On the behavior of the batch arrival queue Mx/M/1 during a busy period

Wolfgang Stadje

Naval Research Logistics (NRL), 1994, vol. 41, issue 2, 153-169

Abstract: The queue size process (t)0≤t≤t0 of the batch arrival queue MX/M/1 is studied under the condition that the duration of its busy period is larger than t0. Explicit formulas for the transition probabilities are given and the limiting Markov process for t0 → ∞ is investigated. Several properties of this process are considered. Its transition probabilities and moments and the distribution of its minimum are derived and a functional limit theorem for the rescaled process is proved. © 1994 John Wiley & Sons, Inc.

Date: 1994
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https://doi.org/10.1002/1520-6750(199403)41:23.0.CO;2-U

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Persistent link: https://EconPapers.repec.org/RePEc:wly:navres:v:41:y:1994:i:2:p:153-169

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