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Fluid approximation of a controlled multiclass tandem network

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Abstract

A two-station, four-class queueing network with dynamic scheduling of servers is analyzed. It is shown that the corresponding Markov decision problem converges under fluid scaling to a fluid optimal control model. The structure of the optimal policy for the fluid network, and of an asymptotically optimal policy for the queueing network are derived in an explicit form. They concur with the tandem μ-rule, if this policy gives priority to the same flow of customers in both stations. In general, they are monotone with a linear switching surface.

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Authors and Affiliations

  1. Mathematical Insitute, University Leiden, Niels Bohrweg 1, P.O. Box 9512, 2300RA, Leiden, The Netherlands

    A. Gajrat & A. Hordijk

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  1. A. Gajrat
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  2. A. Hordijk
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Gajrat, A., Hordijk, A. Fluid approximation of a controlled multiclass tandem network. Queueing Systems 35, 349–380 (2000). https://doi.org/10.1023/A:1019162615537

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