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Analytic evaluation of the cycle time on networked conflicting timed event graphs in the (Max,+) algebra

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Abstract

This work deals with performance evaluation of Conflicting Timed Event Graph (CTEG), a class of Petri net exhibiting phenomena such as synchronization, parallelism and resources sharing. It is well known that the dynamic of Timed Event Graphs (TEG) admits a linear state space representation in the (Max,+) algebra which makes the analysis and control of this class easier. There is also a possibility of associating conflicts with the TEGs by adding conflict places that are mostly considered as safe; this extended class is called CTEG. We first present an analytic evaluation of the cycle time of CTEG as a function of the cycle time of each TEG and of the timers of the conflict places. Finally, in a more general context, we look for a relaxation of the safety hypothesis on the conflict places in order to model and evaluate the cycle time on CTEGs with multiple shared resources.

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Authors and Affiliations

  1. Chair of Automation and Energy Systems, Saarland University, D-66123, Saarbrücken, Germany

    W. M. Boussahel

  2. LURPA – ENS-Cachan 61, Av. du Président Wilson, 94235, Cachan, France

    S. Amari

  3. L2CSP – Mouloud Mammeri University, Hasnaoua Street, 15000, Tizi Ouzou, Algeria

    R. Kara

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  1. W. M. Boussahel
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  2. S. Amari
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  3. R. Kara
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Correspondence to W. M. Boussahel.

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Boussahel, W.M., Amari, S. & Kara, R. Analytic evaluation of the cycle time on networked conflicting timed event graphs in the (Max,+) algebra. Discrete Event Dyn Syst 26, 561–581 (2016). https://doi.org/10.1007/s10626-015-0220-3

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  • DOI: https://doi.org/10.1007/s10626-015-0220-3

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