Geodesic
Transient analysis of a single server discrete-time queue with system disaster
Sudhesh, R.1 ; Sebasthi Priya, R.1 ; Lenin, R. B.2
1 Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, 620024 Tamilnadu, India.
2 Department of Mathematics, University of Central, Arkansas, Conway, 72035 Arkansas, USA.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 123-134

Voir la notice de l'article provenant de la source Numdam

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.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016008
Classification : 60K25
Keywords: Catastrophes, busy period, Catalan numbers, ballot numbers, continued fractions

Sudhesh, R. 1 ; Sebasthi Priya, R. 1 ; Lenin, R. B. 2

1 Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, 620024 Tamilnadu, India.
2 Department of Mathematics, University of Central, Arkansas, Conway, 72035 Arkansas, USA. 
@article{RO_2017__51_1_123_0,
     author = {Sudhesh, R. and Sebasthi Priya, R. and Lenin, R. B.},
     title = {Transient analysis of a single server discrete-time queue with system disaster},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {123--134},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {1},
     year = {2017},
     doi = {10.1051/ro/2016008},
     mrnumber = {3590465},
     zbl = {1360.60170},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ro/2016008/}
}
TY  - JOUR
AU  - Sudhesh, R.
AU  - Sebasthi Priya, R.
AU  - Lenin, R. B.
TI  - Transient analysis of a single server discrete-time queue with system disaster
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2017
SP  - 123
EP  - 134
VL  - 51
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ro/2016008/
DO  - 10.1051/ro/2016008
LA  - en
ID  - RO_2017__51_1_123_0
ER  - 
%0 Journal Article
%A Sudhesh, R.
%A Sebasthi Priya, R.
%A Lenin, R. B.
%T Transient analysis of a single server discrete-time queue with system disaster
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2017
%P 123-134
%V 51
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ro/2016008/
%R 10.1051/ro/2016008
%G en
%F RO_2017__51_1_123_0
Sudhesh, R.; Sebasthi Priya, R.; Lenin, R. B. Transient analysis of a single server discrete-time queue with system disaster. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 1, pp. 123-134. doi: 10.1051/ro/2016008

Cité par Sources :