Age-maintenance of an M/G/1 production system

Many production systems can be modelled as queueing systems. This paper examines the age-maintenance of an M/G/1 queue that is subject to random service interruptions. The frequency of breakdowns can be reduced by scheduling preventive maintenance at shorter intervals. However, the system is down while preventive maintenance is being performed. Too frequent preventive maintenance can be costly, and the disruption on operation, excessive. Determining the preventive maintenance interval that minimizes long-run expected operating costs, where the down times due to preventive maintenance and repair are taken into account explicitly, is a very complex problem. A special case of the problem in which the traffic intensity is high is investigated. The authors formulate the optimization problem as a nonlinear program, and provide theorems for determining the minimum-cost preventive maintenance interval.