Title: Modified Bessel series solution of the single server queueing model with feedback

Authors: Chandra Shekhar; Amit Kumar; Shreekant Varshney

Addresses: Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan, 333 031, India ' Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan, 333 031, India ' Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Rajasthan, 333 031, India

Abstract: In multi-access systems, scheduling mechanism often requires a proper feedback policy. In this paper, the direct and simple transient solution technique for the state of the system in a single server/processor Markovian queueing model with feedback is presented using the modified Bessel function of the second kind. This technique appears to economise in algebra. The expression for a time-dependent measure of effectiveness such as an expected number of the customers in the system is also derived. We demonstrate how fast the state probabilities tend to their equilibrium limits when it exists. The sensitivity of the state of the system and expected number of the customers in the system has been also analysed and the results are depicted in the tables and graphs.

Keywords: single server; feedback policy; modified Bessel function of the second kind; transient solution; Poisson queues.

DOI: 10.1504/IJCSM.2019.10022402

International Journal of Computing Science and Mathematics, 2019 Vol.10 No.3, pp.313 - 326

Received: 05 Jan 2017
Accepted: 19 Jul 2017

Published online: 24 Jul 2019 *

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