Infinite-source, ample-server control variate models for fininte-source, finite-server repairable item systems

Abstract

A new modeling idea for comparing infinite-source, ample-server models (∞/∞) and finite-source, finite-server models (f/f) is considered. This comparison provides an estimate of the error when approximating an f/f system with an ∞/∞ system, and allows analytical solutions of the ∞/∞ model to be used as control variates. This approach is applied to estimate the difference in performance between an M/G/∞ queueing system (∞/∞) and the classical machine repair problem (f/f) and the difference in performance between infinite-source, ample-server multiechelon repairable item inventory systems and finite-source, finite-server multiechelon systems. Using an ∞/∞ model as a control variate is shown to be an effective variance reduction technique for estimating the performance of many f/f systems.