Title: Analysis of MAP/PH(1), PH(2), PH(3)/1 queueing system with two modes of heterogeneous service, standby server, vacation, impatient behaviour of customers, additional service, start-up time, breakdown and phase type repairs

Authors: G. Ayyappan; K. Thilagavathy

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

Abstract: In this article, we consider a single server queue in which customers arrive according to the Markovian arrival process (MAP) and their corresponding two modes of service based on phase-type (PH) distribution. The main server may affect by breakdown while offering service whether it is any one of the modes of service or additional service immediately go for the repair process. At that moment, the service process switchover to the standby server until the main server rejuvenated from the phase-type repair. When vacation completion epoch, the main server will do the start-up process. Using the matrix-analytic method, we investigated the total number of customers in the system under steady-state probability vector. We examined the stability condition, busy period and characteristics of some performance measures of the system are discussed. Numerical results are tabulated and graphical representations are provided for a clear view of our model.

Keywords: PH distribution; Markovian arrival process; MAP; standby server; impatient behaviour; additional service.

DOI: 10.1504/IJOR.2024.136008

International Journal of Operational Research, 2024 Vol.49 No.1, pp.85 - 130

Received: 09 Feb 2021
Accepted: 29 Apr 2021
Published online: 12 Jan 2024 *

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