In this paper, we study the optimal control of service rate in a single server state dependent queue with MMPP input. The objective of this work is find the optimal service rate that minimizes the service rate using matrix method. A performance difierence formula is derived to quantify the difierence of service rate based on varying arrival in the long run. © 2020, Research Publication. All rights reserved.

Vidhya V

Mathematics

School of Advanced Sciences

Chennai Campus

R. Sakthi

R. Raghavendran

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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Journal	Advances in Mathematics: Scientific Journal
Publisher	Research Publication
ISSN	18578365