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New bounds for timed event graphs inspired by stochastic majorization results. (English) Zbl 1073.93039
The paper exploits concepts from the algebraic approaches to Markov chains, in order to develop new principles for studying the boundedness of max-plus systems associated with the dynamics of timed event graphs (TEGs). The max-plus non-homogeneous autonomous dynamics is introduced by analogy with the non-homogeneous Markovian dynamics and it allows the author to formulate general results on comparisons of TEGs. The particular case of U-comparison results represents an extension of the framework proposed by the same author in a previous work. The proposed framework can be applied for computing the bounds of the top max-plus Lyapunov exponent as illustrated by the example of a closed Jackson network with two stations, described by F. Baccelli and D. Hong [Ann. Appl. Probab. 10, No. 3, 779–827 (2000; Zbl 1073.37526)].

MSC:
93C65 Discrete event control/observation systems
93E03 Stochastic systems in control theory (general)
68Q85 Models and methods for concurrent and distributed computing (process algebras, bisimulation, transition nets, etc.)
37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
Citations:
Zbl 1073.37526
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