Title: Distribution of occupied resources on a fractional resource sharing in a queueing system

Authors: T.B. Ravaliminoarimalalason; M. Rakotomalala; F. Randimbindrainibe

Addresses: Ecole Doctorale en Sciences et Techniques de l'Ingénierie et de l'Innovation, Ecole Supérieure Polytechnique d'Antananarivo, University of Antananarivo, Madagascar, East Africa ' Ecole Doctorale en Sciences et Techniques de l'Ingénierie et de l'Innovation, Ecole Supérieure Polytechnique d'Antananarivo, University of Antananarivo, Madagascar, East Africa ' Ecole Doctorale en Sciences et Techniques de l'Ingénierie et de l'Innovation, Ecole Supérieure Polytechnique d'Antananarivo, University of Antananarivo, Madagascar, East Africa

Abstract: Many server systems can share their resources by fractional way not discrete. It can be found in major cases of communication systems sharing power, spectrum or bandwidth resources for example. The objective of this work is to build analytical expressions of the amount of occupied resources in a structure modelled as queueing system. The queue server shares its resources to customers that request services to him. Both infinite and finite capacity are highlighted and the requested resources can be fractional. The amount of occupied resources as real-valued random variable is characterised by its distribution functions that we proposed in this paper. They are validated by simulations, and then can be used to predict the performances of such system or to dimension the appropriate needed capacity. Impacts of system load factor and system capacity has been also analysed.

Keywords: queueing; dimensioning; load factor; resource occupation; resource sharing.

DOI: 10.1504/IJOR.2024.136003

International Journal of Operational Research, 2024 Vol.49 No.1, pp.131 - 145

Received: 04 Mar 2021
Accepted: 11 May 2021
Published online: 12 Jan 2024 *

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