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The k -out-of- n : G System Viewed as a Multi-Server Queue

Author

Listed:
  • Achyutha Krishnamoorthy

    (Department of Mathematics, CMS College Kottayam, Kottayam 686001, India
    Current address: Department of Mathematics, Central University of Kerala, Kasargod 671316, India.)

  • Anu Nuthan Joshua

    (Department of Mathematics, Union Christian College, Aluva 683102, India)

  • Ambily P. Mathew

    (Department of Mathematics, CMS College Kottayam, Kottayam 686001, India)

Abstract

This paper extends the k -out-of- n : G reliability system to a multi-server queue. We study a multi-server reliability-queuing model with the N -policy of repair. The queuing system considered here has n servers, each of which has identically and exponentially distributed service times with parameter μ . Servers are subject to breakdown at an exponential rate γ . The repair process follows the N -policy of repair. Although these servers work independently of each other, service can be provided only when k functional servers are available in the system. We study the model in the steady state, using the matrix analytic method. We evaluate some associated performance measures and provide graphical/numerical illustrations. We consider an optimization problem, and the results of the study are presented.

Suggested Citation

  • Achyutha Krishnamoorthy & Anu Nuthan Joshua & Ambily P. Mathew, 2024. "The k -out-of- n : G System Viewed as a Multi-Server Queue," Mathematics, MDPI, vol. 12(2), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:210-:d:1315242
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