Title: Analysis of MAP/PH/1 queueing system with catastrophic delay action, standby server, balking, working vacation and vacation interruption under N-policy

Authors: G. Ayyappan; K. Thilagavathy

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

Abstract: We consider customers arrival based on a Markovian arrival process (MAP), and their service times are based on a phase-type (PH) distribution, which incorporates the concepts of catastrophic delay action. When a catastrophic event occurs during a busy period, two clocks are immediately activated, one of which is the protection clock and the other is the delay time clock. Unless the protection clock expires first, the system will resume to the state in which the catastrophic event occurred; however, unless the delay time clock expires first, all customers in the system will be flushed out of the system and the server will become idle. The matrix analytic method has been utilised to investigate the expected number of customers in the system under steady-state probability vector. We examined the cost analysis of the system and some characteristic of performance measures of the system. We examine some of the numerical as well as pictorial representation for the clear view of our model.

Keywords: PH-distribution; catastrophic delay action; standby server; Markovian arrival process; MAP; impatient behaviour; matrix analytic method.

DOI: 10.1504/IJMMNO.2023.132290

International Journal of Mathematical Modelling and Numerical Optimisation, 2023 Vol.13 No.3, pp.223 - 243

Received: 17 Jul 2022
Accepted: 27 Nov 2022
Published online: 17 Jul 2023 *

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