Mathematics and Statistics Vol. 11(4), pp. 617 - 624
DOI: 10.13189/ms.2023.110401
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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

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

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[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). APA Format:
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.