Customer delay in M/G/ℝ àrepair systems with spares

The exchangeable-item repair systems considered here are characterized by customers who bring failed items to the system, and are prepared to take in return any serviceable item of the same kind. This exchangeability feature enables the system to keep spare items, either those repaired by the facilities the system operates or newly acquired ones. Rather than only considering the common number of backorders as a measure, the focus of this research is on the delay experienced by customers in an ‘ample-service’ repair system, where repair of a failed item commences upon arrival at the system. The stationary and the nonstationary distributions of this delay are obtained in an analytic closed form in terms of the basic model parameters-the (Poisson) arrival rate, the (arbitrary) repair distribution of an item, and the initial number of spares in the system. The results are applicable to a variety of models that incorporate factors such as item scrapping, replenishment of new items, different modes of failure, and customers bringing several failed items. Successive use of the formulas can extend the spectrum of potential applications to multiechelon systems.