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.
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