Analysis of finite buffer renewal input queue with balking and multiple working vacations

This paper analyzes a finite buffer single server queueing system with multiple working vacations in which customers balk (i.e., refuse to join the queue). The inter-arrival times and service times during regular busy period are, respectively, arbitrarily and exponentially distributed. Vacation time...

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Bibliographic Details
Published in:Opsearch 2013-12, Vol.50 (4), p.548-565
Main Authors: Vijaya Laxmi, P., Jyothsna, K.
Format: Article
Language:English
Subjects:
Buffers
Business and Management
Communications networks
Customer services
Management
Markov analysis
Mathematics
Operations Research/Decision Theory
Probability
Queuing
Random variables
Studies
Theoretical Article
Vacations
Working hours
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Summary:This paper analyzes a finite buffer single server queueing system with multiple working vacations in which customers balk (i.e., refuse to join the queue). The inter-arrival times and service times during regular busy period are, respectively, arbitrarily and exponentially distributed. Vacation times and service times during vacation are exponentially distributed. Using embedded Markov chain and supplementary variable techniques, we obtain the system length distributions at pre-arrival and arbitrary epochs. Various performance measures of the model, waiting time analysis and some special cases are also presented. Finally, a variety of numerical results in the form of tables and graphs are discussed.
ISSN:0030-3887
0975-0320
DOI:10.1007/s12597-013-0123-8