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On the behavior of the batch arrival queue M x /M /1 during a busy period
Author(s) -
Stadje Wolfgang
Publication year - 1994
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(199403)41:2<153::aid-nav3220410203>3.0.co;2-u
Subject(s) - queue , limiting , limit (mathematics) , mathematics , markov process , markov chain , combinatorics , period (music) , process (computing) , discrete mathematics , statistics , computer science , physics , mathematical analysis , acoustics , engineering , mechanical engineering , programming language , operating system
The queue size process ( t ) 0 ≤ t ≤ t 0 of the batch arrival queue M X /M/ 1 is studied under the condition that the duration of its busy period is larger than t 0 . Explicit formulas for the transition probabilities are given and the limiting Markov process for t 0 → ∞ 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.