Title: A MAP/PH₁, PH₂/1 system with two types of heterogeneous service, setup, closedown, vacation, immediate feedback, breakdown and repair

Authors: G. Ayyappan; R. Gowthami

Addresses: Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry – 605014, India ' Department of Mathematics, Pondicherry Engineering College, Pillaichavady, Puducherry – 605014, India

Abstract: In this article, we examine a classical queueing model with single unreliable server which can offer two types of heterogeneous services namely, types I and II. Customers reach the system by following the Markovian arrival process (MAP). The service times of both types of services are considered to be phase-type (PH) distributed. We have considered a service clock which begins at the commencement of the service after the setup/repair process and immediate feedback for the unsatisfied customers. If the service clock expires, the server will start the closedown process and consequently goes on vacation. The assumptions of our model have greater significance on small-scale industries. By utilising the matrix-analytic method, we have examined our model and investigated the active period and the waiting time distribution of our model. We have also carried out the cost analysis for our model. At the end, some numerical and graphical exemplifications are presented for clear insight into our model.

Keywords: PH distribution; Markovian arrival process; MAP; two types of services; vacation; service clock; setup; closedown; immediate feedback; breakdown; repair.

DOI: 10.1504/IJMOR.2022.124136

International Journal of Mathematics in Operational Research, 2022 Vol.22 No.3, pp.313 - 348

Received: 04 May 2021
Accepted: 20 May 2021
Published online: 14 Jul 2022 *

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