Abstract
In Queueing Theory, systems are studied mostly by considering time as a continuous variable. However, in practice we come across systems in which events occur at discrete ‘marks’ along the time axis. Examples of such situations may be of electronic installations whose operations are governed by internal clocks, or missile bases which fire at oncoming aircraft at regular intervals etc. Theoretically, the mathematical formalisms required for these discrete time processes and the corresponding continuous time processes are essentially the same; nevertheless, from the practical point of view, it seems worthwhile to point out the major modifications needed in their treatment. We do so in this section and present some discrete time results corresponding to the continuous time results obtained earlier. It should be noted that the discrete time distribution corresponding to Poisson is Binomial and to Negative Exponential is Geometric. Thus we shall call these systems Geom/G/1 and GI/Geom/1. For the sake of simplicity we shall restrict ourselves to the unit arrival and unit service in both these cases.
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© 1968 Springer-Verlag Berlin · Heidelberg
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Bhat, U.N. (1968). Queueing Systems in Discrete Time. In: A Study of the Queueing Systems M/G/1 and GI/M/1. Lecture Notes in Operations Research and Mathematical Economics, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46136-1_4
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DOI: https://doi.org/10.1007/978-3-642-46136-1_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-04251-8
Online ISBN: 978-3-642-46136-1
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