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The Queue Geo/G/1/N + 1 Revisited

Author

Listed:
  • M. L. Chaudhry

    (Royal Military College of Canada)

  • Veena Goswami

    (Kalinga Institute of Industrial Technology)

Abstract

This paper presents an alternative steady-state solution to the discrete-time Geo/G/1/N + 1 queueing system using roots. The analysis has been carried out for a late-arrival system using the imbedded Markov chain method, and the solutions for the early arrival system have been obtained from those of the late-arrival system. Using roots of the associated characteristic equation, the distributions of the numbers in the system at various epochs are determined. We find a unified approach for solving both finite- and infinite- buffer systems. We investigate the measures of effectiveness and provide numerical illustrations. We establish that, in the limiting case, the results thus obtained converge to the results of the continuous-time counterparts. The applications of discrete-time queues in modeling slotted digital computer and communication systems make the contributions of this paper relevant.

Suggested Citation

  • M. L. Chaudhry & Veena Goswami, 2019. "The Queue Geo/G/1/N + 1 Revisited," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 155-168, March.
    • Handle: RePEc:spr:metcap:v:21:y:2019:i:1:d:10.1007_s11009-018-9645-0
    DOI: 10.1007/s11009-018-9645-0
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    References listed on IDEAS

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    1. Mohan L. Chaudhry & Carl M. Harris & William G. Marchal, 1990. "Robustness of Rootfinding in Single-Server Queueing Models," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 273-286, August.
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