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 firstname.lastname@example.org M. L. Chaudhry email@example.com Department of Mathematics and Computer
Methodology and Computing in Applied Probability – Springer Journals
Published: Jun 4, 2018
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