Int. J. of Industrial and Systems Engineering   »   2014 Vol.18, No.3



Title: State dependent M/M/1/WV queueing system with inspection, controlled arrival rates and delayed repair


Authors: Madhu Jain; G.C. Sharma; Varsha Rani


Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India
Department of Mathematics, Institute of Basic Sciences, Khandari, Agra 282002, India
Department of Mathematics, St. John's College, Agra, 282002, India


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: state dependent queueing systems; working vacation queueing systems; discouragement; delayed repair; inspection, controlled arrival rates; Markov model; performance evaluation; random breakdown; queue size distribution; throughput; delay time.


DOI: 10.1504/IJISE.2014.065541


Int. J. of Industrial and Systems Engineering, 2014 Vol.18, No.3, pp.382 - 403


Available online: 29 Oct 2014



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