Title: Analysis of MAP/PH₁^E, PH₂^O/1 queue with standby server, second optional service, variant arrival rate, Bernoulli schedule vacation, impatient behaviour of customers, breakdown, essential and optional repair

Authors: G. Ayyappan; K. Thilagavathy

Addresses: Department of Mathematics, Pondicherry Engineering College, Puducherry, India ' Department of Mathematics, Pondicherry Engineering College, Puducherry, India

Abstract: In this article, we examine a single-server queueing model in which customers arrive at one of three different rates depending on the system's current state as determined by a Markovian arrival process. After obtaining the server's essential service, customers have the option of pursuing the second optional service. The service time is distributed in a phase-type manner. If the main server successfully completes an essential repair, the server may choose an optional repair option or return to the service station. We examined the total number of customers existing in the system using the matrix-analytic method (MAM) under the steady-state probability vector. We analyse the features of system performance measures. We discussed the stability condition, the analysis of the busy period, and the distribution of waiting times. For a better understanding of our suggested model, numerical results and graphical representations are provided.

Keywords: variant arrival rate; phase type distributions; Markovian arrival process; standby server; impatient behaviour; second optional service and repair.

DOI: 10.1504/IJMOR.2022.127054

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.2, pp.147 - 214

Received: 22 May 2021
Accepted: 23 Jun 2021
Published online: 21 Nov 2022 *

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