Stochastic bounds for two-layers loss systems

This article studies multi-class loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of customers follows an overflow scheme, where arriving customers are preferentially directed to the first layer. Stochastic comparison and coupling techniques are developed for studying how the system is affected by the packing of customers, altered service rates, and altered server configurations. This analysis leads to computationally fast upper and lower bounds for the performance of the system.