Original scientific paper
On transient queue-size distribution in the batch arrival system with the N-policy and setup times
Wojciech M. Kempa
; Institute of Mathematics, Silesian University of Technolgy, Gliwice, Poland
Abstract
In the paper the $M^{X}/G/1$ queueing system with the $N$-policy and setup times is considered. An explicit formula for the Laplace
transform of the transient queue-size distribution is derived using
the approach consisting of few steps. Firstly, a "special''
modification of the original system is investigated and, using the
formula of total probability, the analysis is reduced to the case
of the corresponding system without limitation in the service. Next,
a renewal process generated by successive busy cycles is used to
obtain the general result. Sample numerical computations
illustrating theoretical results are attached as well.
Keywords
batch arrival queueing system; N-policy; queue-size distribution; setup time; transient state
Hrčak ID:
83081
URI
Publication date:
12.6.2012.
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