Sequential iteration of the Erlang fixed-point equations

The link or route blocking probabilities of a loss network are typically used to assess its performance. Unfortunately, closed form expressions for these, whilst being easy to write down, are quite intractable to evaluate computationally. Consequently, a number of approximations to the blocking probabilities have been proposed. One of the most intensively studied of these is the Erlang fixed-point approximation. We study the dynamical behaviour of performing sequential iteration on the Erlang fixed-point equations and prove that, for an arbitrary fixed-routing topology with constant bandwidth on all routes, sequential iteration converges to the Erlang fixed point. (C) 2002 Elsevier Science B.V. All rights reserved.