Convexity of Inverse Blocking Curves in Loss Systems

We study the inverse of the Erlang loss (Erlang–B) formula, namely, the maximum offered load supportable at a fixed blocking target as a function of the number of servers. We show that this inverse blocking curve is strictly increasing and globally convex, yielding an exact economies-of-scale statement for loss-system dimensioning. The proof is based on a tilted-measure representation and extends to the finite-waiting-room multi-server model.