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

M. I. G. Suranga Sampath (), K. Kalidass and Jicheng Liu
Additional contact information
M. I. G. Suranga Sampath: Library, University of Kelaniya
K. Kalidass: Karpagam Academy of Higher Education
Jicheng Liu: Huazhong University of Science and Technology

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 297-320

Abstract: 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.

Keywords: M/M/1 queue; customer impatience; multiple differentiated vacations; transient analysis; Laplace transform; continued fraction; 60K25; 68M20; 90B22 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s13226-020-0402-z

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