DOI: 10.4018/IJORIS.2020010104 International Journal of Operations Research and Information Systems Volume 11 • Issue 1 • January-March 2020 Copyright © 2020, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. 83 An Unreliable Batch Arrival Retrial Queueing System With Bernoulli Vacation Schedule and Linear Repeated Attempts: Unreliable Retrial System With Bernoulli Schedule Gautam Choudhury, Institute of Advanced Study in Science and Technology, Guwahati, India Lotf Tadj, Department of Industrial Engineering, Alfaisal University, Riyadh, Saudi Arabia https://orcid.org/0000-0002-9418-0895 ABSTRACT This article deals with the steady-state behavior of an M X /G/1 retrial queue with the Bernoulli vacation schedule and unreliable server, under linear retrial policy. Breakdowns can occur randomly at any instant while the server is providing service to the customers. Further, the concept of Bernoulli admission mechanism is introduced. This model generalizes both the classical M X /G/1 retrial queue with unreliable server as well as the M X /G/1 retrial queue with the Bernoulli vacation model. The authors carry out an extensive analysis of this model. Namely, the embedded Markov chain, the stationary distribution of the number of units in the orbit, and the state of the server are studied. Some important performance measures and reliability indices of this model are obtained. Finally, numerical illustrations are provided and sensitivity analyses on some of the system parameters are conducted. KeyWORdS Classical Retrial Policy, Random Breakdown, Reliability Indices, Stationary Distribution 1. INTROdUCTION Retrial queues (or queues with repeated attempts) are characterized by the feature that a customer that finds, upon arrival, the server busy, is obliged to leave the service area and repeat his demand for service after some time called “retrial time.” Between trials, the blocked customer joins a pool of unsatisfied customers called “orbit.” Queues in which customers are allowed to conduct retrials have been widely used to model many practical problems in telephone switching systems, telecommunication networks and computers competing to gain service from a central processing unit. Moreover, retrial queues are also used as mathematical models for several computer systems such as packet switching networks, shared bus local area networks operating under the carrier-sense multiple access protocol and collision avoidance star local area networks etc. For a review of the main results and methods, the reader is referred to the survey papers of Yang and Templeton (1987), Falin (1990), Kulkarni This article, originally published under IGI Global’s copyright on January 1, 2020 will proceed with publication as an Open Access article starting on February 1, 2021 in the gold Open Access journal, International Journal of Operations Research and Information Systems (con- verted to gold Open Access January 1, 2021), and will be distributed under the terms of the Creative Commons Attribution License (http:// creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and production in any medium, provided the author of the original work and original publication source are properly credited.