Performance analysis of a warm standby machine repair problem with servers vacation, impatient and controlling F-policy

Abstract

This study is concerned with the threshold-based arrival control policy and server vacation for the machining system with standby provisions. We consider that the failed machines may balk and renege following the exponential distribution. Further, failure and service times of the machine and vacation time of the server are assumed to follow an exponential distribution. In the present model, the state at which the number of failed machines in the system reaches system capacity $K$, the system will not allow further new arrivals to join the system unless the system length reduces to a threshold value $F$, because of which so-termed as $F$-policy. At that moment, the server commences an exponential startup time and starts allowing new arrivals to join the system. Also, the steady-state probability distribution for the system size and system performance measures are developed. A cost function is developed to obtained optimal operating conditions. Finally, the Quasi-Newton method and Direct Search algorithm are implemented to demonstrate the optimal operating condition with minimal system cost and results are delineated in different graphs and tables for the quick glance