Transient solution of fractional M/M/c queue

N. Sujatha and G.V.S.R. Deekshitulu

International Journal of Mathematics in Operational Research, 2023, vol. 26, issue 2, 170-181

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. (search for similar items in EconPapers)
Date: 2023
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