Performance Analysis of \(M^X/M/1\) Queue With Working Vacation, \(N\)-Policy and Customer Impatience

This paper deals the transient analysis of a queueing system with working vacation in which the server may encounter with breakdowns. Customers enter in batches according to a Poisson process and receive service in FCFS mode. Whenever the server finds nobody, the server starts a working vacation dur...

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Bibliographic Details
Published in:Communications in Mathematics and Applications 2022-05, Vol.13 (1), p.87-101
Main Authors: Sridhar, G., Devi, V.N. Rama, Chandan, K.
Format: Article
Language:English
Subjects:
Customer services
Customers
Differential equations
Mathematics
Operations management
Parameter sensitivity
Performance indices
Probability
Queuing theory
Sensitivity analysis
Transient analysis
Vacations
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Summary:This paper deals the transient analysis of a queueing system with working vacation in which the server may encounter with breakdowns. Customers enter in batches according to a Poisson process and receive service in FCFS mode. Whenever the server finds nobody, the server starts a working vacation during which the server renders service at a slower rate than the normal one. Further, we considered two types of customer’s impatience balking and reneging. We solved the system of differential equations to find transient state probabilities and computed various performance indices like average queue length of system, the mean waiting time etc. We then executed sensitivity analysis and observed the impact on different parameters.
ISSN:0976-5905
0975-8607
DOI:10.26713/cma.v13i1.1808