Title: A study on retrial queueing model with additional breakdown services and complete vacation

Authors: R. Madhumidha; S. Balaji

Addresses: Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India ' Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, Tamil Nadu, India

Abstract: In this research, we explore a retrial queuing model with additional breakdown service and complete vacation. If a customer accesses the system and discovers that the server is busy, they enter an orbit, a space with an unlimited capacity. From the orbit, they keep attempting to access the service. The main server crashes as a result of a disaster. In the event of a breakdown, the main server is sent for repair; in the meantime, it will operate more (working breakdown). The server will attempt a complete vacation if the orbit is empty as soon as the working breakdown is completed. By utilising the supplementary variable technique (SVT), the performance metrics are acquired. Also, the mean busy period and mean busy cycle are discussed. Several specific cases of this model are provided. Further, some numerical results are demonstrated to explore the act of different variables on distinct system performance metrics.

Keywords: retrial queues; working breakdown services; repair; complete vacation; supplementary variable technique; SVT.

DOI: 10.1504/IJMOR.2026.154511

International Journal of Mathematics in Operational Research, 2026 Vol.34 No.2, pp.215 - 230

Received: 22 May 2024
Accepted: 08 Jun 2024
Published online: 02 Jul 2026 *

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