http://www.iaeme.com/IJARET/index.asp 1208 editor@iaeme.com International Journal of Advanced Research in Engineering and Technology (IJARET) Volume 11, Issue 11, November 2020, pp. 1208-1217, Article ID: IJARET_11_11_110 Available online at http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=11&IType=11 ISSN Print: 0976-6480 and ISSN Online: 0976-6499 DOI: 10.34218/IJARET.11.11.2020.110 © IAEME Publication Scopus Indexed ANALYSIS OF M/G/1 QUEUE WITH OPTIONAL SERVICES AND DETERMINISTIC REPAIR S. Vanitha SSN College of Engineering, Department of Mathematics, OMR, Kalavakkam, Chennai, India. ABSTRACT We analyze an M/G/1 queue with Poisson arrivals, three optional services, random breakdowns and deterministic repair. The first service is essential and other three services are optional. All arriving customers demand first essential service and after completion of first service, the customer has the option of choosing any one of the three optional services with probability  Otherwise the customer can leave the system without choosing any of the three optional services with probability. The server is subject to random breakdowns and just after a breakdown the server undergoes repairs of fixed (constant) duration ( ) The supplementary variable technique is used to find explicitly the probability generating function of the number in the system and the mean number in the system. Keywords: Poisson arrivals, general service times, probability generating function, random breakdowns, idle state, steady state, deterministic repairs, supplementary variable technique. Cite this Article: S. Vanitha, Analysis of M/G/1 Queue with Optional Services and Deterministic Repair, International Journal of Advanced Research in Engineering and Technology, 11(11), 2020, pp. 1208-1217. http://www.iaeme.com/IJARET/issues.asp?JType=IJARET&VType=11&IType=11 1. INTRODUCTION Queueing and Queueing networks occupy a prominent role in the performance analysis of a wide range of systems in computer-communications, logistics and flexible manufacturing systems. Further, queueing network models have been successfully applied in the optimization of computer systems, telecommunication systems and broadcasting. System design and optimization issues include dynamic routing control of customers (packets), trunk designs, resource allocation, load balancing and throughput maximization. There is a natural interest in the study of queueing systems with server vacations or interruptions. Several excellent surveys on single serving queueing models with vacations have been studied by Doshi [3], Fuhrman [4], Gaver [5], Levi and Yechilai [7], Madan [8, 9, 10], Thangaraj and Vanitha [12].