Asymptotic Shape of the Erlang Capacity Region of a Critically Loaded Multi-Service Shared Resource

This study analyzes a loss model for an unbuffered C-channel resource, shared by multiple service types. Connections arrive via Poisson streams, requesting type-dependent channels, and are blocked if unavailable. Channels are held for a generally distributed period. Assuming large, proportional C and traffic intensities, and a critically loaded resource, the admission control problem with blocking probability bounds is asymptotically investigated. The admissible set's boundary is found to be slightly non-convex. This work completes a prior investigation of critically loaded, overloaded, and underloaded resources.