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Optimal Control of Queuing Systems with Channel Switching

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Abstract

We consider the problem of optimizing the operation of a queuing system in which the number of working service channels can be changed in a controlled manner at control times separated from each other by a fixed time step. It is assumed that, when passing from step to step, the simplest arrival flow intensity changes in accordance with some homogeneous Markov chain. The criterion for choosing a strategy for switching service channels is the minimum total average costs over a multistep planning horizon. The parametric structure of the optimal strategy for switching service channels is revealed.

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Notes

  1. The concept of A-convexity was proposed in [17] to analyze the properties of optimal decision-making (control) strategies in inventory logistics problems with fixed delivery prices that do not depend on the size of the delivery, with the addition of amounts due to the size of the delivery lot.

  2. Fantastic in [16] was the assumption that the warehouse can not only place restocking orders but also return the item to its suppliers.

  3. At present, the term “fantasy problem,” which has been criticized at a number of seminars, has been replaced by “problem of inventory control with returns.”

  4. The application of formula (17) is associated with some stipulations, the essence of which is in that, in some cases listed in [13], the parameter \(R_{1,i}^{(2)} \) is set equal to \(\underline {u_{i}} \). There are other nuances.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997, Russia

    A. S. Mandel

  2. Lomonosov Moscow State University, Moscow, 119991, Russia

    V. A. Laptin

Authors
  1. A. S. Mandel
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  2. V. A. Laptin
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Correspondence to A. S. Mandel or V. A. Laptin.

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Translated by V. Potapchouck

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Mandel, A.S., Laptin, V.A. Optimal Control of Queuing Systems with Channel Switching. Autom Remote Control 82, 1720–1729 (2021). https://doi.org/10.1134/S000511792110009X

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