Title: Cost optimisation of MMAP/PH(1), PH(2)/1 pre-emptive priority retrial queueing model with standby server, orbital search, server breakdowns, phase type repairs and impatient customers

Authors: G. Ayyappan; K. Thilagavathy; Rakesh Kumar

Addresses: Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Statistics and Actuarial Science, Namibia University of Science and Technology, Namibia, India

Abstract: In this paper, we examine a single server queueing model in which priority customers arrive based on the marked Markovian arrival process (MMAP) and their corresponding service process is based on phase-type (PH) distribution. The primary server provides service to high priority or low priority customers, who may be affected by a breakdown, the standby server takes over service until the primary server has been repaired. Whenever either the primary or the standby server becomes idle, an orbital search of low priority customers is performed. We have established the stability condition for the model. Utilising the matrix-analytic method (MAM), the model is solved under steady state. Further, the busy period analysis of the model is carried out. Finally, the cost model is presented and the total cost of the system is analysed with the change in system parameters.

Keywords: MMAP; PH-distribution; standby server; impatient customers; busy period analysis; retrials.

DOI: 10.1504/IJMOR.2025.145759

International Journal of Mathematics in Operational Research, 2025 Vol.30 No.3, pp.350 - 391

Received: 24 Jul 2023
Accepted: 15 Aug 2023
Published online: 23 Apr 2025 *

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