Title: Analysis of a single server batch arrival non-Markovian queuing model approach in classification of foot thermograms

Authors: R. Vanalakshmi; S. Maragathasundari; Josephine Selle Jeyanathan

Addresses: Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil, India ' Department of Mathematics, Kalasalingam Academy of Research and Education, Krishnankoil, India ' Department of Electronics and Communication Engineering, Kalasalingam Academy of Research and Education, Krishnankoil, India

Abstract: In this article, a single server non-Markovian queuing model with Poisson arrivals in stacks of different sizes is discussed. The server provides clients with a general service at a time with a random duration setup time after completing the first level of service. Also, the setup time stage is introduced to carry out the preparatory work required for the stage 2 service and customers may renege during the setup phase. Additionally, the server is subject to random interruption during the third stage of service and it enters into the repair process immediately. The effect of the setup time stage, interruption and reneging in the defined queuing system are well analysed. Using the supplementary variable technique of queuing theory, the duration of the queue length of different states of the system in terms of probability generating functions and the queue performance measures are determined. The issue of characterised lines is very much clarified by a reasonable application and supported by a mathematical portrayal.

Keywords: non-Markovian queuing model; probability distribution; classification of foot thermo grams; setup time; random breakdowns; delay time; probability generating function; steady state equations.

DOI: 10.1504/IJMMNO.2022.126555

International Journal of Mathematical Modelling and Numerical Optimisation, 2022 Vol.12 No.4, pp.327 - 350

Received: 15 Nov 2021
Accepted: 28 Mar 2022
Published online: 28 Oct 2022 *

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