A Discrete-Time GIX/GeoY/1 Queue with Early Arrival System

A discrete-time batch service queue with batch renewal input and random serving capacity rule under the late arrival delayed access system, has recently appeared in the literature (Barbhuiya and Gupta in Queueing Syst 91(3):347–365, 2019b). In this paper, we consider the same model under the early a...

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Bibliographic Details
Published in:International journal of applied and computational mathematics 2019, Vol.5 (5)
Main Authors: Gupta, U. C., Barbhuiya, F. P., Maity, Arunava
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Science and Engineering
Mathematical and Computational Physics
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Nuclear Energy
Operations Research/Decision Theory
Original Paper
Theoretical
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Summary:A discrete-time batch service queue with batch renewal input and random serving capacity rule under the late arrival delayed access system, has recently appeared in the literature (Barbhuiya and Gupta in Queueing Syst 91(3):347–365, 2019b). In this paper, we consider the same model under the early arrival system, since it is more applicable in telecommunication systems where an arriving batch of packets needs to be transmitted in the same slot in which it has arrived. In doing so, we derive the steady-state queue length distributions at various epochs, and show that in limiting case the result gets converted to the continuous-time queue (Barbhuiya and Gupta in J Differ Equ Appl 25(2):1–10, 2019a). We discuss few numerical results as well.
ISSN:2349-5103
2199-5796
DOI:10.1007/s40819-019-0724-x