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A queuing process with bilevel hysteretic service‐rate control

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  • Richard F. Gebhard

Abstract

The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process. A bilevel hysteretic control based on queue length control levels is employed in an M/M/1 queuing system. Expressions are obtained for queue length probabilities, the first two factorial moments of queue length and two figures of merit for describing control performance under the assumption of statistical equilibrium. Computational examples illustrate the effects on queuing processes subject to this type of control. Several cost formulae are considered for comparison of costs when the queue control doctrine is varied. Situations in which hysteretic control is useful are discussed.

Suggested Citation

  • Richard F. Gebhard, 1967. "A queuing process with bilevel hysteretic service‐rate control," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(1), pages 55-67.
    • Handle: RePEc:wly:navlog:v:14:y:1967:i:1:p:55-67
    DOI: 10.1002/nav.3800140106
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    Cited by:

    1. Ciro D’Apice & Maria Pia D’Arienzo & Alexander Dudin & Rosanna Manzo, 2023. "Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers," Mathematics, MDPI, vol. 11(21), pages 1-34, November.
    2. Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.
    3. K. Jeganathan & M. Abdul Reiyas & S. Selvakumar & N. Anbazhagan & S. Amutha & Gyanendra Prasad Joshi & Duckjoong Jeon & Changho Seo, 2022. "Markovian Demands on Two Commodity Inventory System with Queue-Dependent Services and an Optional Retrial Facility," Mathematics, MDPI, vol. 10(12), pages 1-22, June.

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