Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience

Sudhesh, R.; Azhagappan, A.; Dharmaraja, S.

doi:10.1051/ro/2016046

Sudhesh, R.¹ ; Azhagappan, A.² ; Dharmaraja, S.³

¹ Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, 620024 Tamilnadu, India.
² Department of Mathematics, St. Anne’s College of Engineering and Technology, Anna University, Panruti, Cuddalore district, 607110 Tamilnadu, India.
³ Department of Mathematics, Indian Institute of Technology Delhi, Haus Khas, 110016 New Delhi, India.

RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 591-606.

Résumé

This paper studies the time-dependent behavior of a single server queueing model with slow service during single and multiple working vacations, and customers’ impatience due to slow service. The time-dependent system size probabilities for the underlying model are obtained in closed form. Further, time-dependent mean and variance are deduced. Finally, numerical illustrations are shown to visualize the system effect for various values of parameters.

Reçu le : 2016-02-05
Accepté le : 2016-06-20

MR Zbl

DOI : 10.1051/ro/2016046

Classification : 60K25, 33C15
Mots clés : Single server queue, multiple and single working vacation, impatient customers, continued fractions, confluent hypergeometric functions

Affiliations des auteurs :

Sudhesh, R. ¹ ; Azhagappan, A. ² ; Dharmaraja, S. ³

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     title = {Transient analysis of {M/M/1} queue with working vacation, heterogeneous service and customers{\textquoteright} impatience},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {591--606},
     publisher = {EDP-Sciences},
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Sudhesh, R.; Azhagappan, A.; Dharmaraja, S. Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 591-606. doi : 10.1051/ro/2016046. http://archive.numdam.org/articles/10.1051/ro/2016046/

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