Computing Approximate Blocking Probabilities for Large Loss Networks with State-Dependent Routing

We consider a reduced load approximation (also referred to as an Erlang fixed point approximation) for estimating point-to-point blocking probabilities in loss networks (e. g., circuit switched networks) with state-dependent routing. In this approximation scheme, the idle capacity distribution for each link in the network is approximated, assuming that these distributions are independent from link to link. This leads to a set of nonlinear fixed-point equations which can be solved by repeated substitutions. We examine the accuracy and the computational requirements of the approximation procedure for a particular routing scheme, namely least loaded routing. Numerical results for six-node and 36-node asymmetric networks are given. A novel reduced load approximation for multirate networks with state-dependent routing is also presented.