Title: Analysis of (MAP, PH)/(PH, PH)/1 retrial queueing model with standby server, collision of orbital customers, breakdowns, two-way communication, phase type repairs, constant retrial rate and impatient behaviour of customers

Authors: G. Ayyappan; K. Thilagavathy

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

Abstract: Our system was modelled using standby server (SS) whenever a main server (MS) is unavailable due to breakdowns and analysed the constant retrial policy as well as collision for the orbital customers. The incoming arrival (IA) of customers follows the Markovian arrival process (MAP). The outgoing arrival (OA) of customers, service for both incoming and outgoing arrival of customers, and repairs are all based on the phase-type (PH) distributions. Using matrix analytic method, we investigate the steady state probability vector of the system. We described the busy period as well as cost analysis of the system and some performance of the system measures. Then, we examine some of the numerical as well as graphical representations for this model.

Keywords: PH distribution; constant retrial rate; Markovian arrival process; MAP; two-way communication; standby server; impatient behaviour.

DOI: 10.1504/IJOR.2025.143958

International Journal of Operational Research, 2025 Vol.52 No.1, pp.1 - 50

Received: 18 Dec 2021
Accepted: 24 Apr 2022
Published online: 16 Jan 2025 *

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