MAX PLUS ALGEBRA OF TIMED PETRI NET FOR MODELLING SINGLE SERVER QUEUING SYSTEMS

  • Zumrotus Sya'diyah STKIP Gotong Royong Masohi, Indonesia
DOI: https://doi.org/10.30598/barekengvol17iss1pp0155-0164
Keywords: Timed Petri net, single server, queuing system, Lyapunov stability, standard autonomous equation, eigen value

Abstract

This research modified a single server queuing system using timed Petri net. We add two places, a transition and its appropriate arcs. This research also considered all the holding times in the timed Petri net. We found that the Petri net is not stable but stabilizable according to Lyapunov stability criteria. The standard autonomous equation of the system is also determined. Furthermore, this system also has the eigen value which related to its periodical behavior, it is .  This means that the periodical behavior of the system only depends on the value of holding times of place W, R, B, and I.

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Published
2023-04-16
How to Cite
[1]
Z. Sya’diyah, “MAX PLUS ALGEBRA OF TIMED PETRI NET FOR MODELLING SINGLE SERVER QUEUING SYSTEMS”, BAREKENG: J. Math. & App., vol. 17, no. 1, pp. 0155-0164, Apr. 2023.
Issue
Vol 17 No 1 (2023): BAREKENG: Journal of Mathematics and Its Applications
Section
Articles

Copyright (c) 2023 Zumrotus Sya'diyah

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