Title: Mathematical modelling and performance analysis of single server queuing system - eigenspectrum

Authors: E. Mamatha; S. Saritha; C.S. Reddy; P. Rajadurai

Addresses: Department of Mathematics, GITAM Deemed to be University, Bangalore, Karnataka – 562163, India ' Department of Mathematics, GITAM Deemed to be University, Bangalore, Karnataka – 562163, India ' Department of Mathematics, Cambridge Institute of Technology – North Campus, Bangalore, Karnataka – 562110, India ' Department of Mathematics, Srinivasa Ramanujan Center, SASTRA Deemed University, Kumbakonam – 612001, India

Abstract: Classical queuing theory is playing vital role to study and analyse the performance analysis of real-time servicing systems, production inventory and manufacturing systems, telecommunication systems, modern information and communication technology systems and computing sector. In recent decays, bounded and immeasurable queues have been intensively studied; due to its attractive mathematical features with wide spread applicability. Such a system describes units of work, e.g., particles or customers, arriving at a resource, that stay present for some random duration that is independent of other customers. The aim of this paper is to evaluate the performance measures with a single server queuing system. Mathematical model has been developed to study the probability live time of the server using algebraic eigenproperties. These models are indispensable in real-time systems, manufacturing and communication queuing systems, including wireless networks, mobility, and randomly arriving traffic.

Keywords: Markov process; server live probability; latent values and vectors; matrix geometric approach; single server queuing system.

DOI: 10.1504/IJMOR.2020.108408

International Journal of Mathematics in Operational Research, 2020 Vol.16 No.4, pp.455 - 468

Received: 23 Oct 2018
Accepted: 19 Mar 2019
Published online: 13 Jul 2020 *

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