ON THE BEHAVIOR OF THE BATCH ARRIVAL QUEUE M(X)/M/1 DURING A BUSY PERIOD

Autor(en): STADJE, W 
Stichwörter: LIMIT-THEOREM; Operations Research & Management Science; RANDOM-WALK
Erscheinungsdatum: 1994
Herausgeber: JOHN WILEY & SONS INC
Journal: NAVAL RESEARCH LOGISTICS
Volumen: 41
Ausgabe: 2
Startseite: 153
Seitenende: 169
Zusammenfassung: 
The queue size process (Q(t))0 less-than-or-equal-to t less-than-or-equal-to t0 of the batch arrival queue M(x)/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 --> infinity 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. (C) 1994 John Wiley & Sons, Inc.
ISSN: 0894069X
DOI: 10.1002/1520-6750(199403)41:2<153::AID-NAV3220410203>3.0.CO;2-U

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