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

G. Ayyappan and G. Archana Alias Gurulakshmi

International Journal of Mathematics in Operational Research, 2025, vol. 30, issue 2, 206-250

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. (search for similar items in EconPapers)
Date: 2025
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