| Issue |
RAIRO-Oper. Res.
Volume 51, Number 1, January-March 2017
|
|
|---|---|---|
| Page(s) | 123 - 134 | |
| DOI | https://doi.org/10.1051/ro/2016008 | |
| Published online | 15 December 2016 | |
Transient analysis of a single server discrete-time queue with system disaster
1 Department of Mathematics, Bharathidasan Institute of
Technology (BIT) Campus, Anna University, Tiruchirappalli, 620024 Tamilnadu, India.
sudhesh@aucev.edu.in; lpriya@aucev.edu.in
2 Department of Mathematics, University of Central, Arkansas,
Conway, 72035 Arkansas, USA.
rblenin@uca.edu
Received:
1
August
2015
Accepted:
21
January
2016
A discrete-time Geo/Geo/1 queue with system disaster is considered in this paper. The time-dependent and steady state probabilities of number of customers present in the system are obtained in terms of ballot numbers by solving the underlying system of difference equations using the generating function and continued fractions. Further, the busy period distribution is derived in terms of Catalan numbers. For special cases, time-dependent system size probabilities and busy period distribution are verified with the existing results in the literature. Numerical illustrations are provided for different parameter values to see their effect on performance measures and to get more insight of the model behavior.
Mathematics Subject Classification: 60K25
Key words: Catastrophes / busy period / Catalan numbers / ballot numbers / continued fractions
© EDP Sciences, ROADEF, SMAI 2016
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