Approximation formulae for blocking probabilities in a large Erlang loss system: a probabilistic approach

In this paper, we use a probabilistic approach to present a unified view of classical blocking probabilities approximation formulae for a multi-rate Erlang loss system, both in the finite and infinite population cases. Combining our results with the uniform approximation due to Bleistein, we recover the results Mitra and Morrison which were obtained by saddlepoint techniques. We also show that we can avoid using the uniform approximation to get “specialized” formulae for the heavy, critical, generalized critical and light traffic cases. Numerical results for typical loss levels in the ATM case are presented where we compare the uniform approximation (UA) with the specialized approximations (SA)