Title: Analysis of MAP/PH/1 queueing system with discarding customers having imperfect service, single vacation, feedback and impatient customers

Authors: G. Ayyappan; G. Archana Alias Gurulakshmi

Addresses: Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Puducherry Technological University, Puducherry, India

Abstract: In this paper, we analyse a single server queueing model where the service time follows a phase type distribution and the arrival process follows a Markovian arrival process with corresponding representations (D₀, D₁) of order m and (α, T) of order n. When a customer enters for the service, a generalised Erlang clock with r stages is started concurrently. Due to the impatience the customers may balk the system if server is in vacation period. By using matrix analytic method, we find the steady state analysis in this model. Also, we derive the expected waiting time, system performance measures, cost function and busy period. By using some performance measures we provide the numerical results and graphical representations.

Keywords: Markovian arrival process; phase type service; imperfect service; Erlang clock; single vacation; Bernoulli feedback; balking.

DOI: 10.1504/IJMOR.2024.143389

International Journal of Mathematics in Operational Research, 2024 Vol.29 No.4, pp.411 - 440

Received: 25 May 2023
Accepted: 11 Jun 2023
Published online: 17 Dec 2024 *

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