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The Queue G e o/G/1/N + 1 Revisited

The Queue G e o/G/1/N + 1 Revisited This paper presents an alternative steady-state solution to the discrete-time G e o/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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Methodology and Computing in Applied Probability Springer Journals

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References (52)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer Science+Business Media, LLC, part of Springer Nature
Subject
Statistics; Statistics, general; Life Sciences, general; Electrical Engineering; Economics, general; Business and Management, general
ISSN
1387-5841
eISSN
1573-7713
DOI
10.1007/s11009-018-9645-0
Publisher site
See Article on Publisher Site

Abstract

This paper presents an alternative steady-state solution to the discrete-time G e o/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.

Journal

Methodology and Computing in Applied ProbabilitySpringer Journals

Published: Jun 4, 2018

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