Title: Cost optimisation of a heterogeneous server queueing system with working breakdown using PSO

Authors: Radhika Agarwal; Divya Agarwal; Shweta Upadhyaya

Addresses: Amity Institute of Applied Sciences, Amity University, Sector 125, Noida, UP, India ' Amity Institute of Applied Sciences, Amity University, Sector 125, Noida, UP, India ' Amity Institute of Applied Sciences, Amity University, Sector 125, Noida, UP, India

Abstract: Persuaded by the applicability of queueing models, the reliability analysis and cost optimisation of M^X/M/2 system consisting of heterogeneous servers (Server1 and Server2) is discussed in this article. The Server1 is steady and reliable which leaves for vacation as soon as there is no client available in the system while Server2 is unreliable and may breakdown while giving service to the client. No sooner the server fails, immediately the repair process starts and the server works at a lower speed instead of halting. The schematic diagram of the model gives the overview of the model. The sensitivity analysis is done for validation of the model by taking a numerical illustration and the results are visualised and validated with the help of graphs. Finally, the optimal service rates are obtained using particle swarm optimisation (PSO) technique for matrix method.

Keywords: heterogeneous (two) servers; matrix-geometric method; working breakdown; multiple vacations; cost optimisation; particle swarm optimisation; PSO.

DOI: 10.1504/IJMOR.2023.134842

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.3, pp.410 - 424

Received: 20 Oct 2022
Accepted: 23 Oct 2022
Published online: 14 Nov 2023 *

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