A multi-class closed queueing maintenance network model with a parts inventory system

The system we address is a maintenance network of repairable items where a set of bases is supported by a centrally located repair depot and a consumable replacement parts inventory system. If an item fails, a replacement part must be obtained at the parts inventory system before the failed item enters the repair depot. The ordering policy for the parts is the (S,Q) inventory policy. An approximation method for this system is developed to obtain performance measures such as steady-state probabilities of the number of items at each site and the expected backorders at the parts inventory system. The proposed system is modelled as a multi-class closed queueing network with a synchronization station and analyzed using a product-form approximation method. Particularly, the product-form approximation method is adapted so that the computational effort on estimating the parameters of the equivalent multi-class network is minimized. In analyzing a sub-network, a recursive method is used to solve balance equations by exploiting the special structure of the Markov chain. Numerical tests show that the approximation method provides fairly good estimation of the performance measures of interests.