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Throughput maximization of complex resource allocation systems through timed-continuous-Petri-net modeling

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Abstract

Fluid-relaxation-based scheduling is a powerful scheduling method for complex resource allocation systems and other stochastic networks. However, this method has been pursued through rather ad hoc representations and arguments in the past. This paper establishes that timed-continuous Petri nets provide a structured and natural framework for the implementation of this method in the context of complex resource allocation, and highlights the potential advantages of such a more structured approach.

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Notes

  1. The determination of the transition firing rates according to the rule of Eq. 2 implies the adoption of the “infinite-server” semantics for net \({\mathcal N}^{(tc)}\). This choice is justified by the explicit modeling of the resources that regulate the firing of the various transitions of the CRL-modeling GSPN \({\mathcal N}\) through the corresponding “resource” places; please, c.f. Sections 2.3.1 and 3.1 of Mahulea (2007) for a more thorough support of this statement.

  2. However, some more recent realizations that are reported in the closing part of Chapter 5 in Ibrahim (2019), imply that the secondary action-selection criterion of Eq. 24 might not be very pertinent, and the development of the necessary logic for the effective breaking of any ties generated by the primary action-selection criterion of Eq. 23 is a remaining open issue.

  3. A more expansive discussion on the computational complexity and the tractability of the presented scheduling method can be found in Ibrahim and Reveliotis (2019).

  4. We emphasize, however, that this claim presumes that the structure of the DC-RAS modeling PN \({\mathcal N}\) will also encode, both, the applied deadlock avoidance policy and the imposed production-ratio constraints.

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  1. School of Industrial & Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael Ibrahim & Spyros Reveliotis

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  1. Michael Ibrahim
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  2. Spyros Reveliotis
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Correspondence to Spyros Reveliotis.

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This article belongs to the Topical Collection: Smart Manufacturing - A New DES Frontier

Guest Editors: Rong Su and Bengt Lennartson

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Ibrahim, M., Reveliotis, S. Throughput maximization of complex resource allocation systems through timed-continuous-Petri-net modeling. Discrete Event Dyn Syst 29, 393–409 (2019). https://doi.org/10.1007/s10626-019-00289-7

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