M/M/R+r machining system with reneging, spares and interdependent controlled rates

Abstract

The present investigation deals with the multi component machine repair problem by including the concepts of reneging and interdependent controlled rates. We consider a machining system consisting of M operating units, S 1 and S 2 warm spares of two kinds and a repair facility having R permanent repairmen and r additional removable repairmen. When all the spares are used and the operating units fail, the system works in degraded mode. By using interdependent controlled arrival and service rates and reneging parameters along with time-sharing concept, the queueing model is developed for more versatile situations encountered in production/ manufacturing industries. The solution is obtained by using recursive technique. The expressions for the queue size distribution and expected queue length are established. Some more performance indices such as expected number of failed units waiting for the service, expected number of busy repairmen, expected number of both types of spare parts functioning as standbys, etc., are obtained with the help of recursive technique. By taking numerical illustrations, the sensitivity analysis is provided to validate the analytical results.