Analysis of state-dependent discrete-time queue with system disaster
RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1915-1927.

An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the nth state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo/Geo/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2018078
Classification : 60k25
Mots-clés : Generating function, continued fraction, power series, Geo/Geo/1 queue, busy period distribution, ballot numbers
Sudhesh, Ramupillai 1 ; Vaithiyanathan, Arumugam 1

1 
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     title = {Analysis of state-dependent discrete-time queue with system disaster},
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Sudhesh, Ramupillai; Vaithiyanathan, Arumugam. Analysis of state-dependent discrete-time queue with system disaster. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 5, pp. 1915-1927. doi : 10.1051/ro/2018078. http://www.numdam.org/articles/10.1051/ro/2018078/

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