A note on GeoX/G/1 queueing system

Sujit Kumar Samanta and Aysha Parveen

Statistics & Probability Letters, 2024, vol. 207, issue C

Abstract: This article investigates the discrete-time GeoX/G/1 queue with an early arrival system. The system length distributions at outside observer’s, post-departure and random epochs as well as the waiting time distribution of an arbitrary customer in a batch are derived. The system of difference equations developed using the supplementary variable technique allows us to directly compute the probability generating functions for these distributions. Some numerical results are provided in tabular form.

Keywords: Difference equation; Queueing; Early arrival system; Supplementary variable technique; Probability generating function (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110033

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