Abstract
An M/M/1 queueing system subjected to multiple differentiated vacations, customer impatience and a waiting server is analyzed. The explicit transient probabilities of system size are derived using probability generating function technique, Laplace transform, continued fractions and some properties of confluent hypergeometric function. Further, the time-dependent mean and variance are obtained as the performance measures. A numerical example is presented in order to study the behavior of the system.
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Suranga Sampath, M.I.G., Kalidass, K. & Liu, J. Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism. Indian J Pure Appl Math 51, 297–320 (2020). https://doi.org/10.1007/s13226-020-0402-z
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DOI: https://doi.org/10.1007/s13226-020-0402-z
Key words
- M/M/1 queue
- customer impatience
- multiple differentiated vacations
- transient analysis
- Laplace transform
- continued fraction