This paper deals with the transient behavior of the Erlang loss model. After scaling both arrival rate and number of trunks, an asymptotic analysis of the blocking probability is given. Apart from that, the most likely path to blocking is given. Compared to Shwartz and Weiss, more explicit results are obtained by using probabilistic arguments. The computation method is applied to the problem of (real-time) dimensioning of virtual paths in ATM networks, and to the problem of integrating scheduled and switched connections in a single network.