Title: A two-server tandem queueing model with Markovian arrival process, phase type service, working vacation, feedback, re-service, unreliable server, interrupted closedown and customers intolerance

Authors: G. Ayyappan; G. Archana Alias Gurulakshmi

Addresses: Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Avadi, Chennai, Tamil Nadu, India

Abstract: This paper intends to focus on two-server tandem queue with working vacation, feedback, re-service, unreliable server, interrupted closedown and impatient customers. Input flow of customers arrival is modelled using a Markovian arrival process (MAP) and the service time is considered to follow a phase type distribution. Customers impatience has been studied under phenomena of reneging and balking of this model. The essential and sufficient conditions for system stability is found. By using the matrix analytical method, the queueing model's steady-state probability distribution was derived. Additionally, we derived some performance indicators for the model. Finally, certain numerical examples were used to evaluate the impact of system parameters both numerically and graphically.

Keywords: Markovian arrival process; MAP; phase type service; working vacation; re-service; interrupted closedown; reneging; balking; breakdown; repair.

DOI: 10.1504/IJMOR.2025.145605

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.2, pp.206 - 250

Received: 27 Jul 2023
Accepted: 01 Aug 2023
Published online: 09 Apr 2025 *

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