Maintenance policy for a deteriorating single server queuing production system

We consider a single server queuing production system which is subject to gradual deterioration. The system is discussed under two different deteriorating conditions. A planning horizon is considered and server which is a D/M/1 queuing system is gradually deteriorates through time periods. A maintenance policy is taken into account whereby the server is restored to its initial condition before some distinct periods. This system is modeled to obtain optimal values of arrival rates and also optimal maintenance policy which minimizes production, holding and maintenance costs and tries to satisfy demands through time periods