data correction, as well as corrections of the quantitative components of separate states of the system being modeled.

Keywords:

Petri net, Petri net properties analysis, initial labeling, error correction, discrete programming

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