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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

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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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Authors and Affiliations

  1. Library, University of Kelaniya, Kelaniya, 11600, Sri Lanka

    M. I. G. Suranga Sampath

  2. Department of Mathematics, Karpagam Academy of Higher Education, Coimbatore, 641 021, Tamil Nadu, India

    K. Kalidass

  3. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, 430074, China

    Jicheng Liu

Authors
  1. M. I. G. Suranga Sampath
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  2. K. Kalidass
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  3. Jicheng Liu
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Correspondence to M. I. G. Suranga Sampath.

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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

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