The Queue G e o/G/1/N + 1 Revisited

The Queue G e o/G/1/N + 1 Revisited Methodol Comput Appl Probab https://doi.org/10.1007/s11009-018-9645-0 1 2 M. L. Chaudhry · Veena Goswami Received: 19 September 2017 / Accepted: 28 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 vari- ous 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 illustra- tions. 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. Keywords Discrete-time · Finite buffer · Roots · Queue Mathematics Subject Classification 2010 60K25 · 68M20 · 90B22 Veena Goswami veena goswami@yahoo.com M. L. Chaudhry chaudhry-ml@rmc.ca Department of Mathematics and Computer http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Methodology and Computing in Applied Probability Springer Journals

The Queue G e o/G/1/N + 1 Revisited

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Publisher
Springer US
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
D.O.I.
10.1007/s11009-018-9645-0
Publisher site
See Article on Publisher Site

Abstract

Methodol Comput Appl Probab https://doi.org/10.1007/s11009-018-9645-0 1 2 M. L. Chaudhry · Veena Goswami Received: 19 September 2017 / Accepted: 28 May 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 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 vari- ous 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 illustra- tions. 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. Keywords Discrete-time · Finite buffer · Roots · Queue Mathematics Subject Classification 2010 60K25 · 68M20 · 90B22 Veena Goswami veena goswami@yahoo.com M. L. Chaudhry chaudhry-ml@rmc.ca Department of Mathematics and Computer

Journal

Methodology and Computing in Applied ProbabilitySpringer Journals

Published: Jun 4, 2018

References

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