Blocking Probability Evaluation for Non-Hierarchical Overflow Loss Systems

Abstract

Non-hierarchical overflow loss systems (NH-OLSs) with mutual overflow have applications in many telecommunications and service systems, e.g., cellular networks, video-on-demand, emergency healthcare, or cloud services. In this paper, we make fundamental contributions in teletraffic modeling for blocking probability evaluation in NH-OLSs. These are based on the development of the well-known decomposition methodology, which decomposes an NH-OLS into independent subsystems and applies a suitable node model to each subsystem. In particular, we provide new both theoretical and numerical results involving both new and existing approximation methods. We show that these results cover a broad range of NH-OLSs, including those with heterogeneous arrival processes, server group size, and/or routing, with both Poisson and non-Poisson arrivals of fresh requests. Our theoretical results include the first scalable asymptotic exactness results for NH-OLSs. Our new approximations include the first computationally efficient and fairly accurate approximation for NH-OLSs with both mutual overflow and non-Poisson input with asymptotic exactness properties.