Analysis of a Markovian queueing system with single working vacation and impatience of customers

In this paper, we study an infinite capacity single server Markovian queue with a single working vacation and reneging of impatient customers in the queue during working vacation period. Customers arrive to the system following a Poisson distribution. The server goes to vacation when the system is e...

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Bibliographic Details
Published in:Journal of physics. Conference series 2019-10, Vol.1344 (1), p.12018
Main Authors: Laxmi, P. Vijaya, Kassahun, T. W., Bhavani, E. Girija
Format: Article
Language:English
Subjects:
Customer services
Customers
Markov processes
Numerical analysis
Performance measures
Physics
Poisson distribution
Probability distribution functions
Probability generating function
Queuing theory
Reneging
Single working vacation
Stationary probabilities
Statistical analysis
Vacations
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Summary:In this paper, we study an infinite capacity single server Markovian queue with a single working vacation and reneging of impatient customers in the queue during working vacation period. Customers arrive to the system following a Poisson distribution. The server goes to vacation when the system is empty and stay in vacation for a random period of time that is exponentially distributed. During the working vacation period, the server still continue providing service with a slow service rate. After the completion of the vacation, the server returns back to the regular service period and continue providing service with the regular busy period service rate if there are one or more customers in the system or it will stay idle until a new customer arrives to the system. During working vacation, customers in the queue get impatient and renege from the system and the reneging time is assumed to follow an exponential distribution. The system is modeled as a quasi-birth-death process and the stationary probabilities of the model are obtained using probability generating function approach. Some numerical analysis is also carried out to show the effect of some of the parameters on some selected performance measures of the system.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1344/1/012018