New bounds for timed event graphs inspired by stochastic majorization results (Q702191)

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 \textit{F. Baccelli} and \textit{D. Hong} [Ann. Appl. Probab. 10, No. 3, 779--827 (2000; Zbl 1073.37526)].