Surrogate models for performance evaluation of multi-skill multi-layer overflow loss systems

Abstract

We consider a model of overflow loss systems in which server groups are arranged into layers, and alternate routing within each layer creates mutual overflow effects, increasing the amount of traffic that can be carried by the system. Such a model has wide applications in communications and service systems. However, the presence of both hierarchical inter-layer overflow and mutual intra-layer overflow makes accurate, robust, yet scalable blocking probability evaluation of such systems a difficult challenge. To address this challenge, we apply and extend the recently developed Information Exchange Surrogate Approximation (IESA) framework to a multi-layer system, adding new surrogate models to the framework and incorporating moment-matching techniques. In contrast to the conventional fixed-point approximation (FPA) approach, which directly decomposes the overflow loss system into independent subsystems with inherent problems of convergence and uniqueness, IESA performs decomposition on a carefully designed surrogate model with guaranteed convergence and uniqueness. Extensive numerical results demonstrate that IESA is consistently more accurate than the conventional FPA approach, showing an improvement in accuracy of several orders of magnitude in many cases. Furthermore, the new extensions to IESA introduced in this paper provide consistent improvements in accuracy relative to the current state-of-the-art of the IESA framework.