Title: Analysis of MAP/PH/1 queueing model with immediate feedback, starting failures, single vacation, standby server, delayed repair, breakdown and impatient customers

Authors: G. Ayyappan; K. Thilagavathy

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

Abstract: We have analysed the queueing model with a single server in which customers arrive according to the Markovian arrival process, the service process according to phase type distributions and the standby server who is serving at a lower rate also follows the phase type distribution. The total number of customers are present in the system under the steady-state probability vector has been probed by using matrix-analytic method (MAM). We have examined the stability condition, the analysis of the busy period and derived some important performance measures of our model. Numerical results and graphical representation are discussed for the proposed model.

Keywords: Markovian arrival process; MAP; phase type distributions; immediate feedback; standby server; delay time to repair; single vacation.

DOI: 10.1504/IJMOR.2021.116981

International Journal of Mathematics in Operational Research, 2021 Vol.19 No.3, pp.269 - 301

Received: 11 Feb 2020
Accepted: 05 Apr 2020
Published online: 10 Aug 2021 *

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