382 Int. J. Industrial and Systems Engineering, Vol. 18, No. 3, 2014 Copyright © 2014 Inderscience Enterprises Ltd. State dependent M/M/1/WV queueing system with inspection, controlled arrival rates and delayed repair Madhu Jain Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India E-mail: drmadhujain@yahoo.co.in G.C. Sharma Department of Mathematics, Institute of Basic Sciences, Khandari, Agra 282002, India E-mail: gokulchandra5@gmail.com Varsha Rani* Department of Mathematics, St. John’s College, Agra, 282002, India E-mail: versha.mvn@gmail.com *Corresponding author Abstract: The Markov model is developed to explore the performance analysis of a state dependent working vacation queueing system with interdependent rates. The server is subjected to breakdown randomly while providing services. When a breakdown occurs, the server is immediately sent to the repair station where the repairman takes a setup time before starting the repair. The failed server is inspected by the repairman and if there is minor problem, the server is repaired and is sent back to the service station with probability q. If some major fault is diagnosed during inspection, the server requires second phase of repair with probability p = 1 – q. The matrix geometric method is applied to obtain the queue size distribution and other performance indices such as throughput, expected delay time, etc. Various performance measures are computed for varying values of system parameters to facilitate the sensitivity analysis by taking a numerical illustration. Keywords: working vacation; state dependent; discouragement; delayed repair; controlled. Reference to this paper should be made as follows: Jain, M., Sharma, G.C. and Rani, V. (2014) ‘State dependent M/M/1/WV queueing system with inspection, controlled arrival rates and delayed repair’, Int. J. Industrial and Systems Engineering, Vol. 18, No. 3, pp.382–403. Biographical notes: Madhu Jain is an Associate Professor of Mathematics in the Department of Mathematics, IIT Roorkee. She is a recipient of two gold medals of Agra University at MPhil level. She has more than 330 research