An optimal maintenance policy for a deteriorating server of an M/G/1 queueing system

Abstract

An optimal maintenance policy for a deteriorating server of an M/G/1 queueing system is considered. The server has multiple states which indicate the deterioration level of the server. The state transitions of the server are governed by a Markov process with one absorbing state - the failure state. When the server fails, corrective maintenance starts immediately. Preventive maintenance can be taken to avoid the failure. After the maintenance, the server becomes as good as new. At the beginning of maintenance, customers in the system are rejected and the arriving customers during the maintenance are also rejected. A cost of one per rejected customer is incurred and our objective is to find the optimal maintenance policy that minimizes the total expected discounted cost over an infinite time horizon. The problem is formulated as a semi-Markov decision process whose state space is the queue length and the server state. The existence of the optimal controls with switch-curve structure is established under some conditions.