Queueing Analysis of Machine Repair Problem with Controlled Rates and Working Vacation Under F-Policy

Abstract

This paper deals with the queueing characterization of a machine repair problem with single working vacation and controlled arrival of failed machines under F-policy. The server allows the failed machines to enter the system till full capacity K and thereafter the arrival of the failed machines is prohibited which continues till the queue length is reduced to the threshold value F. The server takes some time to start the repair of the failed machines. The life time of the machines, startup time and repair time of the server are exponentially distributed. When the system is empty, the server goes for a single vacation but it keeps on serving the failed units even during vacation at a different pace, and is said to be on working vacation. The matrix method has been used to obtain the steady state probabilities of the system states. Various performance characteristics have been derived. The numerical results have been obtained and shown in tables and graphs.