Machine Repair Problem with K-Type Warm Spares, Multiple Vacations for Repairmen and Reneging

摘要

In this paper, a multi-repairmen machine repair problem comprising of M operating units together with k type of warm spares has been investigated. The failed units are immediately attended by repairmen if available. When there are no failed units in the queue for repair, the repairmen leave for a vacation of random length. When the vacation period is terminated, the repairmen return and check for any failed unit in the queue. If the queue is non-empty, the repairmen start repairing of failed units until the queue becomes empty, and again they leave for another vacation. The repair rate of the repairmen depends upon the workload. The caretaker of the failed machines may renege on finding all repairmen busy. The steady state queue size distribution and other important performance measures have been derived using matrix recursive approach. Furthermore, a numerical example provides a profound understanding of the sensitivity of parameters with respect to various performance measures.