Implied costs in loss networks

Implied costs in loss networks are measures of the rate of change of an objective function with respect to the parameters of the network. This paper considers these costs and the costs predicted by the Erlang fixed-point approximation. It derives exact expressions for the implied costs and considers the asymptotic accuracy of the approximation. The paper shows that the approximation is asymptotically valid in some cases but is not valid in one important limiting regime. It also shows that a linearity approximation for the implied costs is asymptotically correct when taken over suitable subsets of links.