Volume 51, Number 3, July-September 2017
|Page(s)||591 - 606|
|Published online||30 June 2017|
Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience
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.
Received: 5 February 2016
Accepted: 20 June 2016
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.
Mathematics Subject Classification: 60K25 / 33C15
Key words: Single server queue / multiple and single working vacation / impatient customers / continued fractions / confluent hypergeometric functions
© EDP Sciences, ROADEF, SMAI 2017
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