http://www.iaeme.com/IJM/index.asp 2010 editor@iaeme.com International Journal of Management (IJM) Volume 11, Issue 12, December 2020, pp. 2010-2019. Article ID: IJM_11_12_186 Available online at http://www.iaeme.com/ijm/issues.asp?JType=IJM&VType=11&IType=12 Journal Impact Factor (2020): 10.1471 (Calculated by GISI) www.jifactor.com ISSN Print: 0976-6502 and ISSN Online: 0976-6510 DOI: 10.34218/IJM.11.12.2020.186 © IAEME Publication Scopus Indexed M/G/1 QUEUE WITH COMPULSORY VACATION AND THREE PHASE REPAIRS S. Vanitha Assistant Professor, Department of Mathematics, SSN College of Engineering, OMR Road, Kalavakkam, Chennai, India ABSTRACT We study a single server M/G/1 queueing system with Poisson input subject to compulsory server vacation and random breakdowns. The server provides service to all arriving customers on a first come first served basis and service times follow general distribution. However after the completion of each service the server will take compulsory vacation. The system may breakdown at random and it must be send to repair process immediately. Further the repair process involves three phases of repairs with different general repair time distributions. The supplementary variable technique is applied to find explicitly probability generating function of the number in the system Key words: Poisson arrivals, general times, probability generating function, random breakdowns, idle state, steady state, deterministic repairs, supplementary variable technique. Cite this Article: S. Vanitha, M/G/1 Queue with Compulsory Vacation and Three Phase Repairs, International Journal of Management, 11(12), 2020, pp 2010-2019. http://www.iaeme.com/IJM/issues.asp?JType=IJM&VType=11&IType=12 1. INTRODUCTION Single server queueing systems subject to vacations or interruptions have been studied by numerous researchers due to their wide applications in the analysis of processor schedules, the analysis of polling systems, analysis of manufacturing systems and computer communication systems. Vacation may take place when the human server in the system wishes to take a pause or leave the system for a certain period of time. Vacation queues have been studied by several authors including Doshi [1,2], Takagi [10], Levy and Yechiali [4], Madan [5,6,7,9], Thangaraj and Vanitha [11]. In real life situations, a queueing system might suddenly breakdown and hence the server will not be able to provide service unless the system is repaired. Madan and Maraghi [8] have studied batch arrival queueing system with random breakdowns and Bernoulli schedule server vacation having general vacation time. Vanitha [12] analyzed a queueing system with deterministic repair times. The most realistic aspect in modeling of an unreliable server is phase