Title: A study on transient solution of fractional M/M/2 queue with homogeneous and heterogeneous servers

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 with multiple servers, all the servers may not be completely active and may not work with same efficiency. Keeping this in view, a multiserver fractional queue with heterogeneous servers has been analysed in the present paper. Transient state probablities and also performance measures of the model such as average number of customers in the system, average number of customers in the queue, etc. have been computed. Variations in these performance measures have been observed both numerically and graphically with respect to partial activity of the server. Further, efficiency of transient M/M/2 fractional queueing model consisting of heterogeneous servers is compared with efficiency of transient M/M/2 fractional queuing model with homogeneous servers.

Keywords: transient solution; fractional queue; Mittag-Leffler function; heterogeneous servers.

DOI: 10.1504/IJMOR.2025.146361

International Journal of Mathematics in Operational Research, 2025 Vol.31 No.1, pp.95 - 109

Received: 21 Aug 2023
Accepted: 25 Aug 2023
Published online: 27 May 2025 *

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