Mathematics and Statistics 11(4): 617-624, 2023 http://www.hrpub.org DOI: 10.13189/ms.2023.110401 Performance Analysis of a Markovian Model for Two Heterogeneous Servers Accompanied by Retrial, Impatience, Vacation and Additional Server G. Vinitha, P. Godhandaraman, V. Poongothai * Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur – 603 203, Tamilnadu, India Received November 16, 2022; Revised May 11, 2023; Accepted June 9, 2023 Cite This Paper in the Following Citation Styles (a): [1] G. Vinitha, P. Godhandaraman, V. Poongothai , "Performance Analysis of a Markovian Model for Two Heterogeneous Servers Accompanied by Retrial, Impatience, Vacation and Additional Server," Mathematics and Statistics, Vol. 11, No. 4, pp. 617 - 624, 2023. DOI: 10.13189/ms.2023.110401. (b): G. Vinitha, P. Godhandaraman, V. Poongothai (2023). Performance Analysis of a Markovian Model for Two Heterogeneous Servers Accompanied by Retrial, Impatience, Vacation and Additional Server. Mathematics and Statistics, 11(4), 617 - 624. DOI: 10.13189/ms.2023.110401. Copyright©2023 by authors, all rights reserved. Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution License 4.0 International License Abstract The two heterogeneous servers of the Markovian retrial queue model with an additional server, impatience behavior and vacation are presented in this research paper. An arriving customer who finds accessible servers gets immediate service. Otherwise, if both servers are engaged, an entering customer will join in the orbit to retry and get their service after some random time. If any customers in the orbit discover that the waiting time is longer than expected, they may leave without receiving the service. We consider two servers with different service rates to provide the service based on “First Come, First Served”. When the number of customers in orbit increases occasionally, we will instantly activate an additional server to reduce the queue size. After the orbit becomes null, the server goes for maintenance activity. The practical application is given to justify our model. The proposed model was obtained using the birth-death process and the equations were governed using Chapman-Kolmogorov equations. Finally, we have solved the equations using a recursive approach and the performance indices are derived to improve quality and efficiency. Keywords Two Heterogeneous Servers, Impatience, Retrial Queue, Vacation, Additional Server 1. Introduction This paper investigates a model of two-heterogeneous server retrial queue accompanied by additional server, impatience and vacation, which has fascinated many researchers. The domains of computer networks, commerce, manufacturing and service systems heavily rely on this queueing approach. We have all experienced waiting in line to satisfy our demands in various situations, known as the queuing system. The blocking is done in real-time, for typical strategic behavior of the service provider. During the arrival, if a likely customer expects a long waiting time in the queue, the customer is free to choose whether or not to join the system to receive service. For example, the patients are waiting in the line to get their treatment. If any of the patients, on arriving observes a long queue, may refuse to join in the queue and this situation is termed as Balking. In a retrial queue, a customer entering the system seeking service, finds all the servers being engaged and proceeds a customer to the waiting area is known as retrial orbit. On where the customers check the availability of the servers until the server is free. Also, if any customer in the queue decides to leave the orbit without receiving the service presuming that their wait will be longer, this is referred to as reneging. For example in telephone systems, the auto- repeat facilities allow the client to automatically redial a busy telephone until a connection is made.