Title: Analysis of MAP/PH₁, PH₂/2 queueing system with two types of heterogeneous servers, standby server, instantaneous feedback, working vacation, multiple vacations, breakdown, phase type repairs 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: In this article, we discuss two distinct types of heterogeneous servers, one of which is available at all times to provide service to arriving customers while the other is offering service in normal as well as vacation mode. Customers arrive based on the Markovian arrival process (MAP), and the service is distributed according to the phase-type (PH) distribution. While the main server-1 is providing service to the customers, if the main server-1 experiences a breakdown during service moments, the standby server will interrupt the main server-1 and begin providing service at a slower rate than the main server-1's service rate. The matrix-analytic method has been utilised to determine the average number of customers present in the system that was examined under steady-state probability vector. We examined the analysis of the system's busy period and the distribution of waiting time. Numerical and graphical results are presented to our model.

Keywords: PH-distribution; Markovian arrival process; MAP; impatient behaviour; standby server; multiple vacations; working vacation.

DOI: 10.1504/IJSOM.2024.139241

International Journal of Services and Operations Management, 2024 Vol.48 No.3, pp.353 - 394

Received: 28 Jan 2022
Accepted: 09 Apr 2022
Published online: 28 Jun 2024 *

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