Customer delay in M/G/∞ repair systems with spares

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.