On the behavior of the batch arrival queue  during a busy period

On the behavior of the batch arrival queue during a busy period

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Article ID: iaor19942029
Country: United States
Volume: 41
Issue: 2
Start Page Number: 153
End Page Number: 169
Publication Date: Mar 1994
Journal: Naval Research Logistics
Authors:
Abstract:

The queue size process equ2 of the batch arrival queue equ3 is studied under the condition that the duration of its busy period is larger than equ4. Explicit formulas for the transition probabilities are given and the limiting Markov process for equ5 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.

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