On the convergence of the Extended Erlang-BB model

Extended Erlang-BB model (EEB) is widely used in telecommunications, especially in call centers. This model extends the well-known Erlang-BB model to allow some portion of blocked calls to immediately retry. Mathematically, this model involves two iterations, one for the offered loads and the other for the blocked traffic. Nevertheless, analytical verification of the convergence of these two iterations has apparently not been published. This paper presents a mathematical proof of the convergence of the two iterations. Numerical results and a C++ program are provided to illustrate the Extended Erlang-BB model.