Title: Transient analysis of M/M/C queuing model with reneging, finite capacity and population

Authors: Binay Kumar

Addresses: Department of Mathematics, Magadh Mahila College, Patna University, Patna-800001, India

Abstract: The present paper deals with multi-server Markovian queuing model with impatient behaviour of units. The server work in two modes: slow mode and fast mode; and changes its state from slow to fast or vice versa with some exponential distributed time parameters. When the server works in slow mode, the units may leave the system due to impatient behaviour of units. We investigate the present model by two variant, one with finite capacity and other with finite population. Transient probabilities of various states are obtained by solving the set of governing equation via Runge-Kutta method. The various system performance measures are established in terms of transient probability of the system states. The system behaviour for different parameter are analysed by using the graphs and tables.

Keywords: Markovian model; transient probability; multi-server; reneging; Runge-Kutta.

DOI: 10.1504/IJMOR.2022.120339

International Journal of Mathematics in Operational Research, 2022 Vol.21 No.1, pp.1 - 25

Received: 26 Nov 2019
Accepted: 09 Sep 2020
Published online: 14 Jan 2022 *

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