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Towards a tropical automaton product minimizing global completion times

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Abstract

The main contribution of this paper is oriented towards system modeling with resource conflicts, in which a set of tasks must be completed at the earliest. Mutual exclusion between tasks with underlying resource conflicts is modeled as subsystems through local tropical automata. Parallel task execution is explored through a new framework for a synchronous product of tropical automata directly minimizing the global completion time of a set of tasks. A dater-based analysis is proposed to determine an optimal qualitative schedule and relies on proposed definitions of global, private, and synchronizing daters. This approach drastically narrows the solution spectrum, and allows finding the optimal task schedule. The approach is applied to a flow network as a case study, but can be applied to systems of different nature.

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Notes

  1. Both scenarios yG1p = ys(G2,G3) and yG1p > ys(G2,G3) yield the same elements in the alphabet of the product during the execution of s(G2,G3). This is, elements of the type (a1, b1, b1) where a1G1p, and b1s(G2;G3).

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Acknowledgements

This research has been financially supported by Thales Group France, and by the PCP (Post-graduate Cooperation Program) between Venezuela and France involving the collaboration between the academic institutions: ULA (in Spanish: Universidad de Los Andes)—research laboratory: CEMISID in Merida, Venezuela, and the INSA (in French: Université de Lyon, INSA Lyon, Ampere (UMR5005)) in Lyon, France; and the industrial partners Thales Group France, and PDVSA (in Spanish: Petróleos de Venezuela Sociedad Anónima), the Venezuelan oil company.

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Authors and Affiliations

  1. Institut National Des Sciences Appliquées de Lyon, Villeurbanne, France

    Karla Quintero, Eric Niel & Laurent Pietrac

  2. CEMISID, Universidad de Los Andes, La Hechicera, Mérida, Venezuela

    Jose Aguilar

  3. GIDITIC, Universidad EAFIT, Medellín, Colombia

    Jose Aguilar

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  1. Karla Quintero
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  2. Jose Aguilar
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  3. Eric Niel
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  4. Laurent Pietrac
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Correspondence to Jose Aguilar.

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Communicated by Rosana Sueli da Motta Jafelice.

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Quintero, K., Aguilar, J., Niel, E. et al. Towards a tropical automaton product minimizing global completion times. Comp. Appl. Math. 39, 221 (2020). https://doi.org/10.1007/s40314-020-01211-w

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