Stability Condition of a Multi-class Modified Erlang System

Abstract

We consider a modified Erlang loss system where the first priority customers (class-1) are lost if find all servers busy, while the second priority customers (class-2) form an infinite capacity queue. A new feature of this system is that sub-classes of class-1 customers are assigned on servers according to assignment probabilities. All customers follow Poisson inputs and have general class-dependent service time. We show how the product form of class-1 stationary probabilities can be used to obtain the stability condition of the whole system even when subclasses of class-1 customers have different service rates. Also we perform discrete event simulation to confirm theoretical results.