Title: Analysis of MAP₁^I, PH₂^O/PH₁^I, PH₂^O/1 retrial queue with two-way communication, optional service, single vacation, closedown, setup and balking

Authors: G. Ayyappan; G. Archana Alias Gurulakshmi; B. Somasundaram

Addresses: Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Puducherry Technological University, Puducherry, India ' Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Tamil Nadu, India

Abstract: A single server constant retrial queueing model with close down, vacation, setup, optional service and balking are studied in this article. There are two kinds of arrivals, namely incoming and outgoing calls. If the server is idle, arriving incoming calls will be served instantly. After completion of the service, the server becomes idle. The server goes on vacation, while the system is void. Before taking the vacation, the server will closedown the system and after completion of the vacation, the server will set up the system to give the service. The server will give optional service for incoming calls if the customer needs. The incoming calls follow the Markovian arrival process (MAP) and outgoing calls and service times follow PH-type distribution. We derived the busy period analysis and cost analysis. Also, some important performance measures are obtained which are illustrated graphically/numerically.

Keywords: retrial queues; two way communication; vacation; closedown; setup; optional service; balking.

DOI: 10.1504/IJMOR.2022.127751

International Journal of Mathematics in Operational Research, 2022 Vol.23 No.4, pp.427 - 455

Received: 02 Aug 2021
Accepted: 16 Sep 2021
Published online: 15 Dec 2022 *

Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article