Title: Transient solution of fractional M/M/c queue

Authors: N. Sujatha; G.V.S.R. Deekshitulu

Addresses: Department of Mathematics, JNTUK, Kakinada, Andhra Pradesh, India ' UCEK, JNTUK, Kakinada, Andhra Pradesh, India

Abstract: In queuing models, sometimes the server may not work with full efficiency or may stop working also. Such problems are modelled with the help of fractional differential equations. Differential-difference equations involving fractional derivatives in the sense of Mittag-Leffler function have been employed to model the problems with partial activity of the server. In this paper, transient analysis of fractional M/M/c queue has been carried out analytically and results are obtained using MATLAB. The validity and efficiency of the above model is demonstrated with a numerical example. The results obtained by this new approach are justified by comparing them with solutions of classical queue which are available in the literature.

Keywords: transient analysis; fractional derivatives; Mittag-Leffler function.

DOI: 10.1504/IJMOR.2023.134472

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.2, pp.170 - 181

Received: 03 May 2022
Accepted: 28 Jun 2022
Published online: 24 Oct 2023 *

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